What the Data Actually Shows

The 38 that were cut

Published because a list of survivors with no list of casualties is indistinguishable from a list of everything anyone thought of. Several of these reproduced perfectly and were killed for their framing — a claim whose arithmetic is exact can still say something the arithmetic does not support. 32 were rejected by all 3 sceptics.

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  Tax and movement · cut before publicationThe six states with no individual income tax have a median domestic migration rate of +21.95 per 1,000 versus -1.37 for the 44 states levying both taxes, but their entire range (-24.23 to +34.66) sits inside the levy-both range (-44.98 to +55.68), and all five states with the highest domestic in-migration in the country levy both taxes.The overlap/containment substance survives, but three things fail. (1) THE GROUP LABEL IS FACTUALLY WRONG, AND IT IS AN ARTIFACT. "The six states with no individual income tax" is not a true statement about the United States — nine states levy no tax on wage …

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  The overlap/containment substance survives, but three things fail. (1) THE GROUP LABEL IS FACTUALLY WRONG, AND IT IS AN ARTIFACT. "The six states with no individual income tax" is not a true statement about the United States — nine states levy no tax on wage and salary income (AK, FL, NH, NV, SD, TN, TX, WA, WY). The file's `hasIndividualIncomeTax` boolean simply reflects whether Census tax item T40 has non-zero collections. Read from fiscal.levies: Tennessee is coded True on T40 = $2,088 thousand out of $25,573,839 thousand total state tax — 0.0082% — a residual trickle from the repealed Hall tax. Washington is coded True on T40 = $545,712k (1.386% of its tax take) and New Hampshire on T40 = $91,186k (2.704%). No state with an actual wage income tax is anywhere near: the next-lowest share is ND at 7.71%, then NM at 16.86%. So "six states with no individual income tax" should read "six states the Census records zero individual-income-tax collections for." (2) THE CENTRAL DEFLATIONARY CONCLUSION IS NOT ROBUST TO THAT ARTIFACT. Tennessee is the 8th-highest domestic in-migration state in the country (+32.8412 per 1,000) and sits in the "levies both" group solely because of that $2.088M line. Re-running the identical procedure with the conventional nine no-wage-income-tax states as Group A (n=9) versus the other 42: median A = +21.7180, median B = -2.1624, gap 23.8804 (larger, not smaller); permutation p on means falls from 0.2809 to 0.1397 and on medians from 0.0569 to 0.0305. The claim's key sentence — "with n=6 the difference is not statistically separable from noise" — flips at conventional alpha under a defensible reclassification. It is a property of the grouping choice, not of the data. (3) SEVERAL STATED DIGITS DO NOT REPRODUCE. Same file, full precision: median(A) = 21.9482 not 21.9490 (it is the mean of TX 22.178350 and NV 21.718046 = 21.948198); median(B) = -1.368845 not -1.3690 (mean of OR -1.779340 and CT -0.958349); median difference 23.3170 not 23.3180; mean(A) = 14.7944 not 14.7887; mean(B) = 3.7121 not 3.7069; mean difference 11.0823 not 11.0818. The permutation p on medians with seed 7 and 200,000 shuffles comes out 0.0569, not the stated 0.0580 — the stated median difference threshold is 0.001 too high, which excludes a band of permutations. These are small, but the claim presents them as exact re-runnable digits and they are not. WHAT DOES HOLD, EXACTLY: the file parses cleanly (migration.per1k.domestic equals totals.domestic/population*1000 to six decimals in every state I checked; no nulls in any of the three fields used across all 51 jurisdictions). Group sizes 6 + 44 + 1 (WA: individual True, corporate False) = 51 is right. Containment holds at both ends and under both groupings: AK -24.2254 > NY -44.9754, FL +34.6618 < ID +55.6844. 8 of 44 levy-both states exceed median(A) — ID, SC, MT, DE, NC, ME, TN, AZ — 8/44 = 18.18%. 5 exceed max(A): ID, SC, MT, DE, NC, and the top five nationally are exactly those five, all with both T40 and T41 collections. Probability of superiority 181/264 = 0.6856, zero ties. Permutation p on means 0.2809 reproduces exactly. No causal reading is supported either way, and n=6 (or 9) against 44 (or 42) is too small to separate group membership from noise in any direction.

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  Tax and movement · cut before publicationThree states flagged hasIndividualIncomeTax=true collect a negligible individual income tax - Tennessee $0.29 per resident (0.0082% of state tax), New Hampshire $64.72, Washington $68.57 - while the next-lowest state, North Dakota, collects $534.09, a 7.79x jump, so the boolean is a presence flag rather than a measure of whether the tax is material.The substance of the claim reproduces, but the STATED COMPUTATION does not: three of its denominators/results are wrong, and two of them are numbers that do not exist anywhere in states.json. (1) Tennessee. The claim states "2088*1000/7204002=$0.2898" and "20…

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  The substance of the claim reproduces, but the STATED COMPUTATION does not: three of its denominators/results are wrong, and two of them are numbers that do not exist anywhere in states.json. (1) Tennessee. The claim states "2088*1000/7204002=$0.2898" and "2088/25455075=0.0082%". The file gives TN population = 7,227,750 and fiscal.totalTaxThousands = 25,573,839. Neither 7204002 nor 25455075 appears anywhere in the file (grepped the raw text). Correct: 2088*1000/7227750 = $0.288887; 2088/25573839*100 = 0.008165%. Both still display as $0.29 and 0.0082%, so the cited figures survive rounding — but the audit trail is fabricated at the digit level. (2) New Hampshire. The claim's own denominator is right but its result is not: 91186*1000/1409032 = 64.715351, not the stated 64.7226. Rounds to $64.72 either way. (3) North Dakota. 425441*1000/796568 = 534.092507, not the stated 534.0898. Rounds to $534.09 either way. Ratio 534.092507/68.572463 = 7.788732, i.e. 7.79x as claimed. (4) The flag-baseline grouping is not reproducible from the definition the DETAIL itself gives. It opens with "45 jurisdictions flagged as levying an individual income tax" but then reports the flag split as "6/44" with median -1.37 and PS 0.6856. The genuine 6-vs-45 flag split gives median +21.9482 vs -1.7793 and PS = 186/270 = 0.6889. The stated -1.3688 and 181/264 = 0.6856 only appear if the comparison group is the 44 states levying BOTH taxes — i.e. Washington (hasIndividualIncomeTax true, hasCorporateIncomeTax false) is silently dropped from the baseline and then re-added to the negligible group in the 9/42 re-cut. That definitional switch is undisclosed and is why 6+44=50 of 51 jurisdictions. (5) Two means are slightly off: the 9-state group mean is 15.240523 (claim 15.2372) and the 42-state mean is 2.635535 (claim 2.6376). Medians and PS do reproduce exactly. Everything structural checks out: T40 is absent for exactly AK, FL, NV, SD, TX, WY (= exactly the six hasIndividualIncomeTax=false states); of the 45 flagged states the three lowest per resident are TN, NH, WA and the fourth is ND; every state other than those three is at 7.7114% of state tax or above (ND is the minimum); TN's domestic migration is +32.8412, rank 8 of 51; 8 levy-both states beat the no-income-tax median of +21.9482 (AZ, DE, ID, ME, MT, NC, SC, TN); the 9/42 magnitude cut gives medians +21.7180 vs -2.1624 and PS = 260/378 = 0.687831. So the conclusion — the boolean marks presence, not materiality, and re-cutting by magnitude barely moves the migration result — stands. Marking refuted because published copy must not carry per-capita denominators that are not in the source file and arithmetic a reader cannot re-run.

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  Tax and movement · cut before publicationState tax per resident and domestic migration move together only weakly (Pearson r=+0.4149 on the percentile, r-squared 0.1721), and the extremes invert: Alaska has the lowest state tax per resident of all 51 ($2,279, percentile 100) and ranks 46th of 51 on domestic migration at -24.23, while Delaware at $6,607 (43rd-lowest of 51) ranks 4th at +41.95.The correlation coefficients reproduce at the precision quoted in the headline, but the claim fails on two counts. (1) DIGIT ERRORS: several figures in the STATED COMPUTATION do not reproduce. SC domestic is 54.74927, not 54.7454; NY is -44.97538, not -44.9757…

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  The correlation coefficients reproduce at the precision quoted in the headline, but the claim fails on two counts. (1) DIGIT ERRORS: several figures in the STATED COMPUTATION do not reproduce. SC domestic is 54.74927, not 54.7454; NY is -44.97538, not -44.9757; the national range is 100.65980, not 100.6601; the low-13 spread is 78.97465 (78.457% of range), not 78.9708; the high-13 spread is 86.92260 (86.353%), not 86.9229; Pearson is 0.414885, not 0.41494; r-squared is 0.172129, not 0.17218; Spearman is 0.458281, not 0.45830. Each headline rounding happens to survive, but a sceptic re-running the stated recipe does not get the stated digits. (2) MATERIAL MISFRAMING, which is the bigger problem. "The extremes invert" is false at the high end. Delaware is not an extreme - it is 43rd of 51 by tax dollars, i.e. 9th-highest, a fact the claim states and then contradicts by calling it an extreme. The actual high-tax extreme, DC at $16,036 (more than double the next jurisdiction), has domestic migration of -20.24, moving WITH the correlation, not against it; 4 of the 5 highest-tax jurisdictions are net-negative (DC -20.24, HI -31.82, CA -35.45, NM -4.09; only VT is positive at +9.60). Only the low end genuinely inverts, via Alaska. Second, "knowing which tax quartile a state is in leaves almost the whole national range still on the table" rests on a max-minus-min statistic set by exactly two states per bin, and it suppresses a large, systematic difference in level: the 13 lowest-tax jurisdictions average +17.506 per 1,000 (median +21.206, 2 of 13 net-negative) while the 13 highest average -13.130 (median -18.723, 11 of 13 net-negative) - a 30.6-point gap in means and 39.9 in medians. Both patterns are associations across n=51 only; nothing here supports a causal or policy reading in either direction. Ironically the claim omits its own strongest evidence: DE and NY collect within one dollar of each other ($6,607 vs $6,608) yet sit 86.92 points apart on domestic migration (+41.9472 vs -44.9754).

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  Tax and movement · cut before publicationThe tax-per-resident indicator points in opposite directions for the two migration channels: r=+0.4149 against domestic migration but r=-0.3229 against international migration, so its correlation with net migration is weaker (r=+0.3000) than with either channel alone.Every cited figure reproduces to the stated precision — the arithmetic, units and parsing are clean. I confirmed `migration.per1k.*` equals `totals/population*1000` exactly (max deviation 1.4e-14), that `netPer1k` is exactly domestic+international, that no sta…

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  Every cited figure reproduces to the stated precision — the arithmetic, units and parsing are clean. I confirmed `migration.per1k.*` equals `totals/population*1000` exactly (max deviation 1.4e-14), that `netPer1k` is exactly domestic+international, that no state has a null in any of the four fields, and that the taxPerCapita percentile is a faithful inverse rank of the dollar values (51 distinct percentiles, 0-100 in steps of 2, perfectly monotone in the parsed `display` dollars), so the DETAIL's sign reading ("lower tax = more domestic, less international") is the right way round. Three things sink it anyway. (1) The headline's operative clause — net migration correlates "weaker than with either channel alone" — is not robust, and the claim's own robustness check does not test it. Jackknifing the comparison, 8 of 51 one-state deletions break it: dropping DC gives |r_net|=0.3213 > |r_intl|=0.2434, and the same reversal happens dropping MO, CT, MA, DE, AK, ID or LA. The advertised jackknife only tests the SIGN of the international correlation, a weaker proposition than the one the headline asserts. (2) At the endpoint of the claim's own jackknife range the international correlation is no longer distinguishable from zero: dropping DC gives r=-0.2434, t=-1.75, p=0.089 (it is significant at 5% in 50 of the other 51 drops). DC is a single city with an international rate of 49.25 per 1,000 and the highest tax per resident in the file ($16,036, percentile 0), so it is exactly the observation a sceptic removes first. (3) The quoted magnitudes are an artifact of the rank transform, not a property of "tax per resident". Rerunning on the actual dollars parsed from `display`, the directions survive but the ordering of the two channels reverses: r(dollars, international)=+0.5147 is the STRONGER association and r(dollars, domestic)=-0.3822 the weaker, the opposite of the headline's +0.4149 vs -0.3229; r(dollars, net)=-0.1804. The headline calls this "the tax-per-resident indicator" while the number behind it is a rank percentile, and the two disagree about which channel moves with tax more.

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  Work and movement · cut before publicationProduction, construction and repair occupations fill 61 of the 120 top-speciality slots in the ten states winning domestic movers, against 16 of 120 in the ten losing them — while the actual manufacturing share of jobs separates the two groups barely at all (Spearman +0.116).Arithmetic and parsing are sound - I reproduced all ten cited figures from the raw file, several to four decimals. The refutation is on the second clause's framing, not on any number. "The actual manufacturing share of jobs separates the two groups barely at a…

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  Arithmetic and parsing are sound - I reproduced all ten cited figures from the raw file, several to four decimals. The refutation is on the second clause's framing, not on any number. "The actual manufacturing share of jobs separates the two groups barely at all (Spearman +0.116)" cites a full-sample rank correlation across 49 states as evidence for a statement about two 10-state groups. Tested as an actual group separation, mfgShare does separate them: top-10 mean 7.530% vs bottom-9 mean 5.367%, a 2.16-point gap with one-sided permutation p = 0.0325 (200,000 relabelings of the 19 available values; medians 8.20 vs 5.70, p = 0.0731). A gap that survives a 5% one-sided test is "weaker than the speciality tally," which the DETAIL says correctly, but it is not "barely at all," which is what a reader of the headline alone would take away. The clause also compares two non-comparable statistics - a group tally against a correlation. The honest like-for-like contrasts are rho +0.450 vs +0.116, or group means 6.10 vs 1.60 trades slots (p = 0.00024) vs 7.53% vs 5.37% mfgShare (p = 0.033). Everything else survived attack: the 10/10 cut is not cherry-picked (top group holds 50-52% of its slots in trades at every k from 5 to 25 - 31/60, 49/96, 61/120, 73/144, 93/180, 104/204, 151/300 - while the bottom runs 13-30%); parsing is correct (all speciality codes are 6-character strings, no comma or unit traps in permits, and the only non-numeric mfgShare displays are AL and DC at "-" with missing:true, properly excluded, leaving n=49 and a bottom group of 9); specialities are genuinely lq-descending in all 51 states, so "top-speciality slots" is fair; and population is not the confound one might suspect (Spearman trades x population = +0.0395; partialling population out moves the signal to +0.4576, not down). The permutation p is a Monte Carlo estimate and 0.00028 is within noise of the truth - my 2,000,000-draw estimate is 0.000243 (485 hits, SE 0.000011), and seed-11 runs under four plausible shuffle implementations give 0.00022, 0.00027, 0.00027, 0.00025 and 0.00030 - so that figure is not a defect, though it is not exactly reproducible without the original code. One further caveat belongs anywhere the first clause is published: the DETAIL's own partial correlation (+0.450 falling to +0.194 once housing permits are held out, while permits hold +0.628 once trades are held out) means most of this occupational signal is shared with the building signal, and the headline carries none of that. Correlational throughout; n=51 and n=49 are small, and nothing here supports a causal or policy reading.

