[{"type":"thinking","thinking":"The user asked for a status check. STATE.md gives everything. Let me summarize concisely.\n\nCurrent position:\n- Project: NGUYEN-RH-1, Phase 5B (tier ii′) — closing SfBoundProp in Lean before paper submission.\n- Session 040 stopped at a clean boundary: ii′-6-c-i complete (LiSideBounds.lean scaffolding, build green 8770 jobs), next is 6-c-ii (I_III left vertical bound).\n- The D-074 dog-leg repair is the active route, preserving original N₁ = (T₀−1)² ≈ 9×10²⁴.\n- Uncommitted changes: correspondence package (Lagarias F-D letter drafts), Scratch.lean, various build artifacts (bbl/fls files), paperA.pdf etc. The git status shows modified finding-note files — those are correspondence files, which per freeze protocol are drafts (D-073 §8 says correspondence files untouched — but here they're modified... wait, the git status was a snapshot at conversation start; it shows M research/correspondence/lagarias-F-D-package/README.md, finding-note.pdf, finding-note.tex — hmm, these are modified. That may be work outside the agent's session or perhaps from session 040's block B. Actually STATE.md says correspondence files untouched (freeze protocol) as of session 039. The modifications could be the user's own work on the letter-to-lagarias. I shouldn't worry; just report.\n\nActually the gitStatus in system prompt is from conversation start and matches what I just got. So there are uncommitted modifications in the correspondence package. Since the END protocol says commit at every sub-stage, these modified files are uncommitted — possibly user's own work (the letter to Lagarias about finding F-D). I'll mention it briefly.\n\nGive a concise status summary:\n1. Where we are: Phase 5B tier ii′ — closing SfBoundProp in Lean before submitting Paper A.\n2. Recent arc: finding F-D (broken stepping in Lagarias Thm 6.1) → repair via D-074 zero-free dog-leg → preserves original N₁ = 9×10²⁴.\n3. Session 040 accomplishments: DL-0 through DL-6 (LiDogLeg.lean complete, no perimeter), ii′-6-a2 (Bn redefined, convexity re-proved, base points re-certified, N₁ preserved), F-E finding + repair decision, 6-c-i scaffolding green.\n4. Next action: 6-c-ii (I_III left vertical bound) — full recipe banked in STATE.md.\n5. Working tree note: uncommitted changes in the Lagarias correspondence package (letter/finding-note drafts) — not part of the committed research archive state; ask if those should be committed or left alone.\n\nKeep it concise.","signature":""},{"type":"text","text":"## Project status — NGUYEN-RH-1\n\n**Where we are:** Phase 5B (tier ii′) — closing `SfBoundProp` in Lean *before* submitting Paper A. Master is green @ `2979f57` (build 8770–8773 jobs, 3 standard axioms only everywhere).\n\n### Current front: ii′-6-c (four side bounds), D-074 dog-leg route\n\nThe active line is the **F-D repair**: Lagarias's Thm 6.1 stepping is broken at T = √n (D-072); the adopted fix is the **zero-free dog-leg** (D-074) which keeps T_cut = √n and thereby **preserves the original N₁ = (T₀−1)² ≈ 9×10²⁴**.\n\nSession 040 completed:\n- **DL-0 → DL-6** — `LiDogLeg.lean` fully proved (exact identity, V_left/H_high/V_right bounds, direct Dirichlet bound at re = 2√n; **no perimeter, nothing above T_cut**)\n- **ii′-6-a2** — `Bn` redefined with the dog-leg charge (1.5·IIMaj), convexity re-proved (4/3-bracket cherry-picked, `e11ad95`), base points re-certified, margins positive: 13 160 / 88 911 / 2.458×10²⁶ at 8×10⁴ / 10⁵ / N₁\n- **Finding F-E** (I_I kernel off-by-one) — repair adopted: charge I_I as e^{1/3}·IIMaj, absorbed by the fold's free 2π; no Bn/convexity changes\n- **6-c-i** — `LiSideBounds.lean` scaffolding committed (`a8c5b1e`, green)\n\n**Stopped at a clean boundary (user log-off). Next action: 6-c-ii** — the I_III left-vertical bound `‖VIntegral (Jlag n) (-5/2) (-T) T‖ ≤ 4T((2/3)Z2hat T + 10.5 log(T+2) + 48) + 40·1.3352`; full 5-step recipe is banked in STATE.md.\n\n**Remaining map:** 6-c-ii → 6-c-iii (I_I, F-E form) → 6-c-iv (mid-horizontal) → 6-c-v (horizontal assembly) → 6-d (fold ⟹ `sfBoundProp`) → **ii′-7** (closure at original N₁, paper correction note: F-A/F-B/F-D/F-E).\n\n### Side threads\n- Fallbacks parked: c=1.5 branch `wip/c-1.5-margin-redo` (N₁=4×10²⁴), c=2 option, T=√n hidden-cancellation open question (D-073 §8 D4)\n- Paper A frozen/submittable at its 3-hypothesis form; freeze protocol in force until ii′-7\n\n### One thing to flag\nThere are **uncommitted changes** in the working tree: the Lagarias F-D correspondence package (`finding-note.tex/pdf`, `README.md`, plus new untracked `letter-to-lagarias.md`, `evidence.xlsx`, `finding-note_new.pdf`, LaTeX build artifacts) and `Scratch.lean`. These look like your own work on the Lagarias letter. Want me to leave them alone, or commit them?"}]