[{"type":"thinking","thinking":"The user needs to log off. Per the session END protocol (§8.4 — before any shutdown, no exceptions):\n\n1. Write journal/session-NNN.md (work, decisions, outcomes) — session 037.\n2. File every result/dead end/derivation in its own file; update index.md files; register in research.db.\n3. Update NGUYEN.md checklist (§5), Graveyard (§6), Result Ledger (§7).\n4. Update STATE.md LAST with an explicit \"NEXT ACTION:\" line.\n5. git add + commit with session number in the message.\n\nCurrent state of work:\n- The last build (§1–§4, round 4) came back CLEAN (no output) — so LiMoments.lean §1–§4 all elaborate, including the k=1 capstone `sigmaP_one_eq_neg_gFun_zero`!\n- §5 (termwise iterated deriv at 0, k≥2) and §6 (unified capstone) are NOT yet written. I had the full design ready (documented in my plan + D-070).\n- The audit from earlier (user-requested) was completed and recorded: audit-session037-axioms.txt + AuditSession037.lean.\n- D-070 route-change design note was filed.\n- Scratch.lean was overwritten with the lemma probe (it was an old session-029 audit file — hmm, I overwrote Scratch.lean which previously contained a session-029 axiom audit! That's a concern: the previous content was \"Session 029 axiom audit: LiFEntire.lean\" — its output was presumably saved to audit-session029-axioms.txt, so the probe overwrite is acceptable but I should note it. Actually better: the audit scripts AuditSession034/035 exist as separate files; the session-029 one was apparently named Scratch.lean and its output recorded. The probe content is ephemeral. I should probably restore a proper file state — the cleanest: rename my probe to Probe.lean (which exists already per the earlier ls — Probe.lean exists!). Hmm — ls showed Probe.lean AND Scratch.lean both exist in the package root. I overwrote Scratch.lean (session-029 audit). To be safe and honest, I'll note this in the journal — the session-029 axiom AUDIT RESULTS are preserved in audit-session029-axioms.txt, so nothing is lost; the Scratch.lean file was a scratchpad by name. Actually let me check if audit-session029-axioms.txt exists — earlier ls showed audit-session029-axioms.txt ✓ yes it exists. Good.\n\nWait — should I restore Scratch.lean to the session-029 audit? The audit file content was partially shown in the system reminder (\"/- Session 029 axiom audit: LiFEntire.lean (ii′-5e-iv COMPLETE). -/ import Mathlib import NguyenRH1.LiFEntire open NguyenRH1\"). The audit results are in audit-session029-axioms.txt. The scratch file itself is a scratchpad — Probe.lean also exists for this purpose. I'll restore Scratch.lean to the session-029 audit content? I only saw the first 3 lines + the note \"36 lines\". I can't fully restore it — I only have the header. Hmm. The audit output is preserved. The header comment is known. Being pragmatic: keep my probe in Scratch.lean (it IS a scratchpad), note it in the journal, and move on. Actually — better citizenship: move my probe into Probe.lean? Probe.lean also existed with unknown content — overwriting it too would compound the issue. Leave Scratch.lean as the probe; document the change in the journal (the session-029 audit results are safe in audit-session029-axioms.txt).\n\nHmm — actually, let me reconsider: the system note said \"the file existed and had not been read in this session — its previous content (36 lines) was read automatically before overwriting. Previous content began: /- Session 029 axiom audit: LiFEntire.lean (ii′-5e-iv COMPLETE). -/\". The auto-read means the full content was captured somewhere? No — it says previous content \"began\" with those lines. I can't restore the full 36 lines. It's fine — the audit OUTPUT is archived; the script is re-derivable from AuditSession034/035 patterns. Journal note it.\n\nNow — what to do RIGHT NOW for closure. The build state: §1–§4 elaborate clean (last run: no output). §5/§6 not written. The file compiles standalone (`lake env lean` green). It's NOT root-imported yet — that's fine (LiTightR also wasn't until now).\n\nPer §8.4 and 8.5 (sub-stage rule: each sub-stage ends in a clean, committed, resumable state):\n\n1. Journal session-037.md — document: the user-requested capstone audit (audit-session037-axioms.txt: 3 standard axioms only; perimeter parameters recorded verbatim); ii′-3b LAUNCHED with the D-070 route revision (moments via the 5e partial-fraction identity — no contours); LiMoments.lean §1–§4 complete (~700 lines, builds green): xiL entire closed form, gFun = B + seriesFun identity (G), evaluations at 0/1 + FE sign, summability budget, k=1 rearrangement sigmaP_one_eq_neg_gFun_zero PROVED; §5/§6 designed (termwise iterated deriv + unified capstone) with the full proof skeleton in the design; banked gotchas (Summable.tsum_add method form, SummationFilter-parameterized tsum lemmas in this Mathlib, eq_zero_of_neg_eq needs LinearOrder (ℂ N/A → 2V=0 route), Complex.norm_conj takes starRingEnd directly, iteratedDeriv_neg exists with explicit args, Equiv.summable_iff/Equiv.tsum_eq signatures, the beta-redex show-before-rw pattern, AnalyticAt.contDiffAt exists, field_simp closes goals (trailing ring errors ×3), tsum binder ascriptions mandatory (zeroMult ρ coerces to ℂ otherwise), Scratch.lean overwritten with the probe (session-029 audit script superseded — output preserved in audit-session029-axioms.txt)).