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← Session 18 — Lean tier (ii): finite-height proof + certified base points

#717 assistant 2026-08-20 16:53:24.946 UTC · 756→673 tok open ⤢
thinking (1468 chars)
The user wants to proceed with option (a): Lean tier (ii) — split into assembly-first with named hypothesis SfBound, then triage. This is a significant multi-session task. Let me plan: 1. First, understand the current Lean skeleton: `lambda_pos_finite_height` in research/lean/NguyenRH1/. Read the current statement, understand what's there. 2. Read the relevant derivations: D-037 (assembly), D-036 (constants), D-056 (R-bound), D-057 (convexity) to understand the exact logical chain. 3. Design: restate `lambda_pos_finite_height` with explicit named hypothesis `SfBound : ∀ n, |S_f n| ≤ B n` and discharge the assembly conditional on it. 4. Implement in Lean, prove the assembly. 5. Follow session protocol: journal, STATE.md update, db registration, commits. Per the session protocol (§8.3): read STATE.md (done), skim latest journal + results/index.md. I've read STATE.md. Let me start by reading the Lean package structure and the current LiSkeleton.lean file. This is a big task — I should use TaskCreate to track. Let me first explore. Key steps: 1. Read research/lean/NguyenRH1/ structure + LiSkeleton.lean (current lambda_pos_finite_height statement). 2. Read D-037 to extract the exact assembly chain: what hypotheses combine to give λ_n > 0 for n ≤ N₁. 3. Design the SfBound hypothesis + B(n) definition. 4. Implement assembly proof in Lean. 5. Build, PrintAxioms audit. 6. Session protocol: journal-012, STATE.md, db, commit. Let me start exploring.
Proceeding with (a): assembly-first split of tier (ii). Let me set up tracking and study the current Lean skeleton.
tool: TodoWrite
input
{
  "todos": [
    {
      "content": "Read current Lean skeleton (LiSkeleton.lean) + tier-(i) proofs to understand existing structure",
      "status": "in_progress",
      "activeForm": "Reading current Lean skeleton"
    },
    {
      "content": "Extract exact assembly chain from D-037/D-056/D-057 (what combines to give \u03bb_n > 0)",
      "status": "pending",
      "activeForm": "Extracting assembly chain from derivations"
    },
    {
      "content": "Design SfBound hypothesis + B(n) definition (Lean types)",
      "status": "pending",
      "activeForm": "Designing SfBound hypothesis"
    },
    {
      "content": "Implement assembly proof: lambda_pos_finite_height modulo SfBound",
      "status": "pending",
      "activeForm": "Implementing assembly proof in Lean"
    },
    {
      "content": "Build + PrintAxioms audit (3 standard axioms only)",
      "status": "pending",
      "activeForm": "Building and auditing axioms"
    },
    {
      "content": "Session protocol: journal-012, STATE.md, db, commit",
      "status": "pending",
      "activeForm": "Running session-end protocol"
    }
  ]
}
raw content_json (database row) 
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