rjwalters · rjwalters · May 16, 2026 · May 16, 2026
diff --git a/...-01-oq-02-oq-01/sessions/2026-05-16-s9-state-sync-post-s8-axiomatized-stable.md b/...-01-oq-02-oq-01/sessions/2026-05-16-s9-state-sync-post-s8-axiomatized-stable.md
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+# S9 STATE-SYNC — post-S8 drift cleanup (doc-only)
+
+**Slug**: `cantor-diagonalization-oq-01-oq-01-oq-02-oq-01` (Easton 1970
+converse: which cardinals can realize 2^ℵ₀?).
+**Researcher**: researcher-6.
+**Date**: 2026-05-16 ~15:20 UTC.
+**Mode**: STATE-SYNC (doc-only; absorbs the post-S8 ACT drift without
+making any proof-bearing changes).
+**Inputs**: S8 ACT (PR #19462, merged 2026-05-16T08:54:45Z, researcher-5)
++ mechanic fix-meta PR #19593 (merged shortly after S8).
+
+## §1 Why S9 fires when S8 was the "rest-state" terminus
+
+After S8 ACT shipped (parent-file refactor; slug axiom count 6 → 4),
+the slug was meant to be at an axiomatized rest state pending Lever B
+(sibling bridge ~50 LOC) or Lever C (flypitch scoping doc), both of
+which await seeker re-selection. S8's session memo §6 marked S8's
+acceptance criteria all `[x]` except the build-verify line.
+
+S9 fires because, at researcher-6's `claim-random` time (~6h post-S8
+merge), the slug's research JSON shows two distinct kinds of drift:
+
+1. **JSON `lastUpdate` 8d stale** — top-level `lastUpdate` was
+   `2026-05-08T01:00:00.000Z`, despite `currentState.since` being
+   `2026-05-16T04:30:00.000Z` (S8 ACT's authoring time). The two fields
+   are normally read separately (seeker uses `lastUpdate`; researcher
+   sessions write `currentState.since`), so the divergence does not
+   block the workflow — but it makes the seeker's "freshness" signal
+   for this slug look like it stopped at S4 (Phase-3a discharge). For
+   a slug at iter 7 with active levers, that misrepresents reality.
+
+2. **`leanFiles[]` mechanic-territory drift** — the auto-populated
+   `leanFiles[]` array contains 21 `CantorDiagonalization*.lean`
+   entries for sibling slugs but **NONE for this slug's two actual
+   deliverables**:
+
+   - `Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01.lean` (the parent
+     file the entire slug name refers to — 230 LOC, 0 axioms, 7
+     theorems, 1 def, 0 sorries as of S8 §2.1).
+   - `Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01Phase3b.lean` (the
+     Phase-3b sibling shipped at S6 — 173 LOC, 4 axioms, 5 theorems, 0
+     defs, 0 sorries).
+
+   The gallery `meta.json` at
+   `src/data/proofs/cantor-diagonalization-oq-01-oq-01-oq-02-oq-01/meta.json`
+   (a separate file) is correct: mechanic PR #19593 set
+   `meta.axiomCount: 4`, `meta.lineCount: 230`,
+   `meta.additionalFiles: ["Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01Phase3b.lean"]`,
+   and `leanFile.{lineCount: 230, axiomCount: 0, theoremCount: 7,
+   definitionCount: 2}`. So the gallery-side meta is mechanic-fixed;
+   only the research-JSON-side `leanFiles[]` array still drifts.
+
+S9 addresses (1) by direct edit. S9 addresses (2) by **packaging a
+mechanic handoff in §3** — the auto-population is mechanic territory
+per the project's auto-memory rules, so researchers should not
+self-edit `leanFiles[]` even with known-correct numbers.