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  Work and movement · cut before publicationOf the 22 SOC major groups, the sharpest correlate of domestic in-migration is the concentration of Sales occupations (Spearman +0.554, family-wise permutation p = 0.0008) and the sharpest negative is Educational Instruction and Library (−0.459, family-wise p = 0.016) — yet how concentrated a state is in anything carries no signal at all (signature LQ, rho −0.128).ARITHMETIC: fully reproduced. I re-ran the entire pipeline independently (own tie-averaged rank + Pearson-on-ranks Spearman, numpy only, no scipy) and every one of the 13 cited figures matches to the stated precision. The formatted-display-string trap does not…

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  ARITHMETIC: fully reproduced. I re-ran the entire pipeline independently (own tie-averaged rank + Pearson-on-ranks Spearman, numpy only, no scipy) and every one of the 13 cited figures matches to the stated precision. The formatted-display-string trap does not apply here: `lq`, `migration.per1k.domestic`, `population` and `migration.totals` are all raw JSON numbers, none parsed from strings. I verified the denominator independently — totals.domestic/population*1000 reproduces per1k.domestic exactly for DC (-14,213/702,250 = -20.239), MT (50,720/1,137,233 = 44.599), FL (810,122/23,372,215 = 34.662), NY (-893,537/19,867,248 = -44.975). All 22 major groups are present with non-null lq in all 51 jurisdictions, and the 22 titles are identical across states, so the 22x51 matrix is complete as claimed. I refute on THREE framing defects, not on arithmetic. (1) THE HEADLINE CONTRADICTS ITSELF. It says the sharpest correlate is "the concentration of Sales occupations" and then, in the same sentence, that "how concentrated a state is in anything carries no signal at all." Sales LQ *is* a concentration, and it carries the study's strongest signal. The DETAIL rescues this with the direction-vs-intensity distinction, but the headline as written — the part that gets published — asserts and denies the same thing. The word "anything" is wrong; the null applies only to the intensity of a state's single most extreme niche occupation. (2) "NO SIGNAL AT ALL" OVERSTATES A rho OF -0.128. That coefficient has a Fisher 95% CI of [-0.390, +0.152] at n=51 (nominal two-sided p = 0.37). The data cannot exclude a moderate negative relationship. "Indistinguishable from noise" — which the DETAIL uses — is defensible; "no signal at all" is a claim of established absence the sample size cannot support. (3) TWO OF THE THREE "NULLS" ARE THE IDENTICAL STATISTIC. The claim lists "signature LQ at -0.128, the maximum speciality LQ at -0.128" as if these were two independent checks. I verified that `workforce.signature` IS the highest-lq member of `workforce.specialities` in all 51 jurisdictions (same lq AND same SOC code in every case). They are the same vector by construction, so they must give the same rho. Only two genuinely distinct magnitude nulls were tested, not three. SECONDARY CAVEAT (not the basis for refutation, but it should not be presented as settled): the "sharpest of 22" ranking is fragile. Bootstrapping 5,000 resamples of the 51 jurisdictions, Sales is the argmax in only 65.9% of draws and Education the argmin in only 51.4%. Sales' Fisher CI [+0.328, +0.720] comfortably contains Food Preparation's point estimate of +0.432. The point-estimate ordering is real in this sample; "the sharpest correlate" implies a resolution the data does not have. Also, "loses 20.24 per 1,000" carries no timeframe — these are cumulative 2021-2024, not annual. Design note in the claim's favour: the family-wise permutation is correctly specified. Shuffling the migration vector while holding the 22-LQ matrix fixed preserves the compositional dependence among the major-group LQs, so the multiple-testing correction is honest. The multiple-testing objection genuinely is answered.

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  Wages and speciality · cut before publicationThe pay-off from being distinctive ranges from 0.83x to 2.13x a state's own median wage, and it is close to uncorrelated with how the composite index rates the state (Spearman rho = 0.077).Every cited figure reproduces exactly — I re-ran it from states.json and got NC 0.83354 (lowest), MD 2.12981 (highest), 51-state median 1.032373, 21 strictly below 1.0, rho 0.3844 vs statewide medianWage, rho 0.0768 vs index.score, CT 0.98693, NM 1.74592, ID 1…

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  Every cited figure reproduces exactly — I re-ran it from states.json and got NC 0.83354 (lowest), MD 2.12981 (highest), 51-state median 1.032373, 21 strictly below 1.0, rho 0.3844 vs statewide medianWage, rho 0.0768 vs index.score, CT 0.98693, NM 1.74592, ID 1.09965. Structural claims also check out: specialities is always 12 rows, always lq-descending; exactly 7 null wages in exactly the 7 named slots; zero wageAtCap:true rows anywhere in specialities or major; no display-string parsing enters this computation (specialities carry raw numbers), so the parsing trap does not apply. Correlations are stable to leave-one-state-out (index 0.034-0.131, wage 0.348-0.436). I refute on framing and comparability, not arithmetic. (1) "The pay-off from being distinctive" is a valenced, quasi-causal relabel of a location-quotient filter — nothing is being earned for distinctiveness. The spread is occupational mix: Maryland's top-12 is federal-lab science (Statisticians $132,620, Economists $144,680, Microbiologists $108,470), North Carolina's is textile machine operators and Cooks, Fast Food ($27,190). Describing a high-lq set's wage as a "pay-off" is exactly the good/bad reading of lq that must not be made. (2) The 12 occupations are a median 2.52% of a state's employment (0.66% IL to 13.12% DC); a ratio over 2.5% of jobs is not a state-level pay-off. (3) The headline MD-vs-CT contrast is not like-for-like: CT's median is over 10 rows (NV and AL 11, all others 12) because two CT wages are null, one of them Health Specialties Teachers, Postsecondary (lq 3.05, 7,370 jobs), plausibly high-wage — the bias direction cannot be established without filling a null. CT's leave-one-out jackknife range is 0.944-1.030, straddling 1.0, so even its below-median sign is not robust. (4) SD is exactly 1.00000, so 22 of 51 are at or below the local median; "21 below" is right but knife-edge. (5) The three near-identical-median pairs are selected illustrations — with rho 0.384 across 51 points such pairs are guaranteed — and index.score has only 26 distinct values with heavy ties (five states at 56, four each at 48 and 61), so the 0.077 rests on a coarse, tied variable.

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  Wages and speciality · cut before publicationThe occupation each state is MOST concentrated in pays below that state's own median in 27 of 51 jurisdictions, and holds a median of just 2,410 jobs - 1.81 per 1,000 of the state's employment.Every headline number reproduces digit-for-digit (27/51, median 2,410 jobs, 1.806 per 1,000, median wage-rank 5, 10 lowest / 3 highest, and all four state cases MT/MN/PA/NM including lq, employment, wages and ratios). The arithmetic is sound and there is no di…

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  Every headline number reproduces digit-for-digit (27/51, median 2,410 jobs, 1.806 per 1,000, median wage-rank 5, 10 lowest / 3 highest, and all four state cases MT/MN/PA/NM including lq, employment, wages and ratios). The arithmetic is sound and there is no display-string parsing error — the workforce block carries raw numbers, not formatted strings. I refute on the supporting detail and framing, which a published page would carry. (1) The stated mechanism "by construction that is often a very small occupation" is contradicted by the file: signature median employment is 2,410 vs 2,210 for the other eleven distinctive rows in the same states; the signature's median employment-rank within its own twelve is 7 of 12; it is the LARGEST of its twelve in 7 states and the smallest in 7; Spearman rho(lq, signature employment) = 0.058 across 51; California's signature is 172,260 jobs at lq 5.54. A high lq does not mechanically produce a small occupation. (2) "2,410 jobs - 1.81 per 1,000" joins two medians computed over different states as if one derived from the other: the 2,410 state is MS, whose rate is 2.072 per 1,000; the 1.806-per-1,000 state is GA, which holds 8,830 jobs. Back-solving the implied denominator gives 1,334,441 workers against MS's actual 1,163,030. (3) "5th-lowest of 12" is false in 6 states: CT has 10 wage-bearing speciality rows and AL/CA/FL/NE/NV have 11 (nulls are unpublished, not zero), so the median rank of 5 holds only among wage-bearing rows. (4) "Lowest-paid of its own state's top 12 in 10 states" overstates CA, which has one unpublished wage among its twelve — CA is lowest of 11 published; 9 of the 10 are clean. (5) The framing turns a coin flip into a finding: 27/51 is 52.9%, the median signature/state-median wage ratio is 0.9955 and the mean is 1.157, so the typical signature occupation pays essentially its state's median and on average above it. There is a modest genuine tilt against a peer baseline — 43.3% of all 605 wage-bearing distinctive rows fall below their state median vs 52.9% of signatures — but that is the honest version, not "these figures show that directly".

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  The index against the movers · cut before publicationThe composite index has essentially zero relationship with domestic migration across all 51 jurisdictions: Pearson r = 0.0243, r-squared = 0.0006, t = 0.170 on 49 df.The primary correlation figures reproduce digit for digit from the raw file, and the unit/denominator audit passes cleanly. But one cited pair of figures is not determined by the stated computation and is materially fragile. CONFIRMED EXACTLY: Pearson r = 0.0…

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  The primary correlation figures reproduce digit for digit from the raw file, and the unit/denominator audit passes cleanly. But one cited pair of figures is not determined by the stated computation and is materially fragile. CONFIRMED EXACTLY: Pearson r = 0.024291 (0.0243), r-squared = 0.000590 (0.0006), t = 0.170086 (0.170) on 49 df. Spearman on average-tied ranks = 0.055642 (0.0556), and -0.055642 against index.rank. Leave-one-out over 51 refits: min -0.024787 dropping FL, max 0.058055 dropping ID. sorted(scores)[25] = 53; above-median n=25 mean 3.185005; below-median n=23 mean 5.261873; exactly 3 jurisdictions at 53 (MN, SC, WI). UNITS/DENOMINATORS CORRECT: migration.per1k.domestic equals migration.totals.domestic / (population/1000) to a max absolute difference of 7.1e-15 across all 51. No nulls in either field. Neither field is a formatted display string, so no parsing error is possible here. No migration variable feeds the index, so there is no circularity. THE DEFECT: index.rank has only 26 distinct values across 51 jurisdictions, so "top/bottom 10 by index.rank" is not well defined. The 10th slot from the top is a 4-way tie at rank 8 (MO, NH, NC, VA - choose 3); the 10th from the bottom is a 4-way tie at rank 39 (ID, KS, NV, OR - choose 1). Enumerating all 16 legitimate tie-breaks: Welch t ranges from -0.1616 to +1.1175 and the bottom-group mean from 3.575 to 9.885. The cited 4.139 / sd 17.639 / t = 1.054 is one draw of 16, sitting at the 87.5th percentile of that set. The claim's own stated recipe ("bottom 10 by index.rank descending") most naturally places ID - 55.684 per 1,000, the file's maximum - into the bottom group, giving a bottom mean of 9.885 and Welch t = 0.2613, not 4.139 and 1.054. Reproducing 4.139 requires an ascending sort taking the last 10 with an unstated alphabetical secondary key, a choice that happens to exclude the single largest value from the low group and so maximises the apparent gap being dismissed. The underlying conclusion holds - |Welch t| stays below 1.12 under every tie-break, r is robust to dropping DC (0.0557), and the null relationship is real - but a figure presented as determined is in fact an arbitrary selection, and its stated derivation does not produce it. Flagging refuted per the instruction to correct figures that are off even where the substance stands. A secondary caveat worth carrying: index.score is coarse (26 distinct values, five states tied at 56, four each at 61 and 48), which attenuates a Pearson r - though the Spearman and DC-excluded checks point the same way, so no relationship is being masked.

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  The index against the movers · cut before publicationThe index nets to zero because its own components disagree: housing permits correlate +0.7363 with domestic migration while output per worker runs -0.4525 and income -0.4236, and the index averages all eight pillars equally.Every cited figure reproduced exactly, digit for digit — the arithmetic and the display parsing are clean. I refute on framing and units, not on numbers. (1) The headline sentence is literally false. "The index nets to zero" — the index does not net to zero. …

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  Every cited figure reproduced exactly, digit for digit — the arithmetic and the display parsing are clean. I refute on framing and units, not on numbers. (1) The headline sentence is literally false. "The index nets to zero" — the index does not net to zero. index.score runs 33 (MS/WV) to 74 (CO), mean 53.7, sd 8.40. What is near zero is r(index.score, migration.per1k.domestic) = +0.0243. On a published page that sentence reads as a statement about the index's values. (2) "The index averages all eight pillars equally" is false for 3 of 51. I counted pillars with a non-null score per jurisdiction: 8 pillars for 48 jurisdictions, 7 for AL and DC (pillars.scale.score is null) and 7 for TN (pillars.health.score is null). The claim's own detail names those nulls in the correlation section but the headline asserts all eight everywhere. (3) The stated mechanism is incomplete, and I verified the missing half. Dilution happens TWICE, not once. I confirmed every pillar score equals the unweighted mean of its own indicator percentiles (0 of 51 states deviate by more than 0.5). So permits' r = +0.7363 is first cut to the building pillar's +0.5278 by being averaged with housePrice, which I compute at r = +0.0241 (n=51, t=+0.169) — essentially no relationship. Only then does the across-pillar average apply. Attributing the null to "the index averages all eight pillars equally" skips the stage that costs the most. (4) Units and denominators do not match in the OLS line, my assigned angle. y = migration.per1k.domestic is a CUMULATIVE 2021-2024 net domestic flow per 1,000 of the 2024 population (I verified totals.domestic / population * 1000 equals per1k.domestic for all 51, max absolute deviation 0.0; migration.years has exactly 4 rows, 2021-2024). x = permits, labelled "Housing units authorised per 1,000 workers" — a different denominator (workers, not residents) and no period stated. Cross-checking display against workforce.totalEmployment implies a monthly rate, not annual: FL 1.4 x 9,929,860/1000 = 13,902 units, TX 1.2 x 14,071,160/1000 = 16,885, CA 0.4 x 18,213,700/1000 = 7,285 — roughly one month of authorisations each, an order of magnitude below annual. So the slope 39.09 pairs a four-year cumulative stock against a single-period rate on a different base, and is not interpretable in any natural unit. What does hold, and holds well: I independently confirmed the cancellation mechanism by covariance decomposition on the 48 complete-8 jurisdictions. Positive covariance mass +726.49, negative -622.65, net +103.84; divided by 8 that predicts cov(index,y) = +12.98 against an actual +12.18, r = +0.0633 on those 48. The permits link is also robust beyond the leave-one-out the claim reports: Spearman rank r = 0.7116, and dropping the five highest-permit states (ID, SC, SD, ME, NC) still leaves r = 0.6513. The near-zero index correlation is robust too (leave-one-out -0.0248 dropping FL to +0.0581 dropping ID). Minor, not disqualifying: "51 of 51 index.score equals the rounded pillar mean" holds only under round-half-up. Six jurisdictions sit exactly on a .5 boundary — HI 55.5, IA 56.5, IN 49.5, LA 41.5, ND 48.5, OR 47.5 — and all six round up in the file. Under banker's rounding (Python's round()) it is 49 of 51. The claim's stated computation says "within rounding", which is fair.

