[{"type":"thinking","thinking":"`lambda_pos_finite_height_verified` — 3 standard axioms, NO sorryAx. The discharge is complete: **three hypotheses, all perimeter-class + SfBoundProp**.\n\nCommitting this milestone immediately (crash-safe), then the paper reconciliation.","signature":""},{"type":"text","text":"**TIER (ii) STEP 2 COMPLETE**: `lambda_pos_finite_height_verified` audits clean — three hypotheses only, all perimeter-class + the one named analytic bound. Committing."},{"type":"tool_use","id":"Bash_173","name":"Bash","input":{"command":"cd D:/Python/Quantum && git add research/lean/NguyenRH1/NguyenRH1/LiBasePoints.lean research/lean/NguyenRH1/NguyenRH1/LiSkeleton.lean research/lean/NguyenRH1/NguyenRH1.lean research/lean/NguyenRH1/PrintAxioms.lean && git -c user.name=\"NGUYEN-RH-1\" -c user.email=\"research@local\" commit -m \"$(cat <<'EOF'\nSession 012: tier (ii) STEP 2 COMPLETE — base points discharged; lambda_pos_finite_height_verified (3 hypotheses)\n\nLiBasePoints.lean (new, ~560 lines): the two margin evaluations are now\nPROVED by certified rational interval bounds (D-062 §5 plan). Machinery:\nexp upper bounds via (exp(x/16))^16 ≤ (1−x/16)⁻¹⁶ (Real.add_one_le_exp),\npartial-sum lower bounds, d9/d20 rationals for e/π/log 2. Certified:\nlog 80000 ∈ [11.263, 11.3], log 100000 ≥ 11.5, log π ∈ [1.14, 1.15],\nsInftyLower(8×10⁴) ∈ [336000, 339000], sInftyLower(10⁵) ≥ 432500,\nBn(8×10⁴) ∈ [274000, 328000], Bn(10⁵) ≤ 347000. Hence\nmarginTilde_FAlt_80000_pos (≥ 8001; true 15764) and\nmarginTilde_FAlt_80000_lt_100000 (65001 < 85501; true gap ~77000).\n\nlambda_pos_finite_height_verified: R-004 machine-verified modulo ONE\nnamed analytic hypothesis (SfBoundProp) + the declared computational\nperimeter (RHUpTo, LiVerifiedUpTo). PrintAxioms: 3 standard axioms, no\nsorryAx. Caught + fixed en route: a 3e-6-magnitude rounding slip in the\nBn lower-bracket constant (110.34987 → 110.3498).\nEOF\n)\" && git log --oneline -1","description":"Commit tier (ii) step 2"},"extra_content":null}]