{"id":"projection-law-round2-preregistration","title":"Round 2 Preregistration — MatPES MLIP Elastic Constants","subtitle":"Pre-registered protocol: 16 cubic elements, four MatPES potentials, two functionals, and the operator-correction kill conditions.","category":"validation","tags":["mlip","matpes","elasticity","preregistration","projection-law"],"source":"articles/docs/projection-law-round2-preregistration.md","lang":"en","words":1271,"readMinutes":6,"toc":[{"depth":2,"text":"Revision history","id":"revision-history"},{"depth":2,"text":"Systems","id":"systems"},{"depth":2,"text":"Reference targets","id":"reference-targets"},{"depth":3,"text":"Provenance summary per element","id":"provenance-summary-per-element"},{"depth":2,"text":"Model grid","id":"model-grid"},{"depth":2,"text":"Registered hypotheses and kill conditions","id":"registered-hypotheses-and-kill-conditions"},{"depth":3,"text":"H1 — Cleaned effect size","id":"h1-cleaned-effect-size"},{"depth":3,"text":"H2 — Nested constraint hierarchy","id":"h2-nested-constraint-hierarchy"},{"depth":3,"text":"H3 — Rotation link to Layer 3","id":"h3-rotation-link-to-layer-3"},{"depth":3,"text":"H4 — Compute-budget head-to-head","id":"h4-compute-budget-head-to-head"},{"depth":2,"text":"Analysis plan","id":"analysis-plan"},{"depth":2,"text":"Software artifacts","id":"software-artifacts"},{"depth":2,"text":"Scientific-integrity policy","id":"scientific-integrity-policy"}],"html":"

Round 2 Pre-Registration Protocol — The Projection Law Correction Operator

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Version: 2.2 (revised 2026-06-25)
Objective: Definitively test the Projection Law's conservation-rotation mechanism by (1) removing reference-standard confounds through 0K DFT targets, (2) demonstrating operational superiority over ensemble-based UQ, and (3) producing a drop-in LAMMPS extension that any HPC user can adopt.

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Revision history

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DateChangeAuthor
2026-06-25v2.2 — Added Ag and Au targets from published literature (Ag PBE Pandit & Bongiorno 2023; Au PW91-GGA Wang & Li 2008 as fallback). Target set now 16 cubic elemental metals. Updated r2SCAN bulk-shift coverage and evaluated-subset note.researcher
2026-06-26v2.1 — Corrected PBE extraction method (direct from de Jong 2015, not matminer); updated r2SCAN fallback list to Al, Ca, Sr; added evaluated-subset note; recorded provenance for all 14 target elements.researcher

Systems

The target set comprises 16 cubic elemental metals for which a published 0K elastic tensor is available:

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Pb, which was part of the original IMMI set, is absent from the published cubic-elastic compilations and is not in the current target set.

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Evaluated subset (reported in parent benchmark): Ag, Au, Cu, Fe, Ni, Pt, V, W (8 elements). Hypotheses below are registered for the full 16-element set; where the initial benchmark covers a restricted subset, this is noted explicitly.

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Reference targets

Pristine 0K elastic constants (C11, C12, C44) from:

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Each target value carries a provenance record (material_id, source citation, URL, stability flag, and fallback reason where applicable).

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Provenance summary per element

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ElementBaseline sourcer2SCAN methodr2SCAN fallback reason
Al, Ca, Srde Jong 2015PBE baseline retainedNo published r2SCAN bulk modulus available
AgPandit & Bongiorno 2023 (PBE)Scalar bulk shift (Liu 2024)—
AuWang & Li 2008 (PW91-GGA)Scalar bulk shift (Liu 2024)No stable published PBE Au tensor found
Cr, Cu, Fe, Mo, Nb, Ni, Pd, Pt, Ta, V, Wde Jong 2015Scalar bulk shift (Liu 2024)—

Model grid

Layer 1 — Classical interatomic potentials (OpenKIM/NIST):

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Layer 2 — Foundation MLIPs evaluated at 0K via LAMMPS plugins (registered plan):

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Note: The interim benchmark reported here used Layer 1 classical potentials on the 8-element subset Ag, Au, Cu, Fe, Ni, Pt, V, W. Layer 2 MLIP evaluation is staged for the full 16-element set.

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Registered hypotheses and kill conditions

H1 — Cleaned effect size

When evaluated against 0K all-electron references, the functional-clustering effect size for 3d/4d metals meets or exceeds the Round 1 registered threshold (0.30).

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H2 — Nested constraint hierarchy

The binding constraint for 3d/4d metals is the XC functional; for 5d metals a deeper physical constraint (e.g., scalar relativistic / correlation effects) may supersede the XC functional.

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The empirical XC bias vector (T_r2SCAN − T_PBE) aligns directionally with pseudopotential-based DFT error vectors from Layer 3.

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H4 — Compute-budget head-to-head

For elastic-constant prediction, one MLIP run + the Lupine Correction Operator achieves lower out-of-sample MSE than the mean of a 4-model ensemble, with tighter conformal-calibrated intervals.

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Analysis plan

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  1. Geometry: compute participation ratio (PR) of each ensemble error matrix; expect PR ≈ 1.0–1.3.
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  2. Bias extraction: first principal component of the centered error matrix = 1D bias vector b.
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  3. Functional shift: Δf = T_r2SCAN − T_PBE.
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  4. Operator: corrected = raw − b + Δf.
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  5. Uncertainty: split-conformal prediction on leave-one-out residuals; report 90% coverage and interval width.
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  6. Significance: exact permutation tests for functional clustering; report p-values and effect sizes.
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Software artifacts

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Scientific-integrity policy

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