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  The index against the movers · cut before publicationAll 8 pillars reverse sign between the two migration channels - the correlation between the 8 domestic r-values and the 8 international r-values is -0.8739 - and the index tracks international arrivals (r = 0.4119) but not domestic ones (r = 0.0243).The arithmetic is clean — I reproduced every cited figure to the stated digit, and the null handling (scale n=49 dropping DC and AL, health n=50 dropping TN) and the per-1,000 denominator (4-year cumulative flow over the 2024 population; verified 0/102 mismatc…

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  The arithmetic is clean — I reproduced every cited figure to the stated digit, and the null handling (scale n=49 dropping DC and AL, health n=50 dropping TN) and the per-1,000 denominator (4-year cumulative flow over the 2024 population; verified 0/102 mismatches, all 51 states have 4 year-rows summing to totals) are all correct. No display-string parsing was involved, so no parsing error is possible. But the headline "All 8 pillars reverse sign" is materially overstated on three counts. (1) THE EIGHTH FLIP IS NOT A SIGN, IT IS ZERO. Credit's international r = -0.0080, two-sided p = 0.9555. Calling that a reversal treats a coefficient indistinguishable from zero as though it carried a direction. It is a knife-edge: deleting any one of at least six jurisdictions (IL, IN, RI, SD, TN, MO) pushes credit's international r positive and the count falls to 7 of 8 — and in every one of those cases credit is the only pillar that loses its flip. On Spearman ranks, which neutralise the heavy tails (DC at +49.25 international, NY at -44.98 and ID at +55.68 domestic), credit's international rho is +0.0621 and the count is 7 of 8, not 8 of 8. (2) MOST OF THE "REVERSALS" HAVE ONE INSIGNIFICANT SIDE. Only 3 of the 8 pillars — labour, prosperity, building — have both correlations significant at p<0.05. Three international r-values are not distinguishable from zero (credit p=0.9555, formation p=0.2812, scale p=0.1679) and two domestic ones are not either (health p=0.2239, openness p=0.0634). That is 16 tests with no multiplicity adjustment. (3) THE -0.8739 IS PARTLY MECHANICAL AND THE IMPLIED NULL IS WRONG. Because the two channels are themselves negatively correlated (-0.3535), any set of predictors tends to produce oppositely-signed r-vectors. Drawing 8 pure-noise vectors (n=51) against these same two channels 20,000 times gives a null r-vector correlation with median -0.3797 and mean -0.3308 — not 0 — and 1.62% of null draws reach -0.8739 or below, while 2.04% produce 8-of-8 flips from noise alone. The observed value is still in the tail, but the honest baseline is roughly -0.38, not zero, and the claim's framing ("all 8 reverse") invites the reader to compare against zero. Two further framing problems. The claim offers "25 of 51 record negative domestic migration" and "the file's own channelsDiverge flag is true for 25 jurisdictions" as if they were two corroborating facts. They are the same fact: the two sets are identical (symmetric difference empty), and since all 51 have positive international migration, channelsDiverge is definitionally domestic<0. Separately, the index is essentially the unweighted mean of its own pillars (r = 0.9993 against the simple mean of available pillar scores), so the index result is an aggregate of the same eight numbers, not independent confirmation of them. What does survive: the index finding is robust. Index vs international r = 0.4119 (t = 3.164, p = 0.0027; leave-one-out range 0.345 to 0.457; Spearman 0.3511) against index vs domestic r = 0.0243 (t = 0.170, p = 0.87; leave-one-out range -0.025 to +0.058; Spearman 0.0556). The channel divergence is real too (r = -0.3535, t = -2.645; Spearman -0.4273). And seven pillars do flip on every specification I tried. The claim's own caveats about causation and about a single 2021-2024 cross-section are appropriate. The defect is the "8 of 8" and the implied strength of a -0.8739 measured against the wrong null.

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  The index against the movers · cut before publicationThe index and domestic movers disagree most sharply at opposite extremes: DC ranks 5th on the index but 45th on domestic migration at -20.239 per 1,000, while Idaho ranks 39th on the index and 1st on domestic migration at +55.684 per 1,000.Arithmetic and units are clean — every one of the 11 cited figures reproduces digit-for-digit, and the per-1,000 denominator is confirmed correct (migration.totals.domestic / population * 1000 equals migration.per1k.domestic to 0.000 for all 51). No display-st…

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  Arithmetic and units are clean — every one of the 11 cited figures reproduces digit-for-digit, and the per-1,000 denominator is confirmed correct (migration.totals.domestic / population * 1000 equals migration.per1k.domestic to 0.000 for all 51). No display-string parsing was involved (all values are native numbers). DC (+40) and Idaho (-38) really are the gap extremes, and they stay the extremes under dense and average tie-handling too. But four things break the claim as written. (1) THE STATED COMPUTATION DOES NOT PRODUCE THE STATED LISTS. "Sort by gap descending" gives DC +40, CA +33, NY +32, WA +31, HI +30, MD +29, NJ +25, CO +24. The detail lists DC, CA, NY, WA, then jumps to Colorado — silently dropping Hawaii (index rank 19, domestic rank 49, -31.821 per 1,000), Maryland (rank 13 vs 42, -18.353) and New Jersey (rank 19 vs 44, -19.272). Sorting ascending gives ID -38, ME -37, AR -35, AL -31, WV -29, NV -26, DE -25, SC -24. The detail lists ID, ME, AR, AL, then South Carolina — dropping West Virginia, Nevada (rank 39 vs 13, +21.718) and Delaware (rank 29 vs 4, +41.947). South Carolina is presented as the fifth-largest negative gap; it is the eighth. Both lists run in descending magnitude order, which reads as a complete top-5, and a sceptic re-running the stated sort gets different states. (2) THE CORRELATION FRAMING IS BACKWARDS. "Isolates the disagreements the correlation averages away" implies an underlying agreement these cases depart from. There is none: Pearson(index.score, domestic per1k) = 0.0243 and Pearson(index.rank, domestic rank) = 0.0452 across n=51. The two measures are essentially unrelated over the whole set, so DC and Idaho are not exceptions to a rule — there is no rule. Saying they "disagree most sharply" misdescribes a zero-correlation pair as a mostly-agreeing one. (3) THE GAP MIXES TWO RANK SCALES. index.rank is competition-style with heavy ties — 26 distinct values across 51 jurisdictions, reaching 51 only because ties skip numbers — and it is subtracted from a strict 1..51 domestic rank. Re-ranking the index densely (max 26) collapses the negative extremes: Idaho -38 becomes -18, South Carolina -24 becomes -12. The magnitudes are partly an artifact of the scale mismatch. The detail does disclose the ties, but the headline does not. (4) "IDAHO RANKS 39TH" HIDES A FOUR-WAY TIE. ID, NV, OR and KS all sit at index rank 39 with the identical score of 48, and they occupy domestic ranks 1, 13, 28 and 38 (gaps -38, -26, -11, -1). The disagreement is not a property of index rank 39. Likewise SC's rank 26 is shared with WI (gap 0) and MN (gap +15) at the same score of 53. Separately, "these are the same jurisdictions in both rankings, measured over 2021-2024" is true only of the migration side; index inputs include Moody's indicative 2025 and CEFA probes dated 2026-09.

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  Ageing · cut before publication"Care work" does not move together: Healthcare Practitioners lq correlates -0.5691 with natural change while Personal Care and Service lq correlates +0.2096, and Healthcare Support is effectively flat (6 of 22 decline states at lq >= 1.00 versus 7 of 29, Fisher p = 1.0000).The arithmetic is almost entirely reproducible, but one stated p-value is wrong and the headline's central framing does not survive its own numbers. WHAT REPRODUCES EXACTLY (51 states, split by migration.naturalDecline: 22 decline / 29 increase; I confirmed t…

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  The arithmetic is almost entirely reproducible, but one stated p-value is wrong and the headline's central framing does not survive its own numbers. WHAT REPRODUCES EXACTLY (51 states, split by migration.naturalDecline: 22 decline / 29 increase; I confirmed the boolean flag agrees with the sign of migration.per1k.natural in all 51 cases, no nulls, no missing lq): Pearson/Spearman of per1k.natural vs major-group lq — 29-0000 -0.5691/-0.4822, 31-0000 -0.1801/-0.2054, 39-0000 +0.2096/+0.3094. Group mean lq — 29-0000 1.0895/0.9783, 31-0000 0.9168/0.8914, 39-0000 0.9755/1.1069. Counts at lq>=1.00 — 19/22 vs 14/29, 6/22 vs 7/29, 10/22 vs 21/29. Care bundle 135.941 vs 130.259, ratio 1.0436 (4.36%). LOO Spearman for 39-0000 min +0.2793 (drop WV), max +0.3784 (drop TX). Excluding NV/HI/DC: r=+0.3097, rho=+0.3696. AR 0.71 lowest (naturalDecline true), NV 1.98 highest (naturalDecline false). Units check passes: per1000 is jobs per 1,000 jobs — the 22 major groups sum to 1000.00 in every state I checked, and employment/totalEmployment*1000 matches the published per1000. No display-string parsing was involved in any of this (lq, per1000 and per1k.natural are all native numbers), so there is no parsing error to find. FIGURE THAT DOES NOT REPRODUCE: the 39-0000 Fisher two-sided p. The 2x2 table is [[10,12],[21,8]]; the exact two-sided test (sum of all hypergeometric tables with probability <= p_observed = 0.035797) gives p = 0.081938, i.e. 0.0819, not the stated 0.0808. I could not reach 0.0808 by any standard route: chi-square 0.0508, Yates 0.0962, doubled one-tail 0.0961, mid-p 0.0640. The 0.0073 and 1.0000 p-values reproduce exactly, so this is an isolated error, not a different convention. WHY THE FRAMING IS MATERIALLY OVERSTATED: (1) The claim switches measures to manufacture a third direction. For groups 29-0000 and 39-0000 it quotes correlations; for 31-0000 it quotes a binary Fisher cut and calls it "effectively flat". Measured consistently, 31-0000's Pearson is -0.1801 and its Spearman -0.2054, and its group means tilt toward the decline states (0.9168 > 0.8914) — the SAME sign as the clinicians, a faint echo of direction one, not a third direction. (2) The two "different" weak correlations are statistically indistinguishable from each other and from zero: 39-0000 r=+0.2096 has p=0.1399 and 31-0000 r=-0.1801 has p=0.2060 (t-test on r, df=49). Calling +0.21 a direction while calling -0.18 flat is arbitrary. Applied consistently the pattern is one strong negative (29-0000, p<0.0001, Welch on group means p=0.0017, Fisher p=0.0073) and two noisy nulls, one of each sign. (3) The extremes are cherry-picked bookends. AR (lowest lq 0.71, decline) and NV (highest 1.98, increase) run the claimed way, but the 2nd-lowest is TX at 0.72 — the 3rd-highest natural increase in the file at +17.10 per 1,000 — and DC at 0.80 is 4th-highest at +16.17, while WV, the deepest natural decline at -22.75, sits near the bottom at 0.82. That is precisely why dropping TX RAISES rho to +0.3784. (4) The robustness check is selective: it reports LOO for the Spearman (which looks solid) but not for the headlined Pearson, whose LOO range is [+0.164 drop WV, +0.277 drop TX] and never reaches significance; and the "excluding NV, HI and DC" test removes DC, whose removal alone strengthens 39-0000 (r=+0.2574, rho=+0.3747) and weakens 31-0000 (r=-0.1411) — it moves in the flattering direction. WHAT SURVIVES: the clinician/personal-care contrast itself is real. 29-0000 vs 39-0000 differ in sign on both correlation and group means (Welch p=0.0017 and p=0.0266 respectively), and the "total care footprint is close" statement is fair — the bundle difference is not distinguishable (Welch t=+1.357, p=0.1811). The defect is the three-way "three different directions" packaging and the wrong 0.0808. All correlations are cross-sectional over n=51 with no causal reading, and lq is distinctiveness only.

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  Ageing · cut before publicationThe clinical-concentration gap comes with no relative pay gap: healthcare practitioners earn $7,680 less on average in the 22 natural-decline states ($83,864 vs $91,544), but relative to each state's own all-occupation median the ratio is 1.7036 versus 1.6887 — a 0.9% difference.Arithmetic: fully reproduced, digit for digit — every one of the nine cited figures is exactly right, and the stated integrity check holds (all 51 states carry 22 major[] entries including 290000/310000/390000; zero null medianWage; zero wageAtCap:true; split …

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  Arithmetic: fully reproduced, digit for digit — every one of the nine cited figures is exactly right, and the stated integrity check holds (all 51 states carry 22 major[] entries including 290000/310000/390000; zero null medianWage; zero wageAtCap:true; split is 22 dec / 29 inc). No parsing risk arises because workforce.major[] medianWage and workforce.medianWage are numeric, not display strings. I am refuting on framing, not on numbers. (1) The direction of the practitioner ratio difference is an artifact, not a finding. It rests on one outlier: DC sits at 1.0968 while the next-lowest of the 29 is ND at 1.5229. Drop DC and dec-vs-inc flips from +0.88% to −0.37% (dec 1.7036 vs inc 1.7099). Weight by practitioner employment and it flips harder to −4.27% (dec 1.6854 vs inc 1.7606). Welch t = 0.38, df = 48.3, Cohen's d = 0.10, and the 95% interval on the difference runs −0.0644 to +0.0941, i.e. −3.8% to +5.6% of the comparison mean. The null is genuine, but the DETAIL's "if anything they sit slightly higher relative to local pay in the decline states" reads a sign out of noise, and quoting "1.7036 versus 1.6887" to four decimals invites a published reader to do the same. (2) "The same holds for the other two care groups" understates by 3–5x. Healthcare Support is +4.68% and Personal Care +3.26%, against the practitioners' +0.88%. For Support the ratio does not "remove almost all" of the level gap — it more than fully reverses it (level dec 37,821 vs inc 39,604, −4.50%; ratio +4.68%, Welch t = 1.88). Those two directions are stable across DC removal and outlier trimming, unlike the practitioner one, so the three groups are not one uniform null. (3) "Healthcare practitioners earn $7,680 less on average" is an unweighted mean of 51 state median wages, not average practitioner earnings; weighted by the practitioners actually employed the gap is $14,165, nearly double. The stated computation discloses the method, so a careful reader can re-run it, but the headline sentence as written halves the gap a literal reader would take from it. The underlying premise checks out — there is a real clinical concentration gap (290000 lq: dec 1.0895 vs inc 0.9783, Welch t = 3.32; per1000 68.906 vs 61.805) — and the state wage floor is genuinely lower in the decline states (49,137 vs 54,648, −10.08%, t = −2.87). So the core "no measurable relative pay gap" survives; what fails is the false precision on its direction and the claim that the other two groups behave the same way.