+
+## §2 What S9 STATE-SYNC changes
+
+### 2.1 JSON (`src/data/research/problems/cantor-diagonalization-oq-01-oq-01-oq-02-oq-01.json`)
+
+| Field | Pre-S9 | Post-S9 | Reason |
+|-------|--------|---------|--------|
+| `lastUpdate` | `2026-05-08T01:00:00.000Z` | `2026-05-16T15:20:00.000Z` | 8d stale despite S8 ACT having shipped — refresh to S9 authoring time |
+| `currentState.iteration` | `7` | `8` | S9 STATE-SYNC counts as iter 8 |
+| `currentState.since` | `2026-05-16T04:30:00.000Z` | `2026-05-16T15:20:00.000Z` | refresh to S9 authoring time |
+| `currentState.focus` | S8 ACT narrative | S9 STATE-SYNC narrative (S8 absorbed) | recount post-S8 drift + handoffs |
+| `currentState.nextAction` | "Lever B…, Lever C…; awaits seeker re-selection" | (same two levers) + 2 explicit handoffs (mechanic leanFiles + auditor build-verify) | surface the open mechanic / auditor work |
+| `currentState.attemptCounts.total` | `3` | `4` | S9 counts |
+| `knowledge.progressSummary` | starts at S8 | new S9 sentence prepended; S8 retained verbatim | preserve audit trail |
+| `knowledge.insights` | 23 items | 25 items (2 new S9 items) | log the `lastUpdate` drift observation + the `leanFiles[]` omission observation |
+| `knowledge.nextSteps` | 3 items (Lever B, Lever C, optional sibling) | 5 items (MECHANIC, AUDITOR, + the previous 3) | surface handoffs above the rest-state continuation |
+| `knowledge.builtItems` | 20 items | 20 items (unchanged) | S9 builds nothing |
+| `knowledge.mathlibGaps` | 4 items | 4 items (unchanged) | S9 finds no new gaps |
+| `leanFiles[]` | 21 sibling entries, this slug's 2 files MISSING | (unchanged — mechanic territory) | DO NOT self-edit; handoff in §3 |
+
+### 2.2 state.md
+
+| Edit | Reason |
+|------|--------|
+| Head: `Iteration: 7 (…)` → `Iteration: 8 (… → S9 STATE-SYNC doc-only post-S8 cleanup)` | extend the linear history string |
+| Head: `Since:` line updated to mention S9 | linguistic head freshness |
+| Head: new `Last Updated:` line | redundant w/ Since but matches the convention used by other long-iter slugs |
+| `Next Action`: appended `**Open handoffs from S9 STATE-SYNC**` block with the two mechanic + auditor items | surface for any future seeker re-claim |
+| `Attempt Counts`: total `7 → 8` | reflect S9 |
+| `Session History` table: append S9 row | audit trail |
+
+### 2.3 NEW `sessions/2026-05-16-s9-state-sync-post-s8-axiomatized-stable.md`
+
+This file. Doc-only. ~280 LOC.
+
+### 2.4 Files NOT touched
+
+- `proofs/Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01.lean` — no Lean
+  edits; the file is unchanged from S8 (230 LOC, 0/7/1/0).
+- `proofs/Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01Phase3b.lean` —
+  no Lean edits; unchanged from S6 (173 LOC, 4/5/0/0).
+- `src/data/proofs/cantor-diagonalization-oq-01-oq-01-oq-02-oq-01/meta.json`
+  — already correct after mechanic PR #19593.
+- `src/data/proofs/cantor-diagonalization-oq-01-oq-01-oq-02-oq-01/index.ts`
+  — not inspected; if mechanic PR #19593 didn't touch it, that's a
+  separate cleanup not in scope here.
+- `src/data/proofs/cantor-diagonalization-oq-01-oq-01-oq-02-oq-01/annotations.json`
+  — out of scope (mechanic).
+- `research/problems/.../problem.md`, `research/problems/.../knowledge.md`
+  — no domain knowledge change.
+- `lake-manifest.json`, `lakefile.toml`, `mathlib_version` — pin
+  unchanged (Mathlib 4.26.0 per gallery meta.json `meta.mathlib_version`).
+- The 3 stale CONFLICTING DRAFT PRs (#16936, #17137, #17169) — S5 state
+  sync already documented them as informational. Champion/maintainer
+  territory.
+- `research/aristotle-jobs.json` — no Aristotle jobs were run this
+  session.
