← Session 21 — Tier ii′ planning + launch: close SfBoundProp in Lean (D-064)
thinking (1926 chars)
The user is asking a precise audit question: does the current research actually achieve the R-004 theorem with the Lean proof discharging the contour bound |S_f(n)| ≤ B(n) over the required range WITHOUT assuming SfBoundProp as a hypothesis?
From what I know from the session logs:
- Session 012: `lambda_pos_finite_height_verified` PROVED modulo the single named analytic hypothesis SfBoundProp + the declared computational perimeter (RHUpTo, LiVerifiedUpTo).
- D-062 §4: PERIMETER DECISION — Trudgian N(T)/S(T) inside the trusted perimeter; tier ii′ (SfBoundProp contour layers L0–L3) POST-PUBLICATION per session-012-end-notes review.
So the short answer is almost certainly: NO — the current state assumes SfBoundProp as a hypothesis; the Lean-verified contour bound is NOT done (tier ii′ is post-publication). The D-037/D-056 contour was calculated analytically (with constants traced: D-056 reference-point R-bound proved, A=10.5, B₀=48; E-028 verified with 26× slack), but the Lean formalization of that contour bound is NOT done — it's exactly what SfBoundProp stands in for.
But I should verify this carefully by checking the actual files rather than just relying on memory/STATE.md. Let me check:
1. LiSkeleton.lean / LiBasePoints.lean — look at SfBoundProp and what hypotheses the theorem has.
2. D-037 (assembly) and D-056 (R-bound proof) — what was actually calculated.
3. D-062 §4 — the perimeter decision and what's inside/outside.
4. Paper A's statement — what it claims.
Let me read the relevant files. I need to be thorough and precise here — the user is asking for an audit.
Plan:
- Grep for SfBoundProp in the Lean package.
- Read D-062 (triage of SfBoundProp, perimeter decision).
- Read D-037 (assembly) to see the contour calculation.
- Read D-056 (R-bound reference-point proof).
- Check paperA.tex's formal verification appendix to see what's claimed.
Let me do this in parallel where possible.
Good question — this is exactly the right audit to run before circulation. Let me verify against the actual files rather than the summaries.
tool: Grep
input
{
"pattern": "SfBoundProp",
"path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1",
"output_mode": "content",
"-n": true
}
tool: Glob
input
{
"pattern": "research/derivations/D-0{37,56,62}*.md",
"path": "D:\\Python\\Quantum"
}
raw content_json (database row)
[{"type":"thinking","thinking":"The user is asking a precise audit question: does the current research actually achieve the R-004 theorem with the Lean proof discharging the contour bound |S_f(n)| ≤ B(n) over the required range WITHOUT assuming SfBoundProp as a hypothesis?\n\nFrom what I know from the session logs:\n- Session 012: `lambda_pos_finite_height_verified` PROVED modulo the single named analytic hypothesis SfBoundProp + the declared computational perimeter (RHUpTo, LiVerifiedUpTo).\n- D-062 §4: PERIMETER DECISION — Trudgian N(T)/S(T) inside the trusted perimeter; tier ii′ (SfBoundProp contour layers L0–L3) POST-PUBLICATION per session-012-end-notes review.\n\nSo the short answer is almost certainly: NO — the current state assumes SfBoundProp as a hypothesis; the Lean-verified contour bound is NOT done (tier ii′ is post-publication). The D-037/D-056 contour was calculated analytically (with constants traced: D-056 reference-point R-bound proved, A=10.5, B₀=48; E-028 verified with 26× slack), but the Lean formalization of that contour bound is NOT done — it's exactly what SfBoundProp stands in for.\n\nBut I should verify this carefully by checking the actual files rather than just relying on memory/STATE.md. Let me check:\n\n1. LiSkeleton.lean / LiBasePoints.lean — look at SfBoundProp and what hypotheses the theorem has.\n2. D-037 (assembly) and D-056 (R-bound proof) — what was actually calculated.\n3. D-062 §4 — the perimeter decision and what's inside/outside.\n4. Paper A's statement — what it claims.\n\nLet me read the relevant files. I need to be thorough and precise here — the user is asking for an audit.\n\nPlan:\n- Grep for SfBoundProp in the Lean package.\n- Read D-062 (triage of SfBoundProp, perimeter decision).\n- Read D-037 (assembly) to see the contour calculation.\n- Read D-056 (R-bound reference-point proof).\n- Check paperA.tex's formal verification appendix to see what's claimed.\n\nLet me do this in parallel where possible.","signature":""},{"type":"text","text":"Good question — this is exactly the right audit to run before circulation. Let me verify against the actual files rather than the summaries."},{"type":"tool_use","id":"Grep_3","name":"Grep","input":{"pattern":"SfBoundProp","path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1","output_mode":"content","-n":true},"extra_content":null},{"type":"tool_use","id":"Glob_4","name":"Glob","input":{"pattern":"research/derivations/D-0{37,56,62}*.md","path":"D:\\Python\\Quantum"},"extra_content":null}]