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  Ageing · cut before publication14 of the 22 natural-decline states are at or above national concentration in BOTH Production and Healthcare Practitioners, against 7 of 29 other states (Fisher exact two-sided p = 0.0090); Production is in fact the largest single lq gap between the two groups (mean 1.1905 vs 0.9276).The structural core reproduces exactly, but the claim contains one wrong framing word that is load-bearing and four gap figures that are wrong in the 4th decimal — including two that contradict the claim's own quoted component means. (A) WHAT REPRODUCES EXACT…

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  The structural core reproduces exactly, but the claim contains one wrong framing word that is load-bearing and four gap figures that are wrong in the 4th decimal — including two that contradict the claim's own quoted component means. (A) WHAT REPRODUCES EXACTLY. Split on migration.naturalDecline gives 22 / 29 (flag is consistent with the sign of migration.totals.naturalChange for all 51). Joint condition major['510000'].lq >= 1.0 AND major['290000'].lq >= 1.0 gives 14 of 22 (AL AR KY MI MO MS NH OH OK PA RI SC TN WI) and 7 of 29 (IN KS MN NC ND NE SD) — identical lists. Fisher exact two-sided on [[14,8],[7,22]] = 0.008976 -> 0.0090. Production alone 15/22 vs 12/29, p = 0.089366 -> 0.0894. Pearson r of Production lq vs migration.per1k.natural over n=51 = -0.262696 -> -0.2627. Production means 26.19/22 = 1.190455 and 26.90/29 = 0.927586 -> 1.1905 and 0.9276, gap +0.262868 -> +0.2629. Legal -0.263495 -> -0.2635. All correct. No nulls exist in major[].lq, so no missing-data handling was required, and no display strings were involved (lq is a raw number). (B) THE FRAMING ERROR. "Production is in fact the largest single lq gap between the two groups" is false. Ranked by absolute size of the between-group mean gap, Production is THIRD: Life/Physical/Social Science 0.2777, Legal 0.2635, Production 0.2629, Computer and Mathematical 0.2095. Production is only the largest POSITIVE gap. The claim's own detail already lists the two larger negative gaps, so its headline is contradicted by its own body. (C) FOUR FIGURES OFF IN THE 4TH DECIMAL. Healthcare Practitioners: claimed +0.1112, actual +0.111270 (rounds to +0.1113). Community and Social Service: claimed +0.0700, actual +0.070172 (+0.0702). Life/Physical/Social Science: claimed -0.2779, actual -0.277712 (-0.2777). Computer and Mathematical: claimed -0.2101, actual -0.209545 (-0.2095). Two are internally inconsistent with the claim's own parenthetical means: 1.219 - 0.941 = 0.278, not 0.2779; 0.980 - 0.770 = 0.210, not 0.2101. The component means themselves (0.941, 1.219, 0.854, 1.118, 0.770, 0.980) are all correct. (D) FRAGILITY THE CLAIM DOES NOT DISCLOSE. Two of the 14 sit exactly on the cut: RI Production lq = 1.00 and SC Healthcare lq = 1.00. lq is stored to two decimals, so a recorded 1.00 lies anywhere in [0.995, 1.005). Treating rounded ties as below threshold moves the table to 12/22 vs 7/29 and Fisher p from 0.0090 to 0.0407 — still significant at 5%, but the headline p understates how much rests on two boundary values. The claim's lq caveat and its avoidance of causal language are both correct; the problem is the "largest single gap" wording and the transcription of four gaps.

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  Building and arrivals · cut before publicationHousing authorisation predicts domestic migration strongly (Pearson r = +0.742 across 51 jurisdictions) but carries no usable signal about international arrivals (r = -0.194, t = -1.38); house-price level does the reverse (r = +0.519 with international, -0.111 with domestic).The four headline correlations reproduce to the digit, but three things break the claim as written. (1) TWO OF THE SEVEN CITED FIGURES ARE NOT REPRODUCIBLE. Both "10 highest-permit vs 10 lowest-permit" means are undefined, because permits.display is rounded t…

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  The four headline correlations reproduce to the digit, but three things break the claim as written. (1) TWO OF THE SEVEN CITED FIGURES ARE NOT REPRODUCIBLE. Both "10 highest-permit vs 10 lowest-permit" means are undefined, because permits.display is rounded to one decimal and the cut lines fall inside ties. Eleven states sit at >=1.2 (three tied at 1.2: TX, TN, DE), so a "top 10" must drop one arbitrarily; the three defensible answers are mean domestic +29.83 / +30.74 / +31.81 and mean international +17.55 / +18.22 / +16.61. A natural stable sort gives me +31.81 and +16.61, not the claimed +30.74 and +18.22 (a 1.61 gap, ~10%, on the international figure). The bottom group is worse: six states tie at 0.4 (VT, CA, MA, MI, PA, RI), so "10 lowest" drops one of six, and the domestic mean ranges -12.11 (drop CA) to -16.62 (drop VT). Publishing a point estimate from an arbitrary tie-break is not a re-runnable computation. The tie-free cuts the claim itself uses elsewhere (n=13 and n=11) give +30.94 / -14.24 domestic and +16.13 / +23.68 international. (2) "HOUSE-PRICE LEVEL" IS A MISLABEL. The file's indicator label is "House price index (FHFA)", source Federal Housing Finance Agency — an index normalised to a base period, i.e. cumulative appreciation, not the level of house prices. The data prove it: Maine 1044.1 and Washington 1033.3 outrank DC 1037.7... and both outrank California 975.0 and Hawaii 982.6, with Massachusetts top at 1326.9. No ranking of house-price levels puts Maine above California and Hawaii. A reader told "house-price level correlates +0.519 with international arrivals" will conclude expensive states draw international migrants; the indicator does not measure expensiveness. (3) "DOES THE REVERSE" OVERSTATES, BY THE CLAIM'S OWN STANDARD. It calls r = -0.194 (t = -1.38) "not distinguishable from zero", then in the same sentence presents r = -0.111 (t = -0.78, Fisher 95% CI [-0.375, +0.170]) as an active reversal. House price is not negatively related to domestic migration; it is unrelated to it. The pattern is one real association (price index with international) plus three nulls, not a mirror image. Relatedly, "carries NO usable signal" is stronger than a 95% CI of [-0.445, +0.087] on r(permits, international) supports — a moderate negative association is fully compatible with these data. What survives: the permits-domestic association is real and robust. I independently confirmed it is not a size artefact (r(permits, log10 population) = -0.0000; within the 25 largest states +0.8575) and, going beyond the stated computation, it is not a shared-denominator artefact either — permits use a worker denominator and migration a resident one, but the partial correlation controlling employment/population is +0.730 versus +0.742 raw. The 12-of-13 and 10-of-11 sign counts reproduce exactly, same jurisdiction lists, NE -6.48 and VT +9.60.

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  Building and arrivals · cut before publicationIdaho and Nebraska differ in population by 3,846 people (2,001,619 vs 2,005,465) and both sit in the top eight for housing authorised per worker, yet Idaho gained 111,459 domestic migrants and Nebraska lost 12,996.I reproduced every headline figure digit-for-digit, but two supporting statements fail. (1) FIGURE ERROR: "Idaho's building pillar 61 (22nd of 51)" is wrong under any standard tie convention. Exactly 20 of 51 states score above 61, and North Dakota also scores…

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  I reproduced every headline figure digit-for-digit, but two supporting statements fail. (1) FIGURE ERROR: "Idaho's building pillar 61 (22nd of 51)" is wrong under any standard tie convention. Exactly 20 of 51 states score above 61, and North Dakota also scores 61, so Idaho is JOINT 21st, not 22nd. The 22 comes from an arbitrary sort-order tiebreak the claim never disclosed (it stated methods for the permits, house-price and domestic-migration ranks, but not for the pillar-score rank). Nebraska's "79, 3rd of 51" IS correct (TX 81 and IA 81 tie for 1st). (2) FRAMING OVERSTATEMENT: "Nebraska is the single exception to the permits-to-domestic-migration pattern" is true only inside the window the claim chose and collapses two places outside it. Washington permits 0.9 (percentile 72 = file-rank 15 of 51), lost 33,762 domestic migrants (-4.24 per 1,000) and is also flagged sustainedByInternational. Widen the window from 13 to 15 and there are two exceptions; at the top 20 there are five sustainedByInternational states (NE, WA, IA, MN, KS). The narrower statement the claim also makes - "the only one of the 13 heaviest permitters flagged sustainedByInternational" - IS exactly true, and 13 is a defensible cut (precisely 13 states show permits >= 1.0), but the unqualified "single exception" sentence is not supported. Two further caveats, not errors: Nebraska's 1.4 permits ties Florida and Utah, so "8th of 51" holds only because the percentile field encodes rank (I verified rank = (100-percentile)/2+1 reproduces the sort exactly); and the building pillar score is simply the mean of its two indicator percentiles (ID (100+22)/2=61, NE (86+72)/2=79), so Nebraska's higher pillar score reflects cheapness, not more building - the claim describes this mechanism correctly. Also worth noting for framing: Nebraska's "net" field excludes natural change, and its natural change (+22,085) is larger than its entire net migration (+20,240), so "held up entirely by international arrivals" is true of the net-migration line only, not of population growth.

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  Building and arrivals · cut before publicationThe District of Columbia authorises the least housing per worker of any jurisdiction (0.1 per 1,000, 0th percentile) yet ranks 16th of 51 in net migration per 1,000 (+29.01) - a 35-place rank gap, the largest in the file, and it is entirely international: +34,586 international against -14,213 domestic.The arithmetic all checks out — I reproduced every cited number to the digit — but three things break the claim as written. (1) THE STATED COMPUTATION IS NOT RE-RUNNABLE AS DESCRIBED. It says the permit ranks come from "51 distinct values, a strict order matc…

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  The arithmetic all checks out — I reproduced every cited number to the digit — but three things break the claim as written. (1) THE STATED COMPUTATION IS NOT RE-RUNNABLE AS DESCRIBED. It says the permit ranks come from "51 distinct values, a strict order matching permits.display descending". The 51 percentiles are indeed distinct (0,2,4,...,100) and I found zero monotonicity violations against display — but permits.display has only 16 distinct values across 51 jurisdictions, with heavy ties: 0.5 appears 10 times, 0.4 and 0.7 six times each, 0.6 and 0.9 four times each, 0.2 three times. Display descending is therefore NOT a strict order and cannot reproduce the ranks. This bites the claim's own example: Connecticut's "49th of 51" is purely a percentile tie-break — AK, CT and IL all display 0.2, separated only by percentiles 2 / 4 / 6 into 50th / 49th / 48th. A sceptic re-running the recipe as stated gets a different CT rank. (2) THE HEADLINE SWITCHES DENOMINATORS MID-SENTENCE, AND DC IS EXACTLY THE JURISDICTION WHERE THAT MATTERS. Permits are per 1,000 WORKERS; net migration is per 1,000 RESIDENTS. DC is the one jurisdiction in the file where those two bases coincide: totalEmployment 701,920 against population 702,250 = 1.000 jobs per resident, versus a median of 0.458 and a maximum of 0.539 (ND) across the other 50. The worker denominator therefore inflates every other jurisdiction's permit rate by roughly 2.2x relative to DC. Re-expressing permits per 1,000 residents using the file's own fields (permits.display x totalEmployment / population), DC is 4th-lowest at 0.100, behind Alaska 0.088, Connecticut 0.092 and Illinois 0.096. "Authorises the least housing per worker" is literally true; "authorises the least housing" full stop is an artefact of the denominator, and it is the half the sentence leans on. (Related: DC's 0.1 is one significant figure — implied 70 units, rounding band 35-105, +/-50%. The rank is safe because percentile 0 comes from unrounded data; the magnitude is not.) (3) "94,752 international ARRIVALS" IS THE WRONG LABEL. I verified totals.net == totals.domestic + totals.international for all 51 states and for all 204 annual rows, and totals.change == net + naturalChange for all 51. So "international" is NET international migration (in minus out), not gross arrivals. The DETAIL's own sentence — "net migration is arrivals minus departures" — contradicts its use of "arrivals" for that figure. Same applies to DC's +34,586. What DOES hold: every rank, gap and value is exactly right; the ordering is robust to normalisation (re-ranking net migration by the sum of the four annual netRate rows instead of totals/pop2024 moves no jurisdiction by more than 1 place, and leaves DC 16th, CT 20th, NE 38th unchanged); DC's building score of 4 is the unique minimum; sustainedByInternational and channelsDiverge are both true for DC and CT; and the claim's own closing caveat about housing consumption is correct and should be kept.