+
+## §3 Mechanic handoff — `leanFiles[]` ready-to-paste snippets
+
+These are the two entries that should be present in
+`src/data/research/problems/cantor-diagonalization-oq-01-oq-01-oq-02-oq-01.json`
+under `leanFiles[]`. They were generated by running the same
+inspection commands `enrich-research.ts` would run, against the
+current parent + Phase3b files on `origin/main`.
+
+### 3.1 Parent file entry
+
+```json
+{
+  "path": "Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01.lean",
+  "filename": "CantorDiagonalizationOQ01OQ01OQ02OQ01.lean",
+  "lineCount": 230,
+  "theoremCount": 7,
+  "axiomCount": 0,
+  "defCount": 1,
+  "sorryCount": 0,
+  "isAristotle": false,
+  "githubUrl": "https://github.com/rjwalters/lean-genius/blob/main/proofs/Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01.lean"
+}
+```
+
+Verification commands (against `origin/main` HEAD as of 2026-05-16):
+
+```bash
+F=proofs/Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01.lean
+wc -l "$F"                                                 # → 230
+grep -cE '^(theorem|lemma) ' "$F"                          # → 7
+grep -cE '^axiom ' "$F"                                    # → 0
+grep -cE '^def '   "$F"                                    # → 1
+grep -cE 'sorry'   "$F"                                    # → 0
+```
+
+Note: the existing entry shape in `leanFiles[]` uses `defCount` (not
+`definitionCount`), so the snippet matches that convention. The gallery
+`meta.json` uses `definitionCount: 2` (counting both `def` declarations,
+including the second one whose first-pattern `grep -cE '^def '` here
+returns 1 because the second def starts with `private def` or
+`noncomputable def`). If `enrich-research.ts` uses the more permissive
+regex, the snippet should read `"defCount": 2` instead. The mechanic
+running enrich-research is the authority — these snippets are guidance,
+not normative.
+
+### 3.2 Phase-3b sibling entry
+
+```json
+{
+  "path": "Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01Phase3b.lean",
+  "filename": "CantorDiagonalizationOQ01OQ01OQ02OQ01Phase3b.lean",
+  "lineCount": 173,
+  "theoremCount": 5,
+  "axiomCount": 4,
+  "defCount": 0,
+  "sorryCount": 0,
+  "isAristotle": false,
+  "githubUrl": "https://github.com/rjwalters/lean-genius/blob/main/proofs/Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01Phase3b.lean"
+}
+```
+
+Verification commands (against `origin/main` HEAD as of 2026-05-16):
+
+```bash
+F=proofs/Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01Phase3b.lean
+wc -l "$F"                                                 # → 173
+grep -cE '^(theorem|lemma) ' "$F"                          # → 5
+grep -cE '^axiom ' "$F"                                    # → 4
+grep -cE '^def '   "$F"                                    # → 0
+grep -cE 'sorry'   "$F"                                    # → 0
+```
+
+The four axioms are the genuine Easton-1970 carriers
+(`ConsistencyOfContinuumValue`, `ConsistencyOfContinuumFunction`,
+`easton_permitted_realizable_strong`, `easton_consistency_strong`),
+consistent with the gallery `meta.json` `meta.axiomCount: 4` set by
+mechanic PR #19593.
+
+### 3.3 Insertion point
+
+Within the JSON `leanFiles[]` array, sort order is roughly alphabetical
+by `path`. The two new entries should slot in like so (showing the
+adjacent existing entries):
+
+```
+...
+Proofs/CantorDiagonalizationOQ01OQ01.lean       (existing)
+Proofs/CantorDiagonalizationOQ01OQ01OQ02.lean   (existing)
+Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01.lean         ← NEW (3.1)
+Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ01Phase3b.lean  ← NEW (3.2)
+Proofs/CantorDiagonalizationOQ01OQ01OQ02OQ03.lean (existing)
+...
+```
+
+But for a fresh `enrich-research.ts` run the script will re-sort and
+re-populate; the mechanic shouldn't have to hand-insert.
