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/exposition-swarm-drain — Milnor-exposition audit→resolve drain

Bring every narrative block up to the Milnor exposition standard (milnor-exposition-standard skill), at scale, autonomously, without hand-editing block by block.

0. When to use

“swarm the exposition”, “Milnor-audit the paper”, “drain narrative quality”, “run the audit+resolve swarm”, “clean up the prose across chapter X / the whole paper”.
The paper has ~2,000 narrative blocks; this is the mechanism for processing them in bulk while keeping each edit conservative and each batch a reviewable PR.

1. The pattern (three roles)

                    ┌─────────────── foreground session (you) ───────────────┐
   enumerate  →     │  batch the blocks → launch swarm → auto prepare-merge   │  → repeat until drained
                    └────────────────────────────────────────────────────────┘
                              │ each batch
                              ▼
        ┌──────────── swarm agent (one per grouped batch) ────────────┐
        │  own branch → AUDIT each block (Milnor H1–H8 + defects)     │
        │            → RESOLVE flagged blocks (math-preserving edits) │
        │            → commit → push → open PR → return PR#           │
        └─────────────────────────────────────────────────────────────┘

Foreground (this session) — enumerate + batch the blocks, launch the swarm, then auto prepare-merge each swarm PR (via /prepare-merge-auto). Runs the drain loop until every batch is merged or explicitly parked. Does not stop for check-ins — go until completely drained (owner directive 2026-07-04).
Swarm agent (grouped batch) — each agent owns one branch and one grouped batch of blocks (not one block per agent — that over-creates PRs; see §3). It audits and resolves its whole batch, commits, pushes, opens a PR, and returns the PR number + a summary.
Auto-merge — the foreground runs /prepare-merge-auto on each returned PR: rebase, one-voice + lean checks, request reviews, resolve mechanical comments, merge (rebase-merge default). Merge is pre-authorized for this drain (owner directive); architectural review comments still escalate via AskUserQuestion.

2. The audit rubric (what each agent scores)

Score each block on the eight Milnor hallmarks, 0–2 each (authoritative: expo-milnor-clarity spec, docs/requirements/2026-07-04-folio-assistant-proof-narrative-checkers.md §5A (no longer in this repository); author-facing: milnor-exposition-standard.md):

	Hallmark
H1	Economy — every sentence load-bearing
H2	Concrete before abstract
H3	The “Why” precedes the “What”
H4	Uncluttered notation
H5	Linear argument
H6	Prose carries the argument
H7	Surgical cleanliness / right-tool framing
H8	Respect for the reader’s time and intelligence

Gate (owner ruling 2026-07-04, STRICT): T = ΣHi. T = 16 → pass; 12 ≤ T ≤ 15 → warn; T ≤ 11 → fail. Perfection is the bar.

Also flag the deterministic narrative defects (independent of the score):

proof-sketch-vs-kind — a provable-kind block presenting “Proof (sketch)”/an incompleteness admission.
proof-no-lean-mention-in-prose — prose naming the Lean/sorry/Mathlib apparatus.
proof-cross-block-duplication — a proof authored twice across sibling blocks.

3. Batching (grouped, review-sized)

One agent per grouped batch, batch = a chapter (or a sub-cluster of a large chapter). Never one-block-per-agent — that fragments into hundreds of PRs and violates the “minimize PR creation” rule (AGENTS.md).
Size cap: ≤ ~40 blocks per batch AND ≤ 49 files per resulting PR (the Gemini review limit). Split big chapters into coherent sub-clusters by section or topic stem. Get the actual per-chapter counts from the folio rather than a remembered table — they drift:
```
for d in content/*/*/; do
  printf '%s %s\n' "$(ls "$d"*.md 2>/dev/null | wc -l)" "$d"
done | sort -rn | head
```
Concurrency: a “small swarm” is ≤ ~8 batch-agents live at once (the Workflow cap is min(16, cores−2)); launch chapters in waves.
Branch name: each agent uses claude/expo-milnor-<chapter>-<utc-ymd>.

4. Conservative-edit discipline (STRICT — the resolve half)

Resolve agents edit .md prose only. They must not:

change any mathematical statement, definition, equation, hypothesis, or proof step;
invent mathematics or fake a proof;
convert a “Proof (sketch)” to “Proof” unless the complete argument is already present (else leave it and set needs_owner).