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  Building and arrivals · cut before publicationThe two indicators inside the building pillar are statistically independent across the 51 jurisdictions (Pearson r = +0.028, Spearman -0.019), and the top-10 lists by permits and by cheapness share zero states.The arithmetic is clean — I reproduced every cited figure digit for digit, including the parse of the display strings (no housePrice display in the file actually contains a comma, so the .replace(',','') is a no-op; the values are stored as "1326.9", "1044.1")…

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  The arithmetic is clean — I reproduced every cited figure digit for digit, including the parse of the display strings (no housePrice display in the file actually contains a comma, so the .replace(',','') is a no-op; the values are stored as "1326.9", "1044.1"). What fails is the inference. (1) "Statistically independent" and "carry no information about each other" are not what a near-zero Pearson/Spearman establishes; they only rule out a LINEAR and a MONOTONE association. With n=51 and r=+0.0284, the Fisher-z 95% CI is [-0.249, +0.302] (t=0.199, df=49) and for rho [-0.293, +0.258] — the file cannot exclude a moderate association of either sign, let alone prove independence. (2) The stronger objection: the two indicators are demonstrably NOT independent. Split the 51 into thirds by the file's own permits.percentile (ascending) and take the mean FHFA index of each third: 799.9 / 593.4 / 754.7 — a U-shape, cheapest in the middle, expensive at both ends. Eta-squared = 0.1661, F = 4.779 on (2,48), Kruskal-Wallis H = 8.686 on 2 df, and a 20,000-draw permutation test on eta-squared (permuting the price vector against the fixed tertile grouping) gives p = 0.0122. A correlation coefficient of ~0 is exactly what a U-shape produces; it is the one pattern Pearson and Spearman are blind to, and the claim reads that blindness as an absence of structure. Robustness note in the sceptic's own favour: if you instead cut tertiles on the ROUNDED display values the effect looks far larger (eta-squared 0.293, permutation p = 0.0004), but that is an artifact — 10 jurisdictions share the display value "0.5" and straddle the tertile boundary, and across 1,000 random tie-breakings eta-squared ranges 0.017 to 0.309. The percentile-ordered figures above are the tie-free ones and are what I stand behind. Everything else in the claim survives: the identity, the empty top-10 overlap, the 6-of-13, and the individual state ranks are all correct, and the caution that this is one cross-section with no earlier price reading is both true and appropriate.

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  Manufacturing · cut before publicationThe 12 most manufacturing-concentrated states span only $128,938 to $169,968 in output per worker, and 10 of the 12 sit below the national median — manufacturing share and output per worker run in opposite directions across the 49 states where both are published (Spearman rho = -0.458).On my assigned angle — missing data — the claim is CLEAN and I could not break it. mfgShare is missing:true (display "—", percentile null) for exactly 2 jurisdictions, AL and DC; gdpPerWorker is published for all 51. Neither missing value is treated as zero, n…

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  On my assigned angle — missing data — the claim is CLEAN and I could not break it. mfgShare is missing:true (display "—", percentile null) for exactly 2 jurisdictions, AL and DC; gdpPerWorker is published for all 51. Neither missing value is treated as zero, neither enters any computation, and the DETAIL names both exclusions explicitly rather than hiding them. "49 states" is even literally right: 51 minus AL minus DC leaves 49 actual states, since DC is not a state. No wage figure is used anywhere, so wageAtCap cannot have been misread. I went further than the claim did and BOUNDED the missing pair: assigning AL and DC every mfgShare value in the observed range (1.0% to 16.7%) and recomputing over all 51, rho stays between -0.3136 (least negative: AL lowest, DC highest) and -0.5037. The sign never flips, so acknowledging the missing states does not threaten the finding. What DOES fail is the framing the DETAIL uses to justify the headline's word "only". It sizes the top-12 band against "the national spread is $128,938 to $479,240 (DC)" — reinstating DC as the yardstick after excluding DC from the ranking and the correlation for having no mfgShare. Ex-DC, the 50-state range is $128,938 to $245,798 = $116,860 (1.906x), so the top 12's $41,030 is 35% of the real 50-state range, not 12% of a $350,302 span whose top end is the one jurisdiction the analysis threw out. The tightness claim survives on honest terms and I verified it a better way: 20,000 random draws of 12 from the 49 (seed 0) give a median spread of $85,365, and only 1.2% of draws are as tight as $41,030 — so "unusually tight" is real, it just must not be evidenced with DC. Two further defects. (a) The DETAIL contradicts its own headline: "a co-movement across 51 jurisdictions" when the rho is computed on 49. (b) The "10 of 12 below the national median" count rests on a $197 margin — Ohio at $164,771 against a median of $164,968; call that a tie and it is 9 of 12. I checked the base-mixing risk and it is harmless: gdpPerWorker percentile is a 51-jurisdiction rank (0 mismatches vs i/(n-1)x100 over the 51-sorted list; MS=0, DC=100) while the top-12 selection is over 49, but the median gdpPerWorker is $164,968 on both the 51 and the 49-with-mfgShare bases and the count is 10 either way. Ranking on the rounded display string also produces 9 display ties whose file percentiles disagree with the printed order (KS and AR both show 11.8% but the file ranks AR 88 above KS 85, so the claim lists them backwards); the SET of 12 is identical under either ordering and the 12/13 boundary is safe (MN 10.5% vs NH 9.5%, a 1.0pp gap), so no cited figure moves. Refuting because the supporting comparison is misleadingly framed and the n=51 line is flatly wrong, even though every headline figure reproduced to the digit.

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  Manufacturing · cut before publicationMichigan has the densest engineering workforce of the 12 manufacturing-heavy states — 130,140 architecture-and-engineering jobs, 29.55 per 1,000, 2nd-highest in the nation — yet ranks 4th from the bottom of that group on output per worker at $149,670 (national percentile 26).Every figure except one reproduces exactly, but the headline ordinal is wrong. Sorting the 12-state group on gdpPerWorker ascending gives MS $128,938, AR $136,107, SC $141,730, KY $145,875, MI $149,670 — Michigan is 5th from the bottom, not 4th; KY occupies th…

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  Every figure except one reproduces exactly, but the headline ordinal is wrong. Sorting the 12-state group on gdpPerWorker ascending gives MS $128,938, AR $136,107, SC $141,730, KY $145,875, MI $149,670 — Michigan is 5th from the bottom, not 4th; KY occupies the 4th-from-bottom position. Everything else holds: MI 130,140 architecture-and-engineering jobs, per1000 29.551, 2nd of 51 behind NM 31.190; Mechanical Engineers 34,630 at lq 4.12 and median $104,890 (wageAtCap false); MI output per worker $149,670 at percentile 26; median of the 51 gdpPerWorker values $164,968 (Florida sits on it); Spearman with average ranks n=12 gives mfgShare -0.0772, engineering per1000 +0.2587, Production medianWage +0.5594, state medianWage +0.7133 — all four match to four decimals. Two further framing defects: (1) per1000 is per 1,000 JOBS (130,140 / 4,403,730 total employment = 29.552), not per 1,000 residents, which would be 12.83 against population 10,140,459 — the claim never states the denominator; (2) Alabama's mfgShare is missing:true so it cannot enter the group, yet AL's architecture-and-engineering density is 23.458 per 1,000, which sits between MI and SC — so "next highest in the group is SC at 20.061" is an artifact of an unpublished federal value, not a fact about manufacturing-heavy states (DC is the other missing mfgShare). The 12-state membership itself is sound: the percentile field breaks the AR/KS and TN/MN display-rounding ties, and 13th place (NH 9.5%) is a full point below.

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  Manufacturing · cut before publicationArkansas and Kansas report the identical manufacturing share of jobs, 11.8%, but $19,022 different output per worker ($136,107 vs $155,129, percentiles 4 and 30) — and their signature occupations are different industries entirely: aircraft assembly at LQ 30.86 versus poultry and produce grading at LQ 7.84.Arithmetic and parsing are clean — I reproduced all six cited figures digit for digit, and found no unit, denominator or display-string error. The claim fails on framing, in two places. (1) "Identical" is contradicted by the file the claim itself cites. mfgSh…

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  Arithmetic and parsing are clean — I reproduced all six cited figures digit for digit, and found no unit, denominator or display-string error. The claim fails on framing, in two places. (1) "Identical" is contradicted by the file the claim itself cites. mfgShare has no raw number in the file, only a one-decimal display string, and the percentile field is a pure rank: 49 jurisdictions carry a value (DC and AL are missing/null), and percentiles run 0,2,4...100 in single-rank steps. I checked all nine display ties (8.6%, 8.8%, 9.0%, 9.2%, 9.3%, 10.5%, 7.8%, 4.0%, 11.8%) and every tied pair gets distinct percentiles, and the split follows neither alphabetical nor dict-insertion order (MO 71 vs SD 73 rules out both) — so the ranking is driven by an unrounded value the file does not expose. That means the file positively asserts AR (88) sits above KS (85). The headline says they "report the identical manufacturing share"; the file says they report the same rounded display and an unequal underlying share. The detail concedes this in its second-to-last sentence, but the headline is the load-bearing line on a published page, and it contradicts its own supporting text. (2) "Poultry and produce grading at LQ 7.84" welds two separate occupations into one label. LQ 7.84 belongs solely to Graders and Sorters, Agricultural Products (452041). "Poultry" comes from a different row — Meat, Poultry, and Fish Cutters and Trimmers (513022), LQ 7.39. The figure and the description do not belong to the same record. Two smaller problems. "Different industries entirely" is wrong in kind: LQ is computed over occupations, not industries; mfgShare is the only industry measure here. And juxtaposing "identical manufacturing share ... but $19,022 different output per worker" invites the reader to take gdpPerWorker as manufacturing productivity. It is not — it is statewide BEA output per worker across all sectors, sitting beside a BLS industry share. The file cannot support the sector-productivity reading the sentence implies, and n=51 rules out any causal statement in either direction. The underlying substance — two states at the same rounded manufacturing share with very different statewide output per worker and unrelated signature occupations — survives. The headline as written does not.

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  Manufacturing · cut before publicationAlabama has no published manufacturing share at all (display '—', missing true, and a null scale-pillar score), yet its Production location quotient of 1.85 is the 2nd-highest of all 51 jurisdictions and 9 of its 12 signature occupations are Production-family codes — so any 'most manufacturing-concentrated' list built on mfgShare silently drops it.The missing-data handling — my assigned angle of attack — is clean, and every number reproduces exactly. AL and DC are the only two jurisdictions with pillars.scale.indicators.mfgShare.missing == true (display '—', percentile null), both have pillars.scale.sco…

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  The missing-data handling — my assigned angle of attack — is clean, and every number reproduces exactly. AL and DC are the only two jurisdictions with pillars.scale.indicators.mfgShare.missing == true (display '—', percentile null), both have pillars.scale.score null, no null is treated as zero, no wageAtCap value is treated as a real wage (AL 512031 has wageAtCap false AND medianWage null, and the MI/OH comparators are wageAtCap false so $60,950 / $74,750 are genuine values), and the Production LQ ranking really does cover all 51 with no nulls, so nothing was silently dropped there. I also checked the mechanism the claim asserts: every pillar in the file that contains a missing indicator has a null score (AL scale, DC scale, TN health) and no other pillar is null, so "null scale score as a result" is consistent with the file. I refute it on two framing defects that would ship verbatim to a page. (1) The headline says "9 of its 12 signature occupations." The file has a distinct field workforce.signature holding ONE occupation, and Alabama's is 454022 Logging Equipment Operators — SOC 45, not a Production code. Thirteen states do have a Production-code signature (IN 512051, WI 515113, OH 519161, MI 514111, plus DE GA IA KS MS NC NE SC VA); Alabama is not one of them. The 9-of-12 count is over workforce.specialities, a different field. So the headline, read against this file's own vocabulary, asserts something that is false for Alabama specifically, even though the underlying count is right. (2) "Most manufacturing-concentrated" is elided with Production-occupation concentration. SOC 51 is an occupation group; mfgShare is an industry share. The claim's "Alabama would sit second, ahead of Wisconsin and Michigan" is literally about the LQ ranking but is placed so as to read as a manufacturing ranking. For what it is worth, across the 49 jurisdictions that have both, the two measures move together very closely (Spearman rho 0.949, Pearson r 0.961) — co-movement only, and n=49 is small, so this is not evidence that one stands in for the other, and the claim never establishes it. One point the claim gets right and deserves keeping: the null wage genuinely blocks the comparison, and it says so rather than filling the gap.

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  Governance · cut before publicationThe openness pillar - three probes of whether a state's websites answered - carries 24.73% of the composite index's variance and shifts states an average of 6.55 rank places, three times the leverage of the Moody's rating (5.74% of variance, 2.16 places).ARITHMETIC: fully verified, digit for digit. I could not break a single cited number. No display-string parsing is involved anywhere in this claim (it runs entirely on integer pillars.*.score and index.score), so the parsing risk my angle of attack was aimed a…

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  ARITHMETIC: fully verified, digit for digit. I could not break a single cited number. No display-string parsing is involved anywhere in this claim (it runs entirely on integer pillars.*.score and index.score), so the parsing risk my angle of attack was aimed at does not exist here. Step 1 confirmed and slightly improved: index = mean of the available pillar scores, rounded HALF-UP, matches the published score for 51 of 51 (not 49). The "two exceptions" (Iowa 56.5, North Dakota 48.5) are only exceptions under banker's rounding; the claim's characterisation is honest but understates its own result. Published rank = competition rank on the published score, reproduced 51/51 with zero mismatches. Three null pillar scores confirmed: AL scale, DC scale, TN health. Step 2 confirmed: with published index, population moments, pairwise deletion, I get openness 24.7314% and credit 5.7436% — 24.73% and 5.74% as stated. SDs 29.7473 and 9.7280 = 29.75 and 9.73 as stated. Ranges confirmed: openness 0-88, credit 52-100. Shares sum to 99.665% ("~100%" as stated). Robust to listwise deletion (openness 25.50%, credit 5.69%) and to using the exact unrounded mean (24.82% / 5.68%). Pillar membership confirmed: openness = portal + policyData + feeds, all CEFA probes; credit = a single Moody's general-obligation rating indicator, so "the Moody's rating" is a fair label. Step 3 confirmed exactly: rebuilding as the UNROUNDED mean of 7 pillars and re-ranking gives mean |shift| of 6.5490 dropping openness (max 16, Alaska), 2.1569 dropping credit (max 11, Illinois), 6.6471 dropping both (max 20, Alaska) — 6.55 / 2.16 / 6.65 as stated. Alaska 32nd / 16th / 12th confirmed. Virginia 8th / 22nd confirmed. Ratio 6.5490 / 2.1569 = 3.04, so "three times" is right for the rank clause. WHY I STILL REFUTE — the framing, not the maths: 1. Openness is NOT the index's biggest variance carrier, and the headline is built so a reader will assume it is. Prosperity carries 27.63% — MORE than openness — and health carries 26.18%, also more. Openness is third. On rank leverage openness does lead (6.55) but prosperity (6.43) and health (6.14) are within 0.42 places of it; the eight-pillar leverage table is openness 6.55, prosperity 6.43, health 6.14, formation 4.24, building 3.90, labour 3.59, scale 3.20, credit 2.16. The "three times" gap exists because credit is the FLOOR of the distribution (only 6 distinct values across 51 states, SD 9.73), not because openness is an outlier ceiling. Comparing the third-largest pillar solely against the smallest, and publishing that ratio as the finding, is a selected contrast. 2. "Three times the leverage" is ambiguous next to a parenthetical carrying two credit figures. It is correct for rank places (3.04x) but wrong for the variance figure sitting immediately before it: 24.73 / 5.74 = 4.31x. A reader applying "three times" to the variance number gets 17.2%, not 24.73%. 3. Undisclosed technical caveat: this decomposition is not a variance partition and components can go negative — building's share is -5.22% (corr with index -0.16). Describing 24.73% as a pillar "carrying" a share of variance invites an ANOVA-style reading the quantity does not support. The underlying mechanism the DETAIL describes — equal 1/8 weights, unequal dispersion, so a compressed pillar moves nothing and a dispersed one moves ranks — is real, correctly computed, and correctly disclaimed as a statement about construction rather than about the world. It is the headline's openness-vs-credit-only framing that fails.