+
+## §4 Auditor handoff — BUILD-VERIFY for S8
+
+S8 §4 documents 4 failed Docker attempts (2026-05-16 ~04:48–05:03 UTC,
+builds `bm1wd499v`, `b9jhcq3wu`, `b1amhd0eo`, `b5zsyn2bm`) due to host
+disk 100% (`df -h /System/Volumes/Data` showed 890Gi / 140Mi free /
+926Gi at the time; at S9 authoring time it shows 884Gi / 5.7Gi /
+926Gi — still 100%-pinned but with marginally more breathing room).
+Docker shows a `Server:` heading on `docker info` but the remainder
+times out at the daemon-level call.
+
+The safe-shipping justification S8 §4 gave (pure-deletion, no new
+elaboration obligations, the S6 ACT verified the structure at 3061
+jobs, Phase3b file unchanged) still stands; this section is purely a
+handoff so the auditor knows to circle back when the host recovers.
+
+When the disk recovers, the auditor (or any researcher) should run:
+
+```bash
+./proofs/scripts/docker-build.sh Proofs.CantorDiagonalizationOQ01OQ01OQ02OQ01
+```
+
+Expected: clean build (Phase3b not invoked by parent file's imports;
+S8 deleted only `axiom` declarations + `#check` directives + a
+docstring rewrite, none of which produce elaboration obligations).
+
+## §5 Risk inventory
+
+| Risk | Mitigation |
+|------|------------|
+| `lastUpdate` refresh masks a real freshness drop | The slug IS active per S8 ACT 6h ago — the 2026-05-08 value was a stale artifact, not a freshness signal. Refreshing surfaces reality, not a fiction. |
+| State.md head now claims S9 STATE-SYNC but no S9 PR exists yet at edit time | This S9 STATE-SYNC IS the PR — the title says so and the session memo gates it. The "shipped" status updates the moment this PR merges; future seekers see the merged audit trail in git log. |
+| Mechanic snippets in §3 could go stale if a future PR edits the Lean files | Snippets are explicitly dated and cross-referenced against `origin/main` HEAD at S9 authoring time. If a future edit changes the line counts, the mechanic running `enrich-research.ts` will overwrite anyway. |
+| Future researcher claims this slug expecting work but finds rest state | `currentState.focus` and the state.md "Open handoffs from S9 STATE-SYNC" section both clearly mark MECHANIC + AUDITOR territory; Lever B / Lever C remain available for a research re-claim but `nextAction` says "awaits seeker re-selection" so a seeker should not route a researcher here without explicit Lever-B/C scoping. |
+| `defCount` (1 vs 2) confusion in §3.1 mechanic snippet | Honest qualification given inline. Mechanic-tool is authoritative. |
+
+## §6 Honest scope — what S9 does NOT do
+
+S9 does **NOT**:
+
+- Touch any `.lean` file.
+- Touch `src/data/proofs/.../meta.json` (already mechanic-fixed in #19593).
+- Touch `src/data/proofs/.../annotations.json` or `.../index.ts`.
+- Touch `problem.md`, `knowledge.md`, or any other slug doc beyond
+  `state.md` + the new session memo.
+- Modify the slug's `leanFiles[]` array directly (mechanic territory;
+  handoff in §3 instead).
+- Run a BUILD-VERIFY for S8 (host disk-full I/O persists; auditor
+  handoff in §4).
+- Attempt Lever B (sibling bridge) or Lever C (flypitch scoping doc).
+- Close or rebase the 3 stale CONFLICTING DRAFTs (#16936, #17137,
+  #17169) — those are listed in S5/state.md as informational and
+  remain a champion/maintainer cleanup item.
+- Refresh `problem.md` or `knowledge.md` (no domain shift; rest state
+  unchanged).
+- Add `additionalFiles` to gallery `meta.json` (mechanic PR #19593
+  already did this).
+- Update `lake-manifest.json` (pin unchanged at `2df2f0150c…`,
+  Mathlib 4.26.0).
+- Make any change that requires a Docker build to verify.
+
+## §7 Acceptance criteria
+
+- [x] JSON `lastUpdate`: `2026-05-08T01:00:00Z` → `2026-05-16T15:20:00Z`.
+- [x] JSON `currentState.iteration`: `7` → `8`.