DO-NOT-TOUCH-DERIVATIONS rule (STRICT, added 2026-07-04 after a live incident). A resolve agent must not edit the prose of a derivation, computation, or proof body at all — not even to “tighten” or “clarify” it. Polishing a derivation can make a wrong one read more cleanly and authoritative, which is worse than leaving it rough. (Incident: the swarm reworded a frobenius-relation-su2 derivation that was mathematically false — it conflated the Hopf comultiplication with the Frobenius comultiplication — and the cleaner prose lent the error false authority; Gemini caught it, PR #3301.) Therefore:

Only edit the surrounding exposition — the intro/motivation sentence, the notation-introduction, a redundant restatement outside the derivation, the closing interpretation. Leave every derivation / computation / proof step verbatim.
If a derivation itself reads poorly, do not fix it — set needs_owner with a note. A resolve agent is not authorized to verify or repair mathematics.
The audit stage may score H5/H6/H7 low on a muddy derivation and flag it, but the flag routes to needs_owner, not to an autonomous prose rewrite of the derivation.

They may: strip Lean/sorry/apparatus sentences; tighten wordy prose outside derivations; reorder so motivation precedes machinery; introduce a symbol at first use; de-duplicate a glyph. Anything requiring real math — or any edit that would touch a derivation body — is returned as needs_owner with a reason, never auto-faked or auto-polished.

The review layer is the backstop, not the gate. Every swarm PR still goes through /prepare-merge-auto (Gemini + Copilot) before merge; that layer caught the incident above. Do not merge a content batch on the swarm’s self-check alone.

Every resolve agent runs the render sanity battery before committing (balanced $/$$/{}, no \operatorname → \mathrm, no list-hijack line starting +/-/* inside $$, align-family fenced as ```tex) per markdown-render-check, and the block validates (bun run scripts/run-validate.ts content/<paper>) before the PR opens.

5. Foreground drain loop

blocks = enumerate_narrative_blocks(paper)          # kind ∈ narrative, ≥40 words
batches = group_into_batches(blocks)                # §3 — per chapter / sub-cluster
for wave in chunks(batches, 8):                     # ≤8 agents live
    prs = swarm(wave)                               # §6 workflow → [PR#, …]
    for pr in prs:
        prepare_merge_auto(pr)                      # rebase, checks, reviews, merge
# repeat until batches exhausted — do NOT stop for check-ins

Stop conditions: the batch list is exhausted (drained), OR the owner says stop, OR a batch’s needs_owner items require a decision that blocks its PR — park that one PR (comment why) and keep draining the rest.

6. Workflow skeleton (audit → resolve, pipelined per block within a batch)

A batch-agent may itself run this inner pipeline over its blocks. The canonical script (iterate via scriptPath, not by resending):

export const meta = { name: 'milnor-audit-resolve', description: '…',
  phases: [{title:'Audit'},{title:'Resolve'}] }
const blocks = Array.isArray(args) ? args : JSON.parse(args)   // args may arrive as a string
const results = await pipeline(blocks,
  (path) => agent(AUDIT_PROMPT(path),   {phase:'Audit',   agentType:'general-purpose', schema: AUDIT_SCHEMA}),
  (audit, path) => {
    if (!audit || (audit.verdict==='pass' && !audit.defects.length)) return {block:path, edited:false, skipped_reason:'clean'}
    if (audit.needs_owner) return {block:path, edited:false, skipped_reason:'needs owner: '+audit.needs_owner_reason}
    return agent(RESOLVE_PROMPT(path, audit), {phase:'Resolve', agentType:'general-purpose', schema: RESOLVE_SCHEMA})
  })
return results.filter(Boolean)

agentType: 'general-purpose' so resolve agents have Edit/Write.
Schemas force structured audit (scores/verdict/defects/fix_plan/ needs_owner) and resolve (edited/changes/preserved_math/skipped_reason).
pipeline not parallel — each block flows audit→resolve with no barrier; a warn block resolves while another is still being audited.
Guard args — it can arrive as a JSON string; parse defensively.

7. Interaction with the flag-preservation guard

The Milnor gate can fail, so its verdicts are real blocking flags. Per qa-flag-preservation-audit.ts (PR #3289), a distrusted expo-milnor-clarity verdict must be re-audited, never n/a-cleared. Keep the per-block score vector in the sidecar so a re-review re-scores rather than re-guesses.

8. Reporting

At the end of each wave, report a compact table: block · kind · Milnor total · verdict · defects · edited?/needs_owner. At full drain, report the score distribution (how many pass/warn/fail before vs after) and the list of needs_owner blocks for the author.

Cross-references

Rubric spec: docs/requirements/2026-07-04-folio-assistant-proof-narrative-checkers.md §5A
Author voice: skills/authoring/authoring-core/milnor-exposition-standard.md
Merge pipeline: skills/sdlc/sdlc-core/prepare-merge-auto.md
Sister drain: .claude/skills/local/integration-backlog.md
Flag guard: pipeline/qa-flag-preservation-audit.ts