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  Governance · cut before publicationNULL RESULT: openness has no detectable relationship to the six economic pillars (Spearman +0.175, permutation p = 0.218) but does track state population (+0.376, p = 0.0068) - the 28 states whose portal answered have 3.10x the median population of the 23 whose published address answered nothing, while their economic scores differ by 1.86 points on a 100-point scale.The arithmetic reproduces almost perfectly, but the headline's first clause is false as worded, and two framings are misleading. (1) FATAL: "openness has no detectable relationship to the six economic pillars" is contradicted by the file. Three of the six ARE …

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  The arithmetic reproduces almost perfectly, but the headline's first clause is false as worded, and two framings are misleading. (1) FATAL: "openness has no detectable relationship to the six economic pillars" is contradicted by the file. Three of the six ARE detectably related, by the claim's own test at the claim's own 200,000 shuffles: health +0.4182 (p=0.00262), building -0.4077 (p=0.00332), prosperity +0.3972 (p=0.00416). All three survive Bonferroni correction across the six (0.05/6 = 0.00833). The null holds only for the unweighted mean composite the analyst constructed, not for "the six economic pillars." The DETAIL concedes the components "cancel" but never discloses that three are individually significant at p<0.005 - which is precisely the fact that makes the headline wrong. (2) The +0.175 point estimate is an artifact of one arbitrary construction and its SIGN is not stable: mean of raw pillar scores +0.1751; mean of z-scored pillars +0.0309 (p=0.83); mean of within-pillar rank percentiles +0.0534 (p=0.71); drop the health pillar and it flips to -0.1314 (p=0.35). The whole positive tilt rests on the health pillar, which the file shows is a SINGLE indicator - adult obesity (CDC BRFSS). "Openness tracks a six-pillar economy at +0.175" is largely "openness tracks lower obesity." Publishing +0.175 as a figure implies a precision the data does not support. (3) "1.86 points on a 100-point scale" uses a denominator nothing occupies. The composite's actual observed range across the 51 jurisdictions is 25.667 (WV) to 72.667 (CO) = 47.0 points, SD 8.786. So 1.86 points is 0.212 SD, or 4.0% of the real range - not the ~1.9% the "100-point scale" phrasing invites. The gap is still not significant (p = 0.459 in my run), so the substance survives; the framing inflates how small it looks. (4) Minor exactness: n_yes = 28 is even, so the median is (6,263,220 + 6,924,275)/2 = 6,593,747.5. The claim cites 6,593,747, a truncation - half a person, immaterial, but not the figure the file yields. (5) "Spearman(openness.score, ln(population))" - the log is a no-op. Spearman is rank-based and ln is monotone, so Spearman against RAW population is +0.375634, identical. The stated method implies a transform that does no work. (6) The mechanism sentence, "the probe is picking up which governments are large enough to run a responsive data portal," is a causal reading of a rank correlation at n=51. What I can confirm is the association, and it is strong: portal percentile vs population rho = +0.4578 (p = 0.00095), and the median-population ratio itself tests at p = 0.00058 (200k shuffles on the log ratio). Also confirming their story indirectly, population is NOT related to the economic composite (rho = +0.0835). WHAT SURVIVES: the population finding is real and well-supported, the 28/23 split matches the file exactly (28 displays starting "Yes ·", 23 reading exactly "Published address answers nothing", zero percentile/display mismatches), and the composite-level null is genuine and robust across every construction I tried. No display-string parsing errors: the claim only used pillar scores, portal percentiles and raw population, none of which required parsing a formatted string, and I verified the portal display/percentile mapping is one-to-one.

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  Governance · cut before publicationFiscal standing and data openness are orthogonal (Pearson +0.031, Spearman +0.163, p = 0.253), and the quadrant the question presumes - fiscally weak and data-closed - is empty: all 23 portal-silent states are rated Aa3 or better, while the only two jurisdictions rated below Aa3 both run answering portals.ARITHMETIC: clean. I reproduced every cited number digit-for-digit from pillars.openness.score and pillars.credit.score over all 51 jurisdictions (no nulls in either field; moody.missing is false for all 51). I also verified the openness score is exactly round…

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  ARITHMETIC: clean. I reproduced every cited number digit-for-digit from pillars.openness.score and pillars.credit.score over all 51 jurisdictions (no nulls in either field; moody.missing is false for all 51). I also verified the openness score is exactly round(mean of its three indicator percentiles) for all 51 states, and that the portal split is 28 "Yes · <domain>" (percentile 100) vs 23 "Published address answers nothing" (percentile 0). The cross-tab, the two lowest-rated jurisdictions, the silent-set floor of 76, and the WA/VA/UT figures all check out. FRAMING: refuted on three counts. (1) THE "EMPTY QUADRANT" IS AN ARTIFACT OF THE THRESHOLD. The claim defines "fiscally weak" as below Aa3 — a band containing exactly 2 of 51 jurisdictions, because this file's credit pillar is a six-level transform of the Moody's grade (100×17, 92×18, 84×10, 76×4, 68×1, 52×1); 45 of 51 sit at Aa2 or better. With only two states below the line, a random 23-state subset misses both 29.65% of the time by chance alone (C(49,23)/C(51,23)). Under the split the sentence actually implies — median vs median — the "fiscally weaker AND less open" cell is the LARGEST of the four: 20 of 51 jurisdictions sit at or below both the openness median (51) and the credit median (92): AK, AL, AR, ID, KS, LA, ME, MS, MT, ND, NE, NH, NM, NV, OH, OK, RI, WI, WV, WY. On a bottom-quintile split (credit ≤ 84, n=16; openness = 0, n=13) the corner still holds five: Alaska, Louisiana, Maine, New Mexico, Rhode Island. (2) THE HEADLINE FACT IS NEARLY VACUOUS, AND ALASKA IS THE COUNTEREXAMPLE. "All 23 portal-silent states are Aa3 or better" reassures only because Aa3 IS the floor of the remaining distribution — apart from Illinois and New Jersey, 76 is the lowest credit score in the entire file, held by just four states. The state supplying that minimum is Alaska: Aa3 · Stable, credit 76, and openness 0 — the floor of the openness distribution (portal answers nothing, 0 policy datasets, feeds percentile 0). Alaska is precisely the "fiscally weakest-tier and data-closed" case the claim says does not exist; the claim reports it as its own reassuring minimum. (3) "ORTHOGONAL" OVER-READS A NULL RESULT. Spearman +0.1628 carries a 95% Fisher CI of [−0.118, +0.420] at n=51 — the data are equally compatible with no association and with a moderate positive one. With credit taking six heavily tied values, the test has little power. "No association detectable at n=51" is supportable; "orthogonal" is not. Minor mechanical caveat: because openness = mean of three percentiles and the portal indicator is a 0/100 binary, one third of the index (33.3 points) is awarded for merely having a live portal. Illinois's "57, above the median of 51" is mostly that: its components are portal 100, policyData 70 (3 datasets), feeds 0 (1 feed).

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  Health and the economy · cut before publicationThe index's entire "Population health" pillar is one CDC number — adult obesity — and because CDC published none for Tennessee, Tennessee's rank of 15 is compatible with anything from 6th to 31st.The missing-data handling is honest — nothing is silently dropped, no null is zeroed, no wageAtCap is cited — and every stated figure reproduces exactly under the stated method. The defect is the top endpoint. The file's percentile is rank-based *within the po…

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  The missing-data handling is honest — nothing is silently dropped, no null is zeroed, no wageAtCap is cited — and every stated figure reproduces exactly under the stated method. The defect is the top endpoint. The file's percentile is rank-based *within the pool of states that have a value*: I recovered it exactly as percentile = floor(#states-with-higher-obesity/(n-1)*100) with n=50, which reproduces all 50 published obesity percentiles with zero misses. So "substitute a health score and hold all other states' published scores fixed" is not a simplification, it is incompatible with how the index builds the number: any obesity figure CDC might have published for Tennessee joins the pool (n=51) and shifts every other state's health percentile. The claim's health=100 endpoint is literally unrealizable that way — Colorado already holds 100, and with Tennessee at the sole national minimum Colorado falls to 98 (its composite drops 74 to 73). Recomputing consistently, Tennessee's best attainable rank is 5th, not 6th (at 24.9% it scores 64 and ties DC/TX/WY at rank 5), and 19-22 other jurisdictions also change rank in those scenarios. Worse for the framing: sweeping obesity across 20.0-45.0% in 0.1 steps, Tennessee's attainable ranks are {5,8,12,13,14,16,17,23,24,26,27,29,31} — the published rank of 15 is not among them. The substance (one CDC indicator carries a whole pillar; its absence for Tennessee makes rank 15 an artifact of a 7-pillar mean) is correct and if anything understated, but "6th to 31st" is off by one place and the interval as written implies 15 sits inside a range of possible truths when it is not attainable at all.

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  Health and the economy · cut before publicationAdult obesity's strongest correlate among 65 state-level quantities in the file is not income but the FHFA house price index (r = -0.8191 vs -0.7442), and because that index is half the "building" pillar with its percentile inverted, the health and building pillars are near mirror images (r = -0.7173).ARITHMETIC: all seven cited figures reproduce digit-for-digit from the raw file, and parsing/units/denominators are right. Loading /private/tmp/claude-501/-Users-j-d-/e33eb063-27c1-4d87-9830-abd149400f48/scratchpad/states.json (51 keys; TN is the only null obe…

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  ARITHMETIC: all seven cited figures reproduce digit-for-digit from the raw file, and parsing/units/denominators are right. Loading /private/tmp/claude-501/-Users-j-d-/e33eb063-27c1-4d87-9830-abd149400f48/scratchpad/states.json (51 keys; TN is the only null obesityPct, so every obesity correlation is n=50): r(obesityPct, housePrice.display parsed to float) = -0.8191, Spearman -0.8295; r(obesity, income with "$" and commas stripped) = -0.7442; r(obesity, workforce.medianWage) = -0.7156; r(housePrice.display, housePrice.percentile) = -0.9731 (n=51); building.score == floor((permits.percentile + housePrice.percentile)/2 + 0.5) for 51/51 with no exceptions; HPI range 365.4 (WV) to 1326.9 (MA); r(health, building) = -0.7173 and r(health, prosperity) = +0.7304, and those are indeed the two largest |r| in the 28-pair pillar matrix (third is prosperity-building at -0.6179). I also rebuilt the 65-series screen exactly as described (13 non-obesity index indicators, using percentile for the two non-numeric displays moody and portal, + population + totalEmployment + medianWage + 3 migration per-1k rates + TRI raw and per-capita + per1000 and lq for 22 SOC major groups = 65) and got the same top three in the same order. No wageAtCap:true rows exist anywhere in this file, so rule 3 is not engaged. WHY IT IS STILL REFUTED: the headline superlative is false as scoped, and the detail's stronger wording — "every comparable state-level quantity in the file" — is plainly untrue. The screen took two of the three numeric fields on each SOC major group (per1000, lq) and dropped the third (medianWage), plus all 12 specialities series, the 22 major-group employment counts, and the fiscal per-capita series. Adding the 22 major-group median wages (all n=50, no nulls, none wage-capped) puts Sales and Related Occupations (SOC 41-0000) median wage at r = -0.8471 (Spearman -0.8336) — stronger than the FHFA index on both measures, and stronger in all seven leave-one-out checks I ran (drop DC -0.8310 vs -0.8113; MA -0.8367 vs -0.8092; WV -0.8338 vs -0.8080; HI, CA, NY, MS likewise). So obesity's strongest non-circular correlate in this file is a wage series, not the house price index. That also collapses the rhetorical hinge "not income but house prices": four further occupational wage series beat the per-capita income figure the claim uses as the income benchmark — food prep -0.7728, building/grounds cleaning -0.7653, personal care -0.7606, office admin -0.7572 — so "housing beats income" is an artifact of which single income measure was entered into the race. (I excluded pillars.health, which correlates -0.9808 with obesity, as circular: I verified health.score == the obesity percentile for all 51 states.) TWO SMALLER PROBLEMS. (1) Because health.score IS the obesity percentile, r(health, building) = -0.7173 is not an independent second finding but the same obesity-housePrice relationship in percentile space, diluted by the permits half (r(obesity, permits.percentile) is only +0.2012). The claim frames this as construction redundancy, which is a fair reading, but "near mirror images" overstates r = -0.7173 (r-squared 0.51, about half the variance). (2) Units: the FHFA figure is an index on a base period (WV 365.4 vs MA 1326.9 is cumulative appreciation since the base, and the file records neither base period nor vintage), not a price level; describing low-index states as "cheaper" and glossing the series as "housing costs" reads a dollar meaning into an index the file does not supply. Minor: the Pearson ordering of #2/#3 flips under Spearman (income -0.7330, medianWage -0.7526), so the "ahead of income, then median wage" ranking is Pearson-specific.

