{"id":"hyp-dband-correlation","title":"D-Band Controls Error Correlation","subtitle":"Refuted — full-sample ρ = −0.02; the signal was a sample-size confounder.","category":"conjectures","tags":["d-band","confounder","matched-n"],"source":"articles/docs/conjectures/dband-correlation.md","lang":"en","words":185,"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":"<h1 id=\"d-band-controls-error-correlation\">D-Band Controls Error Correlation</h1><p><strong>Status: Refuted by us</strong></p>\n<h2 id=\"claim-as-originally-proposed\">Claim (as originally proposed)</h2><p>A metal&#39;s d-band character governs how well potentials predict its elastic-constant\nerrors — d-band filling would explain the reference↔prediction correlation structure.</p>\n<h2 id=\"how-we-tested-it\">How we tested it</h2><p>Computed the correlation on the <strong>full sample</strong>, then ran a matched-n analysis to\nseparate a real d-band effect from a sample-size artifact (elements with more potentials\nhave tighter correlations regardless of physics).</p>\n<h2 id=\"result-refuted\">Result — refuted</h2><ul>\n<li>Full-sample correlation: <strong>ρ = −0.02</strong> — essentially nothing.</li>\n<li>The apparent signal was a <strong>sample-size confounder</strong>: ρ = −0.50 to −0.66 when\nconditioned on n, not on d-band.</li>\n<li>A residual d-band signal <em>only</em> recovers on the n ≥ 3 subset (ρ = +0.52) — i.e. it is\nvisible only where the confounder is controlled, and is weak.</li>\n</ul>\n<h2 id=\"why-it-matters\">Why it matters</h2><p>This is the first clean demonstration of the program&#39;s self-correction discipline: an\nattractive mechanistic story, killed by a fair test, with the confounder named\n(sample size). The same matched-n method later refuted the\n<a href=\"#/read/hyp-meam-intrinsic-2d\">MEAM intrinsically-2D claim</a> — one method, two refutations.</p>\n<h2 id=\"next\">Next</h2><p>Treat sample-size imbalance as a first-class confounder in every cross-element claim;\nreport matched-n alongside any pooled correlation.</p>\n"}