\n\nProcess note (2026-07-02): these two rounds ran with pass/kill\nthresholds on questions that were, in truth, exploratory cartography — and\nR2-H1's "KILL by 2.6%" against an arbitrary threshold shows the cost: the\nverdict frame can bury the finding (bias eliminated, variance persists).\nGoing forward, registration with thresholds is reserved for claims where we\nare the interested party (uplift claims about our own correction operator)\nand for publication-bound claims. Exploratory results are reported as\ndescriptive findings with coupling-aware nulls and uncertainty — the\nstatistics stay, the verdict theater goes. The rounds below are preserved\nas recorded, per the retraction-preserving discipline.
\n
\n\nRegistered protocol:
\ny-matrix-cross-property-preregistration-2026-07-01.md.\nData: 57 GPU cells (19 materials × MACE-MP-small / MACE-MP-medium / CHGNet),\n345 reference-bound properties, 57/57 evidence-derived Lean modules\ntype-checked (data/y_matrix_runs/bound/binding_report.json).\nAnalysis artifacts:data/y_matrix_runs/analysis/confirmatory_*.json\n(seed 20260701, 1,000 null draws, 1,000 bootstrap).\nMatrices: primary 15 metals × {a₀, B₀, E_vac, γ₁₀₀, γ₁₁₀} (Cr dropped by\nmatched-n — coarse B₀ reference; Fe included per the registered amendment);\nsecondary 7 fcc metals × 7 properties (+γ₁₁₁, γ_SFE).
| Hypothesis | \nVerdict | \nDetail | \n
|---|---|---|
| H1 cross-property low dimensionality | \nNOT CONFIRMED (2/6 pass) | \nPR mostly within the coupling-aware null band. Primary: MACE-small 2.76 (null p05 2.34), MACE-medium 2.36 (2.11) — fail; CHGNet 2.00 < 2.17 — pass. Secondary: MACE-medium 1.47 < 1.50 — pass; others fail. | \n
| H2 shared leading error mode | \nKILLED (0/3 pairs, both matrices) | \nRaw cosines up to 0.96 — but the family-permutation null's p95 reaches 0.98: the apparent shared mode is carried by within-family magnitude structure, which the null preserves. No pair exceeds its null. | \n
| H3 defect ≫ bulk errors | \nPASSED, all models, both matrices | \nMedian |rel. err.|: bulk ~0.5–0.8%, defect ~11–31%. Ratios: MACE-small 18.9×, MACE-medium 15.3×, CHGNet 57.0× (primary; secondary 21×/16×/62×). Registered threshold 2×; kill 1.5×. All bootstrap CI95 lower bounds > 1. | \n
PR < null p05, which is stricter. Under the literal\n(flawed) wording H1 would "pass" nearly everywhere; under the intended test\nit passes 2/6. We report the intended test as primary and record the wording\ndefect here rather than silently choosing the favorable reading.The turbo's gearing is per-family. The elastic-era low-dimensionality does\nnot extend across property families as a universal ribbon: once within-family\ncoupling is granted to the null, only isolated (model, matrix) combinations\nshow compression below it, and no shared cross-model mode survives H2. A\ncorrection operator learned on one family should not be assumed to transfer\nacross families via a shared low-dimensional mode. This refutes the strongest\nform of the cross-property universality thesis for this X×Y slice — and it is\na result, registered in advance, with the kill conditions doing their job.
\nWhat IS universal is the training-distribution split. H3 is the cleanest\neffect this program has measured: every model, both matrices, defect-family\nerrors 15–60× bulk-family errors, consistent with the published PES-softening\npathology of MPtrj-trained potentials. Bulk properties (a₀ at ~0.5%, ΔH_f at\n~3%) are essentially solved by current foundation models; defect physics\n(vacancies, surfaces, stacking faults) is where they fail, predictably and\nenormously. The correction program's highest-ROI target is therefore\nfamily-targeted defect corrections, not a global mode.
\nThe coupling-aware null prevented two false positives. A naive analysis\nwould have reported cosine 0.96 cross-model mode alignment and "low" PRs as\nconfirmation of universality. Both are inside their null bands. The\nmethodological discipline — registered before data, nulls that preserve\nwithin-family structure — is itself a result worth publishing alongside the\nphysics.
\nINCONCLUSIVE — neither the registered pass nor the registered kill fired,\nfor any model. The kill's precondition failed everywhere: the LOO stiffness\nscalar (s = 1.057 / 1.081 / 1.125 for MACE-small / MACE-medium / CHGNet) does\nnot improve even the EOS family it was fitted on — per-material B₀ softening\nis too heterogeneous (Fe ≈ 2×, most metals 1.03–1.15) for any single\nper-model scalar. No family significantly degrades; two isolated\nbootstrap-significant improvements (CHGNet surfaces 0.285→0.215; MACE-medium\nplanar fault 0.682→0.665) are candidate gears requiring replication before\nrouting. Substantive finding: the correction structure is finer-grained\nthan (model) or (model, family) — at least (model, family, material-class).\nArtifact: analysis/h4_transfer.json (seed 20260702, deviations: none);\nverdict theorems: lean/Round1_H4.lean (type-checked).
A 104-agent deep-research pass (25 claims verified 3-0 or merged; 22 primary\nsources; full artifact in the session transcript) situates Round 1:
\nPESCalculator.load_universal()\nas the X-axis expansion path (7+ architectures, one interface); CPS-style\nmulti-property scoring; the 47-metric Ni suite as an external cross-check\nfor our Ni cells; fixed-and-reported displacement magnitudes for any\nphonon lane (ORB/eqV2 degrade at small displacements, arXiv:2412.10516).Registered verdict: KILL — by 2.6% (ratio 7.86 vs registered threshold\n7.66). The decomposition, reported alongside because both halves are decidable\nfacts (lean/Round2_Verdicts.lean, type-checked):
Artifact: analysis/r2_mpa0_confirmatory.json (joint 4-model run, matched\n15-metal set unchanged).