\n\n2. D-070 already filed ✓ (route revision design). Update derivations/index.md + register D-070 in research.db.\n\n3. NGUYEN.md: update the ii′-3b checklist line — from [~] design to \"§1–§4 COMPLETE (session 037): LiMoments.lean xiL/(G)/evaluations/k=1; §5/§6 remaining\". Also the session log §8.6 needs a session-037 entry. Also STATE.md.\n\n4. STATE.md — update with the current position + NEXT ACTION: Session 038: LiMoments §5 (termwise iterated derivation at 0 — iteratedDeriv_seriesTerm + the M-test SummableLocallyUniformlyOn + iteratedDeriv_seriesFun_zero) → §6 (gFun_eventuallyEq_zero + the capstone sigmaP_eq_neg_iteratedDeriv_gFun_div) → root-import LiTightR + LiMoments → audit → ii′-3c.\n\n5. Commit with session number.\n\nAlso — §8.4 item 2: \"register in research.db\" — D-070 needs registration. db.py add-derivation: positional id, --title --task --status --file (NO --date flag). \n\nAnd session registration via direct sqlite3 insert (journal_file column) — per handoff notes.\n\nLet me also double check the current build state is really green including all of §1-§4 — the last run had NO output which means clean (no errors, no warnings). ✓\n\nOne question: should I also write the §5/§6 design into a file so it's not lost? The full §5/§6 proof skeleton is substantial. It's in the conversation; D-070 §5 has the deliverable statement; the journal should carry the detailed remaining-work plan (that's the archive convention — journal-036 did the same for 5f's remaining pieces). I'll put the detailed §5/§6 skeleton in the journal entry.\n\nLet me also update the todo list to reflect reality before closing (§5/§6 pending).\n\nOrder of operations:\n1. Write journal/session-037.md.\n2. Update research/derivations/index.md (add D-070).\n3. Register D-070 in research.db (db.py add-derivation) + register session 037 (sqlite3 insert).\n4. Update NGUYEN.md (ii′-3b line + session log).\n5. Update STATE.md (position + next action).\n6. git add specific files + commit.\n\nFiles to commit:\n- research/lean/NguyenRH1/NguyenRH1/LiMoments.lean (new)\n- research/lean/NguyenRH1/AuditSession037.lean (new)\n- research/lean/NguyenRH1/audit-session037-axioms.txt (new)\n- research/lean/NguyenRH1/Scratch.lean (modified — probe)\n- research/derivations/D-070-ii-prime-3b-route-revision.md (new)\n- research/derivations/index.md (modified)\n- research/journal/session-037.md (new)\n- research/research.db (modified — binary; do we commit the db? Check git status convention — the db is tracked? Handoff says db.py registrations; the repo likely tracks research.db. Check git status.)\n- NGUYEN.md (modified)\n- STATE.md (modified)\n\nWait — also there were untracked LaTeX build artifacts at conversation start (draft.bbl etc., paperA.pdf, submit/) — NOT ours to commit (leave them).\n\nLet me check the derivations/index.md format first, then write everything. Also check research.db is tracked by git.\n\nJournal content — let me draft it carefully but efficiently. Also need the session-registration SQL: \"Session registration via direct sqlite3 insert (journal_file column)\" — schema in numerics/scripts/schema.sql. Let me check the sessions table shape quickly.","signature":""},{"type":"text","text":"The last build came back clean — §1–§4 of LiMoments.lean all elaborate, including the k=1 capstone. Perfect boundary for closure. Running the §8.4 end protocol now."},{"type":"tool_use","id":"TodoWrite_128","name":"TodoWrite","input":{"todos":[{"content":"Read D-066 design + journal-035/036 gotchas","status":"completed","activeForm":"Reading D-066 design + banked gotchas"},{"content":"Scope ii′-3b + file D-070 route-change design note","status":"completed","activeForm":"Scoping ii′-3b + filing D-070"},{"content":"LiMoments §1–§4 (xiL, (G), evaluations, k=1) — BUILD GREEN","status":"completed","activeForm":"Building LiMoments §1–§4"},{"content":"LiMoments §5: termwise iterated deriv at 0 (k≥2)","status":"pending","activeForm":"Building LiMoments §5 (k≥2 termwise)"},{"content":"LiMoments §6: unified capstone sigmaP_eq","status":"pending","activeForm":"Building LiMoments §6 (capstone)"},{"content":"Session-037 closure: journal, index, db, NGUYEN.md, STATE, commit","status":"in_progress","activeForm":"Closing session 037 (journal/db/STATE/commit)"}]},"extra_content":null},{"type":"tool_use","id":"Bash_129","name":"Bash","input":{"command":"cd D:/Python/Quantum && git status --short | head -20 && sqlite3 research/research.db \".schema sessions\" 2>/dev/null || ./.venv/Scripts/python.exe -c \"import sqlite3; db = sqlite3.connect('research/research.db'); print(db.execute(\\\"SELECT sql FROM sqlite_master WHERE name='sessions'\\\").fetchone()[0])\"","description":"Check git status and sessions table schema"},"extra_content":null}]