[{"type":"text","text":"Both pieces of the mathematician's advice are executed. Final state:\n\n## 1. hbase/hbase2 discharged — the headline upgrade landed\n\n`LiBasePoints.lean` (~560 lines, compiled clean): both margin evaluations are now **proved in Lean** by certified rational interval bounds (the `exp x ≤ (1−x/16)⁻¹⁶` trick + partial sums + d9/d20 rationals for e/π/log 2). The headline theorem is now:\n\n```\nlambda_pos_finite_height_verified\n    (hRH : RHUpTo (3×10¹²)) (hfinite : LiVerifiedUpTo (5×10⁵))\n    (hSf : SfBoundProp)\n```\n**Three hypotheses — one named analytic bound + the declared computational perimeter.** PrintAxioms: 3 standard axioms, no `sorryAx`. Exactly the upgrade moment the reviewer flagged.\n\nNotable: Lean caught a genuine 3×10⁻⁶ rounding slip of mine en route (the Bn bracket constant `110.34987` had to round *down* to `110.3498`) — the methodology working as intended.\n\n## 2. Margin trail reconciled in the paper\n\n- §3.1 Step 4 main text now says **15 764** (the Lean-consumed FAlt value) with a footnote carrying the full trail: 16 020 (E-028) → 15 764 (FAlt, cost 0.9√n) → **≥ 8 001** (the certified interval bound the discharge consumes).\n- Step 5 overlap factor updated for the 10⁵ split; numerics bullet cross-referenced; the appendix formal-status paragraph finalized at three hypotheses. Compile clean, 12 pp.\n\n## 3. Guidance adopted for what comes next\n\nTier ii′ (the rectangle-contour interior of `SfBoundProp`) is logged as **post-publication** work — STATE.md's NEXT ACTION now offers: (a) Paper A finalization/split, (b) E-023b acb M₀ certificate, (c) tier ii′, (d) Paper-B (★) opening. The Part-2 standing objections (Theorem 3's FT bookkeeping, L3/L4, authorship policy) are recorded as unchanged.\n\nCommits: `fc2e55e` (step 2), `f022f6e` (docs + paper + archived review notes). Journal, STATE, NGUYEN.md, research.db all current."}]