{"id":"formal-proof-ledger","title":"Formal Proof Ledger","subtitle":"Which claims a Lean theorem backs — proven, fabricated, or deliberately not formalized.","category":"formalization","tags":["lean","proof-ledger","audit"],"source":"articles/docs/formal-proof-ledger.md","lang":"en","words":344,"readMinutes":2,"toc":[{"depth":2,"text":"Verdicts","id":"verdicts"},{"depth":2,"text":"How to read this","id":"how-to-read-this"},{"depth":2,"text":"The epistemic stance","id":"the-epistemic-stance"},{"depth":2,"text":"Next","id":"next"}],"html":"<h1 id=\"formal-proof-ledger\">Formal Proof Ledger</h1><p>Which empirical claims are backed by a <strong>machine-checked Lean 4 theorem</strong>, which are\nproven-but-synthetic, and which are deliberately <em>not</em> formalized. The Lean\nspecification is the adversary of the prose: where the two disagree, the prose loses.</p>\n<p>The authoritative artifact is the <a href=\"#/read/formal-audit\">Formal Audit Report</a> — generated\n<em>by</em> the Lean spec, not written by hand. This ledger maps audit verdicts to the\n<a href=\"#/read/conjecture-ledger\">conjecture ledger</a>.</p>\n<h2 id=\"verdicts\">Verdicts</h2><div class=\"table-wrap\"><table><thead><tr>\n<th>Claim</th>\n<th>Lean module / theorem</th>\n<th>Verdict</th>\n</tr>\n</thead><tbody><tr>\n<td data-label=\"Claim\">Hyper-ribbon manifold dimensionality (PR/n &lt; 0.5)</td>\n<td data-label=\"Lean module / theorem\"><code>Materials/Theory/HyperRibbonEmpirical</code></td>\n<td data-label=\"Verdict\"><strong>Proven — empirically grounded.</strong> Originally consistent only with synthetic data; now grounded on the real corpus. → <a href=\"#/read/hyp-hyper-ribbon-universality\">conjecture</a></td>\n</tr>\n<tr>\n<td data-label=\"Claim\">Simpson&#39;s paradox in BCC elastic constants</td>\n<td data-label=\"Lean module / theorem\"><code>noSimpsonsInBccEam</code> (<code>Materials/Analysis/Causal</code>)</td>\n<td data-label=\"Verdict\"><strong>Claim fabricated.</strong> The causal graph has no bypass from element to error, so elemental stratification cannot produce Simpson&#39;s paradox in real data.</td>\n</tr>\n<tr>\n<td data-label=\"Claim\">Parameter / sloppiness bound</td>\n<td data-label=\"Lean module / theorem\"><code>Materials/Theory/ParameterBound</code></td>\n<td data-label=\"Verdict\">Proven structural bound (analytic, not data-dependent).</td>\n</tr>\n<tr>\n<td data-label=\"Claim\">Validation scope &amp; rank gate</td>\n<td data-label=\"Lean module / theorem\"><code>Materials/Scope/Validity</code>, <code>Materials/Validation/RankGate</code></td>\n<td data-label=\"Verdict\">Proven guard conditions used by the live loop.</td>\n</tr>\n<tr>\n<td data-label=\"Claim\">Weak acceleration/refusal scalar gate</td>\n<td data-label=\"Lean module / theorem\"><code>Materials/Theory/WeakAcceleration</code></td>\n<td data-label=\"Verdict\">Proven theorem-shaped guard: the scalar speedup lower bound stays &gt;= 1 under coverage/reach/threshold conditions and does not depend on a spectral rho threshold. Full Lipschitz/reach formalization remains open.</td>\n</tr>\n</tbody></table></div><h2 id=\"how-to-read-this\">How to read this</h2><ul>\n<li><strong>Proven — empirically grounded</strong> is the strongest tier: a Lean theorem <em>and</em> real\ndata behind it. Only the hyper-ribbon dimensionality claim currently holds it.</li>\n<li><strong>Claim fabricated</strong> is the most important row. The original paper asserted a\nSimpson&#39;s paradox; the formal spec proved it <em>cannot exist</em> under the real causal\ngraph. This is self-correction enforced by machine, not by authors — and it is why\nthe BCC/FCC story is filed as <a href=\"#/read/hyp-bccfcc-causal-shield\">self-corrected</a>.</li>\n<li>The empirical-only conjectures (d-band, MEAM-2D, Au escape, Fe outlier) are <strong>not</strong>\nformalized: they are statistical claims about a corpus, not theorems. We do not dress\nstatistics in proof clothing.</li>\n</ul>\n<h2 id=\"the-epistemic-stance\">The epistemic stance</h2><p>We formalize <em>before</em> we simulate where the claim is structural, and we let the spec\noverrule the narrative. See <a href=\"#/read/formal-methodology\">In the In Between</a> and\n<a href=\"#/read/formal-vision\">The Open Distillation Factory — Executable Vision</a>.</p>\n<h2 id=\"next\">Next</h2><p>Formalize the matched-n fairness condition itself, so &quot;this refutation controlled its\nconfounder&quot; becomes a checked property rather than a methodological promise.</p>\n"}