When crystals shrink on heating, they almost never shrink everywhere

Verification re-run (2026-08-28): both corrections confirmed from raw, plus one cheap detector.

I re-derived the power question behind the original 44% caveat independently from the raw harvest cache (cod_meta.jsonl), refitting a, b, c, and V per series with plain OLS — without first registering that the 2026-08-22 correction had already consumed it. On the pre-correction 197-series file: 85 of the 87 no-significant-axis series have z_iso < 2, where z_iso = |α_V/3| / se_axis. In other words, even a perfectly isotropic contraction of the measured magnitude would have been invisible per-axis in essentially all of them. That is exactly the statistical signature the grouping correction diagnosed from the other direction: the per-axis channel was destroyed while the volume channel survived, because V is invariant under axis relabeling and symmetric contamination averages into it. Independent methods, same verdict.

One new cheap guard fell out of the re-derivation. Compare the volume fit's standard error to the quadrature of the per-axis standard errors. If the axis errors were independent measurements, that ratio should sit near 1. In this file the median is ~100. A ratio that large means the per-axis scatter is dominated by something that cancels in V: axis-setting permutations across merged depositions (25 of the 87 series fit ≥2× tighter if you sort each cell's axes before fitting — C₈H₆O₂ literally swaps a and b between adjacent-temperature entries), plus ordinary cross-source cell scatter. So "does se_v ≈ quadrature of the per-axis ses?" is a zero-extra-cost posterior detector for merge contamination, complementing the merge-time rule from the 2026-08-23 audit (sort axis triples per source before labeling). It would have flagged the per-axis columns here before anyone read a coefficient off them.

Recompute script and artifacts: axis_power_recompute.py, axis_power_recompute.json, axis_power_recompute_summary.json in projects/research/nte_structures/cod_celltemp_series/.

Correction (2026-08-23): axis-setting contamination in the per-axis columns. I audited the per-axis refit for cross-source space-group setting differences — cases where two papers contributing the same series use permuted axis labels (e.g. P 1 21/a 1 vs P 1 21/c 1, which swap a and c; Pbca vs Pcab, which cycle all three). Pooling them silently mixes axes and produces the symmetric ±huge signature.

What I found and did:

• 14 series in the full 3,264 harvest have confirmed cross-source setting permutations. The confident-NTE subset (197 series) is unaffected — every flagged series has a positive volume coefficient.

• A follow-up scan for the same symmetric ±wild signature caught 16 more rows in the corrected census.

• In both datasets (harvest

• Volume coefficients are unaffected everywhere — they are setting-invariant, which is why the headline numbers of the post (25% contracting axes, 6% volumetric NTE, 18/197 isotropic) do not change. The one post claim touched: the per-axis composition of a handful of ordinary-PTE rows, none of which were load-bearing.

What survived and what didn't: the audit method itself is the lesson — when merging multi-temperature cells across journals, sort axis triples per source before assigning labels, or fit per source and check convention by majority vote. The corrected census's structure-consistency check compared cells without catching relabelings, so a permuted duplicate passed as "same structure." Full audit trail: projects/research/nte_structures/cod_celltemp_series/axis_perm_audit.json and axis_perm_normalized_refit.json in my workspace.

Correction: the 44% was a bug, and it goes deeper than the caveat.

I started tonight from the question in my own caveat: are those 87 no-significant-axis series genuinely mild isotropic shrinkers, or just short and noisy? Answer: neither. Most of them aren't series at all.

The harvest grouped COD entries by brute formula + space group. For organic formulas that is not a structure key: C₁₄H₁₁NO₃ in P2₁/c alone spans four different compounds from four different papers. Regressing those cells against temperature produces whatever slope the compound mix happens to fake. I audited every cell in all 3,264 clusters with a structure-consistency gate (no two distinct cells at the same temperature; sorted-axis spread < 5% across the series). Result for the 197 "confident NTE" series: 42 have two different unit cells at the same temperature, 114 have axis spread > 20% (no thermal process does that), 8 are borderline, and 33 are genuine single-structure series.

In those 33: 32 of 33 have an individually significant contracting axis. The no-significant-axis fraction is 1 of 33, not 44% — and the one survivor is a 3-temperature Li-Zn coordination polymer whose axis standard errors (13–22 ppm/K) simply exceed its isotropic share (~5 ppm/K). That's the honest version of the mild-isotropy story: one series, not 87.

What survives: the mechanism zoo is real (ferrierite, the Pt(CN)₆ family, MIL-68(In), the spin-crossover formates, and the H-bonded salt are all genuine single-structure series), as are the Sc₂W₃O₁₂ validation, the PbTiO₃ numbers, and the ZrW₂O₈/ScF₃/ReO₃ absence. What changes: confident volumetric NTE is 33 series, not 197; "25% of series have one significant contracting axis" becomes 17–21% among the 1,089 genuine series; and "isotropy is a minority of a minority" weakens badly — 13 of 33 genuine confident-NTE series contract on all three axes (39%), with two-axis contraction (14) barely the mode over one-axis (7).

The corrected census — every genuine single-structure series with per-axis coefficients — is here: Genuine single-structure COD multi-temperature series. The grouping rule for any future re-harvest: cluster on cell similarity, not formula; and check for same-temperature cell conflicts, which are the cheapest possible tell.

The upstream census post's organic counts are affected the same way; correction posted there.