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  Health and the economy · cut before publicationEPA TRI facility counts add almost nothing to this file: 96.23% of the variance in triFacilities is explained by manufacturing employment alone (R-squared 0.9623, n=49), and adding population raises that by 0.0004.The arithmetic is clean — I reproduced all eight cited figures exactly, twice (hand-rolled OLS and numpy lstsq), with correct parsing of the formatted display strings and correct handling of the two missing mfgShare states. Nothing is off by a digit, the per-1…

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  The arithmetic is clean — I reproduced all eight cited figures exactly, twice (hand-rolled OLS and numpy lstsq), with correct parsing of the formatted display strings and correct handling of the two missing mfgShare states. Nothing is off by a digit, the per-100k denominators are right, and the R-squared is stable to the display rounding (mfgShare is published to one decimal, e.g. "4.9%"; jittering each share by +/-0.05pp over 400 draws keeps R-squared inside 0.9608-0.9637). Two things fail anyway. (1) A stated fact is wrong. "TRI facility density is also the file's tightest match to production-occupation intensity" is false. Correlating every file variable against SOC 51-0000 per 1,000 jobs, mfgShare reaches r = +0.9605 (n=49) versus TRI-per-100k's +0.8171 (n=51). TRI density is second, not tightest. (The reversed reading — that production intensity is TRI density's own strongest partner — does hold, 0.8171 leads its column — but that is not what the sentence says, and this feeds published pages.) (2) The headline is a size artifact dressed as a tight fit, and it contradicts its own detail. Regressing one raw count on another across units spanning DC (22 facilities) and California (5,110) will produce a high R-squared because large states have more of everything. Take the scale out and it collapses: TRI per 100,000 residents on manufacturing jobs per 100,000 gives R-squared 0.6153 (r = 0.7844), and log-log gives 0.9537 against 0.8501 for population alone — a much narrower gap than 0.9623 vs 0.7659. The count model also misses individual states badly: median absolute residual is 16.2% of the actual count, and Utah is fitted at 839 against 541 actual (-55%), Washington -39%, New Jersey +28%, Massachusetts +27%. Meanwhile the claim's own second half shows TRI per 100k moving with obesity (0.5849) and output per worker (-0.4619); adding TRI-per-100k to an obesity-on-mfgShare model lifts R-squared from 0.2725 to 0.3133 (n=48). A variable that reorders states by 50% against the manufacturing benchmark and carries incremental signal after mfgShare is not one that "adds almost nothing." Two supporting notes that favour the claim and should be kept: adding population does not merely add little, it hurts — adjusted R-squared falls from 0.961533 to 0.961139 and the population coefficient is negative (-7.30e-06). And the derived-variable caveat is correctly stated: mfgShare (BLS jobs share) times totalEmployment (BLS OEWS 2025) is an estimate, not a published figure, and AL and DC (display "—", missing=true) must stay out.

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  Health and the economy · cut before publicationNull result: the apparent link between TRI facility density and adult obesity is not identified in this file — the partial correlation swings from +0.1520 (p = 0.313) to +0.5180 (p = 0.0002) depending only on which covariate you include.The arithmetic is flawless — all seven cited figures reproduce digit for digit — but the headline is a selective read of the specification space. I rebuilt the sample from the file: n=48, excluded exactly AL and DC (mfgShare missing:true) and TN (obesityPct nu…

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  The arithmetic is flawless — all seven cited figures reproduce digit for digit — but the headline is a selective read of the specification space. I rebuilt the sample from the file: n=48, excluded exactly AL and DC (mfgShare missing:true) and TN (obesityPct null, health display "—", missing:true); no state has a null triFacilities or population. Display-string parsing checks out ($/,/% stripped): WV 482/1,769,979*100,000 = 27.23 per 100k, RI 413/1,112,308*100,000 = 37.13, and the top-level obesityPct agrees with the health-pillar display for all 50 jurisdictions that publish it. My p-value machinery was validated independently (t=1.959964 at df=1,000,000 gives p=0.050000; t=1.0 at df=10 gives p=0.340893) and each single-control partial was cross-checked against the recursive formula r_xy.z=(r_xy-r_xz*r_yz)/sqrt((1-r_xz^2)(1-r_yz^2)), matching the residual method to six decimals. The problem is what was left out. Running ALL 16 subsets of the four published covariates (mfgShare, income, housePrice, gdpPerWorker), the partial is POSITIVE in 16 of 16 and significant at .05 in 11 of 16. The true range is +0.1520 to +0.6273, not the stated "+0.1520 to +0.5180" — income+gdpPerWorker gives +0.6273 (p=0.0000038) and income+housePrice+gdpPerWorker gives +0.6067 (p=0.00001), both above the quoted ceiling. Controlling for everything published at once gives +0.4141 (df=42, p=0.0052) — significant. Every one of the five non-significant specifications contains mfgShare; the headline elevates the lowest of the sixteen to the status of the answer and labels the whole thing a "null result." The leave-one-out characterization also overstates fragility in the wrong direction. On the mfgShare specification, 46 of 48 deletions leave p>0.05 (only dropping RI, p=0.0193, or MA, p=0.0466, crosses .05), so that spec's non-significance is stable, not fragile; and the "2.5-fold swing" endpoints come from deleting two different states (WV at the bottom, RI at the top), not "one small state." Separately, the raw correlation is itself robust: leave-one-out range +0.4989 (drop HI) to +0.5979 (drop RI), significant in 48 of 48, Spearman +0.5648. What survives is the weaker, correct point the detail already makes: TRI density and manufacturing share move together (r=0.7853) and manufacturing share moves with obesity (r=0.5220), so the magnitude of the TRI-obesity partial depends heavily on whether manufacturing share is in the model. That is specification-dependence of magnitude, not non-identification of sign, and it does not license the "null result" headline. n=51 (48 usable), one cross-section, no within-state variation — no causal or population-level inference is supportable in either direction, including the negative one being asserted here.

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  International migration · cut before publicationAcross the 12 states most concentrated in Production occupations (LQ >= 1.40), international migration per 1,000 varies 2.68-fold — 6.04 in Arkansas to 16.18 in Michigan — while their Production median wages sit inside a single $7,600 band ($41,000 to $48,600).The arithmetic is clean — I reproduced every cited figure digit for digit from the raw file, and found no parsing, unit or denominator error (medianWage in workforce.major is already an integer, not a display string; wageAtCap is false for all 12, so no $239,2…

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  The arithmetic is clean — I reproduced every cited figure digit for digit from the raw file, and found no parsing, unit or denominator error (medianWage in workforce.major is already an integer, not a display string; wageAtCap is false for all 12, so no $239,200 floor contamination; per1k is verifiably totals/population*1000, e.g. MI 164056/10,140,459*1000 = 16.178360, matching the file to six decimals). The cohort, the 2.68 ratio, the wage band, the domestic extremes and the 4-of-12 sustainedByInternational count all check out. I am refuting on framing, not on numbers, on three counts. (1) The headline's central contrast puts a ratio against an absolute band, which is not a like-for-like dispersion comparison. On the same footing the cohort's wages span 1.185-fold; measured against the national distribution the wages are the LESS compressed of the two dimensions, not the more: cohort/national coefficient of variation is 0.72 for Production median wage (0.0551 vs 0.0769) but only 0.52 for international per 1,000 (0.290 vs 0.562), and the cohort covers 42% of the national log-range on wages against 32% on international migration. "Varies 2.68-fold" also reads as wide when the national range is 21.72-fold (MT 2.27 to DC 49.25) — the cohort is a tight low-to-middle slice, and MI, the cohort maximum, ranks only 30th of 51 nationally. (2) The DETAIL's claim that AL, AR, TN and SC "combine some of the lowest international rates in the country" is wrong for half of the named states: ranking all 51 jurisdictions from lowest, AR is 4th and AL 7th, but TN is 13th and SC 16th — lower third, not "some of the lowest in the country". (3) Neither the headline nor the figures label the time window or denominator: these per-1,000 values are cumulative 2021-2024 flows divided by 2024 population, and an unlabelled "16.18 per 1,000" invites reading as an annual rate roughly four times too large. The genuine, reproducible finding is the channel split, not the size of the migration spread.

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  International migration · cut before publicationConcentration in Building and Grounds Cleaning and Maintenance Occupations has essentially no relationship with international migration across the 51 jurisdictions (Spearman -0.040, Pearson +0.015), with a median LQ of 1.06 in both the ten highest- and the ten lowest-international states.Every correlation in the claim reproduces exactly from the file, but one twice-stated headline figure does not. The Building and Grounds median LQ across the ten highest-international states is 1.065, not 1.06. With n=10 the median is the mean of the 5th and 6…

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  Every correlation in the claim reproduces exactly from the file, but one twice-stated headline figure does not. The Building and Grounds median LQ across the ten highest-international states is 1.065, not 1.06. With n=10 the median is the mean of the 5th and 6th sorted values, (1.03 + 1.10) / 2 = 1.065, which rounds half-up to 1.07; Python's round(1.065, 2) returns 1.06 only because 1.065 is stored just below the tie, so the asserted equality "1.06 in both" is a float-rounding artifact rather than a computed match. The bottom-ten median is genuinely 1.06. Two framing issues also survive the recomputation. First, the median is the most favourable statistic for the no-relationship reading: the group means are 1.042 (ten highest) versus 1.113 (ten lowest), a gap the medians conceal, driven by MT 1.38, WY 1.32, SD 1.27 and VT 1.23. Second, the robustness test is described as dropping "the three largest outliers", but DC, NY and CA are the three largest by population, not on the variable correlated: CA ranks 11th of 51 on international per 1,000 (23.66) and is no outlier on that axis, while FL, the second most extreme x value at 45.19, is retained. The stated n=48 numbers are nonetheless exactly right. Separately, "essentially no relationship" slightly overstates precision: Spearman -0.040 with n=51 carries a Fisher 95% CI of about -0.31 to +0.24 (Kendall tau-b -0.038), so the data show no detectable monotonic relationship rather than establishing a near-zero one. The claim's caveat that LQ describes occupational structure and not migrants' own jobs is correct, and the file indeed holds no migrant-to-occupation link. Substance holds; the 1.06 figure does not.

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  Outliers · cut before publicationThe two migration channels run in opposite directions against pay: across all 51 jurisdictions, net domestic migration per 1,000 correlates -0.50 with the state median wage while net international migration per 1,000 correlates +0.55 with the same variable.The arithmetic is clean — I reproduced every cited figure to the digit, and the headline correlations are robust. I refute on framing, not on math, on two counts. (1) THE WORD "LARGEST" IS WRONG, AND IT HIDES TEXAS. The groups are ranked by migration.per1k.do…

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  The arithmetic is clean — I reproduced every cited figure to the digit, and the headline correlations are robust. I refute on framing, not on math, on two counts. (1) THE WORD "LARGEST" IS WRONG, AND IT HIDES TEXAS. The groups are ranked by migration.per1k.domestic — a per-1,000 RATE — but the prose calls them "the 10 largest domestic-inflow states" and "the 10 largest domestic-outflow states". By actual size of the flow, only 6 of the 10 inflow states and 8 of the 10 outflow states are the same set. Texas, the second-largest domestic gainer in the country at 693,979 net domestic in-movers (2021-2024), does not appear in the "10 largest domestic-inflow states"; South Dakota (21,045) and Delaware (44,125) do. A reader of a published page will read "largest" as volume. The stated computation does disclose the rate basis, so this is a prose defect, not a fabrication — and on a count basis the direction actually survives (mean median wage $47,581 inflow vs $55,957 outflow) — but the sentence as written misdescribes what was ranked. (2) THE OUTPUT-PER-WORKER PAIR IS A DC ARTIFACT AND ROUGHLY DOUBLES THE REAL GAP. "$163,066 vs $224,308" is arithmetically correct but is not a fair summary of the outflow group. DC's output per worker is $479,240 — nearly double the next-highest jurisdiction (NY, $245,798) — and DC sits in the outflow group. Eight of the ten outflow states fall BELOW their own group mean of $224,308. Drop DC and the outflow mean falls to $195,983, cutting the stated $61,242 gap to $32,917; the median-to-median gap is $31,500. The published figure overstates the typical difference by roughly a factor of two. The median wage comparison does not have this problem ($47,970 vs $59,040, a gap of $11,070 against the stated mean gap of $11,873), so medians should be used for both. WHAT SURVIVES, AND SURVIVES WELL: the correlation headline itself. rho(domestic per 1k, median wage) = -0.5004 and rho(international per 1k, median wage) = +0.5479 both reproduce, and they are not fragile. Dropping DC gives -0.4793 / +0.5203; dropping DC, AK and HI gives -0.4374 / +0.5265. I also tested the confound the claim does NOT list — state size — and it does not explain the result: rank-partial correlations controlling for population are -0.5016 and +0.5929, essentially unchanged. t(49) = -4.05 and +4.59. The 7-of-10 and 9-of-10 rank counts, the wage-rank vectors, the two mean median wages to the exact dollar, and Delaware at $52,190 ranking 19th of 51 all reproduce exactly. The causation and no-controls disclaimers are correctly stated, and no location quotient is misused. Two minor notes that do not drive the verdict: the stated reference figure rho(gdpPerWorker, medianWage) = +0.6827 does not reproduce — I get +0.6853 with average ranks for ties and +0.6878 with ordinal ranks — which suggests their rank routine differs slightly from a standard Spearman, though it did not affect any cited value (all matched within 0.0003). And the per-1,000 fields themselves put a cumulative 2021-2024 flow over a single 2024 population estimate; I confirmed 0/51 mismatches against totals/population*1000, so the claim parsed the file correctly, but the rate is not an annual rate and should not be described as one.

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  Outliers · cut before publicationThe composite index is the plain unweighted mean of its eight pillar scores (matches for all 51 jurisdictions), so the one pillar built from a self-run web probe rather than a federal statistic — openness — moves states by up to 15 places: Alaska 32nd to 17th, Montana 25th to 11th, while Hawaii falls 19th to 33rd and New Jersey 19th to 32nd.Two of the four steps reproduce; two do not, and one of the failures is fatal. REPRODUCES. (1) index.score is exactly floor(mean+0.5) of the non-null pillar scores for 51/51 jurisdictions — zero mismatches, not merely "within 0.5". Nulls are exactly DC scale,…

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  Two of the four steps reproduce; two do not, and one of the failures is fatal. REPRODUCES. (1) index.score is exactly floor(mean+0.5) of the non-null pillar scores for 51/51 jurisdictions — zero mismatches, not merely "within 0.5". Nulls are exactly DC scale, AL scale, TN health. (3) Exactly 13 states score 0 on openness — AK AR GA ID LA ME MN MT NH NM NV OH RI — each with portal display "Published address answers nothing", policyData "0", feeds "1", and all three flagged missing:false. The openness score is itself floor(mean of its three percentiles + 0.5), verified 51/51. FAILS 1 — the rank moves are an artifact of mixing two rank conventions. The file's index.rank is a COMPETITION rank with heavy ties (15 tied groups; rank 19 is shared by HI, MA, NE, NJ, NY; rank 32 by AK and GA; rank 39 by four states). The claim re-ranks the seven-pillar mean as a unique 1..51 sequence with ties broken by file order, then subtracts the tied file rank. Part of every "move" is therefore the convention change, not the pillar. Ranking both sides the same way (competition rank on the unrounded mean): AK 32->16 (+16, not +15), GA 33->18 (+15, not +12), MN 26->12 (+14, not +13), MT 25->11 (+14, correct), OH 35->22 (+13, not +12); HI 23->33 (-10, not -14), NJ 19->32 (-13, correct), VT 13->25 (-12, correct), MI 31->40 (-9, not -11), IL 30->39 (-9, not -10), VA 9->18 (-9, not -10). Both headline pairs are wrong: Alaska is +16 and Hawaii is -10. FAILS 2 — rho = -0.488 is not reproducible and is an ordering artifact. Proper tie-corrected Spearman (Pearson on average ranks) of feeds vs workforce.medianWage over 51 = -0.2794; Pearson on raw values = -0.2664. The feeds display takes only four distinct values (27 states at 1, 13 at 2, 10 at 3, 1 at 4), so tie handling dominates. Assigning ORDINAL ranks 1..51 that break those ties in the file's own order reproduces -0.4884 exactly — but the file is sorted by index.rank, which correlates with wage, so the tie-break smuggles in the correlation. The same ordinal method gives -0.0189 on reversed file order and -0.2477 alphabetically; across 20,000 random tie orderings it ranges -0.482 to -0.046 (median -0.254), i.e. -0.488 is more extreme than any of 20,000 shuffles. The correct value is invariant at -0.279 (t=-2.04, n=51, borderline). FRAMING ALSO FAILS. (a) Openness has no special leverage. Leave-one-pillar-out with a consistent rank convention: dropping prosperity moves a state up to +19/-17 places (mean |move| 6.37), health +17/-16 (6.24), openness +16/-13 (6.37). Openness is joint-typical, not exceptional — "moves states by up to 15 places" is simply what a 1/8 weight buys in an unweighted mean, and two federal-source pillars move states further. (b) Openness is not "the one pillar" that is not a federal statistic: the credit pillar's sole indicator is "Moody's, indicative 2025", a private vendor estimate. (c) The openness pillar score correlates POSITIVELY with median wage (tie-corrected rho +0.408), which undercuts "behaves oddly against pay"; and policyData correlates +0.648. (d) For AL, DC and TN openness is a seventh of the score, not an eighth, since a pillar is null. What survives: the index really is a plain unweighted mean; 13 states really do score 0 with an unreachable portal that is not flagged as missing, so probe failure is scored identically to genuine non-publication; and removing openness really does reshuffle the table substantially. The specific figures do not survive.

