[{"type":"text","text":"**Session 011 complete — task (a) done: Lean proof tier (i) fully eliminated.**\n\n## Results\n\n| Theorem | Status | Axioms |\n|---|---|---|\n| `chain_rule_sqrt_shift` | PROVED (pre-crash instance, `53cc122`) | 3 standard only |\n| `sInfty_lower_bound` | PROVED (`9e2616f`) | 3 standard only |\n| `marginTilde_convex` | PROVED (`40c4265`) | 3 standard only |\n\n**`sInfty_lower_bound`** (D-037 §3): Bernoulli truncation at K ≈ n/2 + the two γ-shifted harmonic bounds (from Mathlib's `eulerMascheroniSeq` machinery). The γ/log 2/log π pieces cancel *exactly* by parity algebra — no decimal estimates needed. The `tsum` summability honesty note on `SInfty` is now discharged (`sInf_series_summable`).\n\n**`marginTilde_convex`** (D-057, ~700 new lines): the full 8-block ψ-table with sign proofs, the IIMaj/B̃₄ exponential bound (`iimaj_bracket_bound`: factor-monotone split, ≤ 1.316 < 2, analytically proving E-029's grid-measured 0.189 < 1), and assembly via `convexOn_of_deriv2_nonneg`: margiñ″(n) = 1/(2n) − 2ψ_F/(4n) − Σwᵢψᵢ/(4n) − IIMaj″(n) ≥ 1/(2n) − IIMaj″(n) > 0.\n\n**sorryAx now remains only where designed**: `lambda_pos_finite_height` (tier ii), Suzuki (tier iv), 4 valley statements (tier iii). Build green (8706 jobs).\n\nAll session-end protocol done: journal-011 written, D-061/NGUYEN.md/STATE.md updated, db registered, everything committed (`22f865a`). The pre-crash instance's work was preserved and built upon — zero loss from the crash.\n\n**Session 012 options:** (a) Lean tier (ii) — the traced contour bound inside `lambda_pos_finite_height` (the big one); (b) E-023b acb M₀ upgrade; (c) paper figures; (d) (★) symbol-space opening."}]