{
  "command": "cd /d/Python/Quantum && ./.venv/Scripts/python.exe research/numerics/scripts/db.py add-derivation D-041 --title \"Task 2.9-D1: Krein frame + deficiency-convergence theorem; reduction (1.12) iff spec(D) real; D-040 Delta-constraint folded in\" --task 2.9 --status complete --file research/derivations/D-041-krein-frame-deficiency-convergence.md && ./.venv/Scripts/python.exe research/numerics/scripts/db.py add-derivation D-038 --title \"Task 2.11: transition-scale lower bound \u2014 consolidation functional R(a)=(aZ/pi)e^{-Delta(a)}, onset criterion Delta-prime > 1/a, a* > 12\" --task 2.11 --status complete --file research/derivations/D-038-transition-scale.md",
  "description": "Register D-041 and D-038 in db"
}

{
  "file_path": "D:\\Python\\Quantum\\research\\derivations\\index.md",
  "old_string": "| D-040 | Task 2.10: spectral-measure convergence \u2014 valley observable (K_a(z,z) dips at true \u03b3's), weight-channel \u03b3-encoding, fixed-\u03b8 saturation \u0394(a) \u2248 3.33 \u2212 4.76/a; constraint on 2.9-D1 \u03b8(a) flow | 2.10 | complete | 2026-08-19 |",
  "new_string": "| D-040 | Task 2.10: spectral-measure convergence \u2014 valley observable (K_a(z,z) dips at true \u03b3's), weight-channel \u03b3-encoding, fixed-\u03b8 saturation \u0394(a) \u2248 3.33 \u2212 4.76/a; constraint on 2.9-D1 \u03b8(a) flow | 2.10 | complete | 2026-08-19 |\n| D-038 | Task 2.11: transition-scale lower bound \u2014 consolidation functional R(a) = (aZ/\u03c0)e^{\u2212\u0394(a)} (validated 15%), onset criterion \u0394\u2032 > 1/a, margin C(a) = \u0394 \u2212 log a decreasing 0.77\u21920.46; a* > 12; fixed-\u03b8 consolidation asymptotically impossible | 2.11 | complete | 2026-08-19 |\n| D-041 | Task 2.9-D1: Krein frame + Theorem D1 (deficiency convergence \u27fa strong resolvent convergence) + reduction \"(1.12) \u27fa spec(D) \u2282 \u211d\"; lemma map L0\u2013L4/W1\u2013W3; limit extension = \u03c0/2; D-040 \u0394-constraint as necessary conditions N1\u2013N3 | 2.9 | complete | 2026-08-19 |"
}

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  "oldString": "    {% endfor %}\n    </tbody>\n  </table>\n</section>\n{% endblock %}",
  "newString": "    {% endfor %}\n    </tbody>\n  </table>\n  <p class=\"muted\">The session-013 audit predates the tier-ii\u2032 closure:\n  its 5 <code>sorryAx</code> lines are the intended skeleton statements\n  (1 Suzuki + 4 valley \u2014 future tiers, not used by the closed theorem).\n  Every later audit is fully clean.</p>\n</section>\n{% endblock %}",
  "originalFile": "{% extends \"dashboard/base.html\" %}\n{% block title %}Lean Proofs{% endblock %}\n{% block nav_lean %}active{% endblock %}\n{% block content %}\n<h1>Formal Verification \u2014 Lean 4</h1>\n<p class=\"muted\">The machine-checked proof chain behind the finite-height\nLi theorem (package <code>research/lean/NguyenRH1/</code>, built against\nMathlib + the vendored zeta-23-lean). Toolchain: <code>{{ toolchain }}</code>.</p>\n\n<div class=\"stat-grid\">\n  <div class=\"stat\"><div class=\"stat-num\">{{ totals.files }}</div>\n    <div class=\"stat-label\">source files</div></div>\n  <div class=\"stat\"><div class=\"stat-num\">{{ totals.lines }}</div>\n    <div class=\"stat-label\">lines of Lean</div></div>\n  <div class=\"stat\"><div class=\"stat-num\">{{ totals.decls }}</div>\n    <div class=\"stat-label\">declarations</div></div>\n  <div class=\"stat\"><div class=\"stat-num\">{{ totals.sorries }}</div>\n    <div class=\"stat-label\">sorries (skeletons only)</div></div>\n  <div class=\"stat\"><div class=\"stat-num\">{{ totals.audits }}</div>\n    <div class=\"stat-label\">axiom audits</div></div>\n  <div class=\"stat\"><div class=\"stat-num\">{{ totals.audit_decls }}</div>\n    <div class=\"stat-label\">declarations audited</div></div>\n</div>\n\n<section class=\"card\">\n  <h2>Axiom policy \u2014 the transparency guarantee</h2>\n  <p>Every proved declaration in the chain depends on <b>exactly the three\n  standard axioms</b>: <code>propext</code>, <code>Classical.choice</code>,\n  <code>Quot.sound</code> \u2014 the same axioms any Mathlib proof uses.