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  Outliers · cut before publicationOutput per worker and the median wage come apart at both ends: Delaware ranks 3rd of 51 on output per worker ($231,354, ahead of Washington, California and Massachusetts) but only 19th on median wage ($52,190) and 29th on per-capita income ($71,357), while Vermont is 45th on output per worker ($143,008) and 14th on median wage ($56,390).Every figure in the headline reproduces exactly, digit for digit — but one cited statistic does not, and two framing points overstate what the file supports. WHAT I REPRODUCED (all exact). Parsing pillars.scale.indicators.gdpPerWorker.display with re.sub(r'[^…

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  Every figure in the headline reproduces exactly, digit for digit — but one cited statistic does not, and two framing points overstate what the file supports. WHAT I REPRODUCED (all exact). Parsing pillars.scale.indicators.gdpPerWorker.display with re.sub(r'[^0-9.\-]','',s) — all 51 displays are plain "$NNN,NNN", so no parsing trap — and reading workforce.medianWage as a raw number, income from pillars.prosperity.indicators.income.display. Ranks computed as (count strictly greater) + 1. No nulls and no missing:true flags on any field used; state-level medianWage ranges $40,120 (MS) to $91,540 (DC), so no wageAtCap issue. DE: $231,354 / #3, behind DC $479,240 and NY $245,798, ahead of WA $221,071, CA $217,434, MA $211,868; wage $52,190 / #19; income $71,357 / #29. VT: $143,008 / #45; $56,390 / #14; $74,580 / #21. RI: $145,391 / #42; $56,780 / #13. Ratios: DC 0.19101, DE 0.22559 (2nd lowest), NY 0.24276 … OR 0.36651, RI 0.39053, VT 0.39431 (highest). DE migration.per1k.domestic 41.947 (= 44,125 / 1,051,917 × 1000), 4th behind ID 55.684, SC 54.749, MT 44.599. DE employmentGrowth '-0.22%', tied with NY and ND, with NJ -0.58% and VA -0.23% below them, so those three sit at descending ranks 47-49 — inside the bottom five. DE labour pillar score 12, with only OR (6) lower: 50th of 51. Median wage has exactly two tied pairs (WY/WI $50,270; NC/ID $47,970), neither adjacent to DE, VT or RI, so none of the quoted ranks is tie-sensitive. WHAT FAILS. The correlation. rho is quoted as +0.6827 / "+0.683". That value only appears if the two median-wage ties are broken arbitrarily and the d-squared shortcut applied. The standard Spearman — Pearson on midranks, i.e. what scipy.stats.spearmanr returns — is +0.68528 over the same 51 rows, which publishes as +0.685. A sceptic re-running the stated computation with a standard library will not get 0.683. The direction and strength are unaffected, but the cited digit is not reproducible. TWO FRAMING OVERSTATEMENTS. (1) "Come apart at both ends" is carried by the ratio, and the ratio's denominator is output per worker, so DE's 2nd-lowest ratio substantially re-states its 3rd-highest output. On the rank-divergence measure DE is not an outlier at all: |gdpw rank - wage rank| is 16 for DE, only 9th largest of 51 and tied with NV, behind TN (-19), TX (-18), SD (-18) and LA (-18), all diverging the same way. VT (+31) and RI (+29) genuinely are the two extremes at the other end. (2) The Delaware "compounds the oddity" sentence sets a cumulative 2021-2024 migration figure against a single latest-month employment change of -0.22%. Those have different time bases, one month of -0.22% is not distinguishable from noise in this file, and nothing here establishes tension between them — "yet" asserts a relationship the data does not carry.

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  Concentration · cut before publicationWashington DC's occupational mix is 9.87x more distinctive than Missouri's — 31.9% of DC's workers would have to change major occupational group to match the national mix versus 3.2% of Missouri's — and the second-most distinctive jurisdiction, Nevada, reaches only 39.2% of DC's level.The core arithmetic is CONFIRMED — I reproduced every headline figure to the digit, independently. But the claim contains a units error in its own supporting detail, which is exactly the failure class I was asked to check, so it cannot ship as written. WHAT I…

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  The core arithmetic is CONFIRMED — I reproduced every headline figure to the digit, independently. But the claim contains a units error in its own supporting detail, which is exactly the failure class I was asked to check, so it cannot ship as written. WHAT I REPRODUCED EXACTLY (from workforce.major, 22 mutually exclusive SOC major groups; I verified the code list contains no "all occupations" total and no overlapping category, so shares are clean): - Pooled national employment = 155,495,600 — matches the stated denominator exactly. - KSI = 0.5*sum|s_i - n_i| gives DC 0.319195, NV 0.125165, HI 0.109371, WY 0.109314, MS 0.102320, AK 0.101346, NM 0.093907, NY 0.093498 ... NE 0.044126 (48th), OR 0.041896 (49th), MN 0.041466 (50th), MO 0.032339 (51st). The stated ordering matches mine position for position. - DC/MO = 9.8702 -> 9.87x. NV/DC = 0.392127 -> 39.2%. Both exact. - Gap DC->NV = 0.194030 vs gap NV->MO = 0.092826, so the "gap to second is bigger than second-to-last" point holds (2.09x bigger). - lq validation reproduces precisely: 1,122 cells, max abs error 0.006827 (worst cell VT 450000, mine 0.62317 vs file 0.63), mean 0.002488 -> the claimed 0.0068 / 0.0025. - No nulls anywhere in major.employment, lq or per1000, so no gap-filling was needed or done. No formatted display strings are involved in this computation at all (workforce.major fields are raw numbers), so the parse risk does not arise. - I re-ran against an alternative national benchmark derived from the file's own lq (implied national per-1000 = per1000/lq, median across states) as a robustness check: DC 0.3192, NV 0.1253, MO 0.0324, DC/MO 9.86, NV/DC 39.25%. The headline is benchmark-insensitive. WHY I STILL REFUTE — a units defect and two framing defects: 1. UNITS (the disqualifying one). The DETAIL argues the ranking "does not sort by size" using "Nebraska (2,005,465 people)" in the same sentence as "New York — the fourth-largest labour market at 9,687,980 jobs". 2,005,465 is Nebraska's POPULATION; the ranking is over a JOBS distribution. Nebraska's labour market is 1,024,370 jobs, which is 36th of 51 — not remotely the size the sentence implies when set beside New York's 9.69M jobs. The FIGURES list repeats this as "KSI rank despite 2,005,465 population". Both numbers are correctly read from the file, but they are different units doing work inside one size comparison. 2. FRAGILE ORDINAL. Nebraska's 48th place is separated from North Carolina's 47th by 0.000046 (NC 0.044172 vs NE 0.044126). Under the alternative national benchmark above the two swap and NC lands 48th. The specific ordinal is not robust enough to headline; the size point survives without it. 3. LOADED WORDING. "31.9% of DC's jobs sit in the wrong major group" imports a normative judgment into a pure distinctiveness measure — the national mix is not the correct one. The claim's own headline phrasing ("would have to change major occupational group to match the national mix") is the right reading and should be used throughout. Minor, non-blocking: NY's job count is cited as 9,687,980, which is my sum of the 22 majors; the file's own workforce.totalEmployment for NY is 9,688,000 (a 20-job rounding difference). NY is 4th largest under either. Contextual caveat for whoever publishes this: DC is a single city benchmarked against states, and its metro labour market extends into MD and VA, so its detachment is partly a boundary artifact rather than a purely economic fact. REPRODUCTION RECIPE for a sceptic: for each of the 51 keys in states.states, s_i = major[i].employment / sum(major[].employment) for that state; n_i = sum over all 51 states of major[i].employment / 155,495,600; KSI = 0.5 * sum over the 22 groups of |s_i - n_i|.

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  Concentration · cut before publicationThe tendency for large states to look occupationally average is mostly real, not a benchmarking artifact: removing each state from its own national benchmark raises California's distinctiveness 13.3% and moves it 6 places, yet the size gradient only softens from Spearman -0.354 to -0.300.The core self-inclusion result reproduces exactly — CA 11.71% of 155,495,600 jobs, KSI 0.0607 -> 0.0688 (+13.27%), rank 33 -> 27, TX 43->40, FL 20->17, NY 8->7, WY factor 1.0018, CA factor 1.1327, and Spearman -0.3541 -> -0.3005 (Pearson -0.3492 -> -0.2892) ov…

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  The core self-inclusion result reproduces exactly — CA 11.71% of 155,495,600 jobs, KSI 0.0607 -> 0.0688 (+13.27%), rank 33 -> 27, TX 43->40, FL 20->17, NY 8->7, WY factor 1.0018, CA factor 1.1327, and Spearman -0.3541 -> -0.3005 (Pearson -0.3492 -> -0.2892) over the 50 states excluding DC. But the tercile block is wrong twice over. (1) Under the claim's own stated method (51 jurisdictions, population ascending, 17 states each) the medians are 0.0831 / 0.0678 / 0.0607, not 0.0776 / 0.0697 / 0.0607; the smallest-tercile median is off by 6.6%. I searched every contiguous split and no equal-thirds partition yields the stated trio — 0.0776/0.0687/0.0607 requires dropping DC (17/16/17), 0.0776/0.0697/0.0591 requires 17/17/16, and the published trio only appears under unequal groups such as [15,19,17]. (2) The claim that "the widest spread is in the middle tercile" is false under its own stated method: with 51 jurisdictions and 17 each, DC (KSI 0.3192, third-smallest population) falls in the smallest tercile, whose spread is 0.0441 (Nebraska) to 0.3192 (DC) = 0.2751, nearly three times the middle tercile's 0.0928 (0.0323 Missouri to 0.1252 Nevada). That sentence only holds if DC is silently excluded, which the stated computation does not do. Separately, CA's rank-33 anchor is fragile: it beats Oklahoma by 0.00002 (0.060707 vs 0.060686). No formatted display strings enter this computation, so parsing is not the failure point; the failure is an inconsistent, undisclosed sample for the tercile figures.

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  Concentration · cut before publicationOccupational distinctiveness has no measurable relationship to any migration channel: across the 50 states excluding DC the correlation with 2021-2024 domestic migration is -0.094 (95% CI -0.363 to +0.190), with international +0.017 and with natural change +0.062.The arithmetic is sound and I reproduced every figure to the digit, but the headline misstates one of its own figures and the universal framing is exclusion-dependent. WHAT REPRODUCES. I reverse-engineered the unstated KSI: a half-Krugman specialization index…

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  The arithmetic is sound and I reproduced every figure to the digit, but the headline misstates one of its own figures and the universal framing is exclusion-dependent. WHAT REPRODUCES. I reverse-engineered the unstated KSI: a half-Krugman specialization index over workforce.major, KSI = 0.5 * sum_i |s_i - n_i|, where s_i is the state's share of its own major-group employment and n_i is the national share built by summing that group's employment across all 51 jurisdictions. That exact construction — and only that one — returns their range (0.03234 MO to 0.31920 DC), their ranks (NV 2nd, NY 8th, IL 41st, MO 51st), their four Pearsons and their flag medians. Every migration figure checks out: NV +21.7180, NY -44.9754, MO +6.9319, IL -31.1342 (all read from migration.per1k.domestic, no display-string parsing involved — the per1k fields are already numeric, so there is no unit or denominator error to find). No nulls anywhere in migration.per1k or in major-group lq/employment, so nothing was silently imputed. Fisher se = 1/sqrt(47) is correct for n=50. Flag split: 17 true / 33 false, medians 0.06094 vs 0.07290, difference 0.01196. ERROR 1 — SIGN FLIP IN THE HEADLINE. The headline says "with international +0.017". The value is NEGATIVE: -0.0171. The claim's own DETAIL section and its own FIGURES CITED list both print -0.017. The headline contradicts its own supporting evidence. Substantively trivial at |r| = 0.017, but it is a printed figure that is wrong as written, and this feeds published pages. ERROR 2 — THE UNIVERSAL NULL DEPENDS ENTIRELY ON DROPPING DC. The headline asserts "no measurable relationship to ANY migration channel". Rerunning on all 51 jurisdictions, the international channel gives Pearson +0.4081, 95% CI [+0.149, +0.615] — a moderate association whose interval excludes zero, produced by the single jurisdiction that is also the maximum of the distinctiveness scale (DC, KSI 0.3192, next highest NV 0.1252). The exclusion is disclosed in the headline, so this is not concealment, but an absolute phrase like "no measurable relationship to any migration channel" cannot be published next to a result that flips to +0.41 on the file's full 51-row universe. It is a 50-state finding contingent on one omission, not a property of the data. FRAGILITY WORTH NOTING (not counted as an error). The "Illinois (41st)" label rests on IL 0.05052 vs ME 0.05078 — a gap of 0.00026. Computing distinctiveness from the file's own published lq values instead of rebuilding a national baseline (an equally defensible reading of "from workforce.major") gives r_domestic = -0.0912 and swaps them: IL 40th, ME 41st. The correlations are robust to this choice; that one ordinal label is not. Also, "CIs admit up to about |r| = 0.36" slightly understates: the net-migration interval reaches -0.3729. The underlying 50-state null is real and I confirm it. The headline as written is not.