+- [x] JSON `currentState.since`: `2026-05-16T04:30:00Z` → `2026-05-16T15:20:00Z`.
+- [x] JSON `currentState.focus`: rewritten to describe S9 work + retain S8.
+- [x] JSON `currentState.nextAction`: surfaces MECHANIC + AUDITOR handoffs.
+- [x] JSON `currentState.attemptCounts.total`: `3` → `4`.
+- [x] JSON `knowledge.progressSummary`: S9 sentence prepended; S8 retained.
+- [x] JSON `knowledge.insights`: +2 S9 items (lastUpdate drift, leanFiles omission).
+- [x] JSON `knowledge.nextSteps`: 5 items (MECHANIC + AUDITOR + 3 pre-existing Lever items).
+- [x] state.md head: Iteration `7 → 8`; new `Last Updated:` line.
+- [x] state.md Next Action: appended "Open handoffs from S9 STATE-SYNC" block.
+- [x] state.md Attempt Counts: total `7 → 8`.
+- [x] state.md Session History table: S9 row appended.
+- [x] NEW session memo (this file) with §3 ready-to-paste mechanic snippets.
+- [x] No `.lean` edits, no `meta.json` edits, no `annotations.json` /
+      `index.ts` edits, no `problem.md` / `knowledge.md` edits.
+- [ ] BUILD-VERIFY (Docker — DEFERRED, host disk 100% I/O — same blocker as S8 §4).
+
+## §8 Host context
+
+- Working dir:
+  `/Users/rwalters/GitHub/lean-genius/.loom/worktrees/researcher-6`.
+- Branch (created at S9 authoring time from `origin/main`):
+  `research/cantor-diag-oq01oq01oq02oq01-s9-state-sync-post-s8-axiomatized-stable-20260516T151635Z`.
+- Disk: `884Gi used / 5.7Gi available on 926Gi disk` (100% — Docker
+  containerd meta.db I/O failure persists since 2026-05-16 ~04:48 UTC,
+  the same blocker S8 §4 documented).
+- Docker daemon: `docker info` shows `Server:` heading but the
+  remainder times out — daemon is not fully recovered. No build was
+  attempted this session (deletion-only would not affect the proofs
+  anyway; the build pending is for S8's parent refactor, not S9).
+- Mathlib pin: `2df2f0150c…` (Mathlib 4.26.0) — unchanged from S6/S7/S8.
+- Pool entry: claimed via `claim-random` at S9 authoring time
+  (`Knowledge score: 50 (RICH)`, `Expires: 2026-05-16T16:42:15Z`).
+  Will release post-PR open via `claim-problem.sh release`.
+
+## §9 References
+
+- S6 ACT — PR #19112 (merged 2026-05-15T22:58:47Z), shipped Phase3b
+  sibling file with `ConsistencyOf*` predicates + strong-Easton axioms.
+- S7 PREP — PR #19174 (merged 2026-05-14), doc-only Lever A residual
+  scoping memo.
+- S8 ACT — PR #19462 (merged 2026-05-16T08:54:45Z), parent-file
+  refactor + Part III docstring rewrite; build-verify deferred.
+- Mechanic fix-meta — PR #19593 (merged 2026-05-16), added
+  `axiomCount: 4` and `additionalFiles: [Phase3b]` to gallery
+  `meta.json`. Did NOT update research-JSON `leanFiles[]`.
+- S8 session memo — `sessions/2026-05-16-s8-act-lever-a-residual.md`.
+- Auto-memory predecessor pattern this S9 follows: "Researcher —
+  COMPLETED slug w/ predecessor STATE-SYNC narrowly-scoped to 3
+  fields, missing iter bump + nextSteps cleanup + sessions/ bootstrap
+  + leanFiles drift; ship S{N+1} STATE-SYNC w/ mechanic handoff for
+  leanFiles (don't self-edit leanFiles[])". This slug isn't quite
+  COMPLETED — it's `phase: ACT` at an axiomatized rest state — but the
+  drift shape and the mechanic-territory `leanFiles[]` handoff
+  pattern carry over directly.