\n  <b>Zero <code>sorryAx</code></b> (no skipped proofs) anywhere in the proved\n  chain; the {{ totals.sorries }} sorries below are confined to the two\n  skeleton files (Suzuki / valley \u2014 future tiers, not used by the closed\n  theorem). The audit transcripts at the bottom of this page are the raw\n  <code>#print axioms</code> output verifying this, per declaration.</p>\n</section>\n\n<section class=\"card\">\n  <h2>The closed theorem \u2014 <code>LiClosed.lean</code> (verbatim)</h2>\n  <pre class=\"json-box code-box\">{{ closed_source }}</pre>\n</section>\n\n<section class=\"card\">\n  <h2>The declared perimeter \u2014 7 hypotheses</h2>\n  <p class=\"muted\">The theorem is conditional on these seven statements\n  (two published computational certificates + five analytic perimeter\n  Props from the declared literature). Each is shown verbatim from source;\n  click to expand.</p>\n  {% for p in perimeter %}\n    <details class=\"perim\">\n      <summary><b>{{ p.name }}</b>\n        <span class=\"muted\">\u2014 {{ p.note }}\n          (<code>{{ p.file }}</code>{% if p.line %}, line {{ p.line }}{% endif %})</span></summary>\n      <pre class=\"json-box code-box\">{{ p.text }}</pre>\n    </details>\n  {% endfor %}\n</section>\n\n<section class=\"card\">\n  <h2>Source files</h2>\n  <table class=\"tbl\">\n    <thead><tr><th>File</th><th>Lines</th><th>Declarations</th><th>Sorries</th><th>Updated</th></tr></thead>\n    <tbody>\n    {% for f in files %}\n      <tr>\n        <td><a href=\"/lean/{{ f.name|urlencode }}/\">{{ f.file }}</a></td>\n        <td>{{ f.lines }}</td><td>{{ f.decls }}</td>\n        <td>{% if f.sorries %}<span class=\"tag tag-cond\">{{ f.sorries }} (skeleton)</span>{% else %}0{% endif %}</td>\n        <td>{{ f.mtime|slice:\":10\" }}</td>\n      </tr>\n    {% endfor %}\n    </tbody>\n  </table>\n</section>\n\n<section class=\"card\">\n  <h2>Axiom audits (<code>#print axioms</code> transcripts)</h2>\n  <table class=\"tbl\">\n    <thead><tr><th>Audit</th><th>Declarations</th><th>Status</th><th>Updated</th></tr></thead>\n    <tbody>\n    {% for a in audits %}\n      <tr>\n        <td><a href=\"/lean/audit/{{ a.name|urlencode }}/\">{{ a.file }}</a></td>\n        <td>{{ a.decls }}</td>\n        <td>{% if a.clean %}<span class=\"tag tag-ok\">3 standard axioms only</span>\n            {% else %}<span class=\"tag tag-cond\">{{ a.sorries }} sorryAx \u2014 intended skeletons</span>{% endif %}</td>\n        <td>{{ a.mtime|slice:\":10\" }}</td>\n      </tr>\n    {% endfor %}\n    </tbody>\n  </table>\n</section>\n{% endblock %}\n",
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        "+  <p class=\"muted\">The session-013 audit predates the tier-ii\u2032 closure:",
        "+  its 5 <code>sorryAx</code> lines are the intended skeleton statements",
        "+  (1 Suzuki + 4 valley \u2014 future tiers, not used by the closed theorem).",
        "+  Every later audit is fully clean.</p>",
        " </section>",
        " {% endblock %}",
        " "
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