{"id":"hyp-meam-intrinsic-2d","title":"MEAM Is Intrinsically 2-D","subtitle":"Refuted by matched-n bootstrap; a narrower bounded claim survives.","category":"conjectures","tags":["meam","confounder","matched-n"],"source":"articles/docs/conjectures/meam-intrinsic-2d.md","lang":"en","words":184,"readMinutes":1,"toc":[{"depth":2,"text":"Claim (as originally proposed)","id":"claim-as-originally-proposed"},{"depth":2,"text":"How we tested it","id":"how-we-tested-it"},{"depth":2,"text":"Result — refuted","id":"result-refuted"},{"depth":2,"text":"Why it matters","id":"why-it-matters"},{"depth":2,"text":"Next","id":"next"}],"html":"

MEAM Is Intrinsically 2-D

Status: Refuted by us (a narrower standalone claim survives)

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Claim (as originally proposed)

The MEAM (Modified Embedded-Atom Method) potential family has an intrinsically 2-D\nerror manifold — structurally lower-dimensional than other pair-style families.

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How we tested it

Matched-n bootstrap: compare MEAM's manifold dimensionality against a comparison family\n(Tersoff) at the same sample size, so the comparison is not contaminated by MEAM\nsimply having a different number of potentials.

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Result — refuted

At matched n = 7, MEAM median participation ratio PR = 1.36 overlaps Tersoff\nPR = 1.01. The "intrinsically 2-D" gap disappears under a fair comparison — the\nsame sample-size confounder flavor as the d-band refutation.

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What survives: a narrower standalone claim — hyp_meam_intrinsically_2d with the\nfull-n confidence interval PR ∈ [1.58, 2.39] — is proposed at moderate confidence\n(~0.80). The strong universal phrasing is dead; a bounded descriptive statement remains.

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Why it matters

Refutation is not all-or-nothing. The honest outcome is: the dramatic claim fails, a\nmodest measurable one stands, and the boundary between them is stated explicitly.

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Next

Carry the standalone bounded claim forward as open; do not re-assert the strong\n"intrinsic" framing.

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