perf(ABCExceptions): simplify geometry and index-set proofs

[Vilin97]

ABCExceptions repeatedly normalizes large arithmetic expressions merely to rearrange sums. This replaces that work with distributivity, associative/commutative equality, and small targeted ring identities, preserving every existing elaborated declaration.

Selected project: ABCExceptions (abc-exceptions). Base: 1b904d772c79dee8eb9b9611308dba2262fd45b5. Head: ebd629c8e300cf75e0252542a7936bb7823b9269. Lean v4.34.0; Mathlib 5ed2965256430c3649e86755f9576b54eca72435 (unchanged).

Changes and selection evidence

• GeometryBound.subSums: replace fourteen ring_nf calls with explicit mul_add rewriting and ac_rfl; preserve all seven mathematical cases and their chosen finite sets.
• GeometryBound.s21_application_basic: normalize finite sums with an explicit simp list, then prove the additive and maximum arguments separately instead of normalizing two hypotheses and the entire conjunction.
• GeometryBound.left_comm / right_comm: prove the required permutations by associativity/commutativity.
• FourierBound.symm: restrict simplification to max_comm.
• mem_indexSet: replace aesop with explicit cast and conjunction simplification.

Among inspected candidates, ABCExceptions offered two ~1,600-line proof modules initially building in 7.2–7.4 s, compared with Apportionment's 2.3 s main module; ChannelCapacity's inspected imports were already focused. Profiling identified the repeated normalization above. This is a focused proof optimization, with two files changed and no statement, definition, import, notation, namespace, metadata, or gate changes.

Semantic invariant

645/645 pre-existing declarations match exactly; none removed or changed. The head has 653 declarations: eight additional compiler-generated simplifier lemmas, with no reused names.

Before editing, a standalone Lean environment inspector recorded all project declarations, including private and generated declarations. It imports at .private level and records structural Expr representations of fully elaborated types, universe parameter lists, names, declaration kind, safety/partial flags, exported visibility, reducibility/inductive/constructor/recursor metadata, and all non-theorem values. Only theorem proof bodies are excluded. After rebuilding, the comparison requires equality for every field of every base record and reports all additions separately. All eight additions are _simp_... helpers supporting the optimized proofs. The source statement comparison also reports no changed, renamed, added, or removed source declarations.

Manifest SHA-256:

• base: 780598d516394c1e5a56600f969b7904fb83e674105c9f03148d41166cd4e7e3
• head: b468735c2be2d4593221bb1adb7337cedff4e928b0a31249a1cceda8bdf490e2

Measurements

Same Azure VM, dependency cache and pinned toolchain. Each project trial deletes only ABCExceptions' build outputs under .lake/build/lib/lean/LeanPool/ and .lake/build/ir/LeanPool/, then runs lake build LeanPool.ABCExceptions. Dependencies remain warm; these are project-clean builds, not cold dependency builds.

Measurement (seconds)	Base trials	Head trials	Median base → head
Default parallel project build	9.411, 9.498, 9.499	9.595, 9.391, 9.499	9.498 → 9.499
Isolated Section4, one Lean thread	12.420, 12.414, 12.639	11.629, 11.304, 11.453	12.420 → 11.453 (7.8% faster)

The isolated trials alternate base/head order, re-elaborate the original and optimized source copies with lake env lean -j1 --setup .lake/build/ir/LeanPool/ABCExceptions/Section4.setup.json <source>, and include process/import overhead. The setup supplies the unchanged repository options and module identity. Imports of Section4 are unchanged. No improvement in the default parallel project wall time is claimed. Its slower Section2 module remains on the critical path.

Observed raw profiler heartbeat counts (same profiler flags on both versions; these include profiling overhead and are not wall times or the scaled maxHeartbeats units):

Proof	Base	Head	Reduction
GeometryBound.subSums	28,762,155	12,542,751	56.4%
GeometryBound.s21_application_basic	15,284,562	7,534,186	50.7%
FourierBound.symm	2,264,329	104,778	95.4%
GeometryBound.left_comm	1,365,535	387,858	71.6%
GeometryBound.right_comm	1,362,782	387,712	71.5%
mem_indexSet	4,220,815	388,642	90.8%
Six-proof total	53,260,178	21,345,927	59.9%

Section4's .olean.private shrank from 6,231,032 to 5,912,664 bytes (5.1%). Imported environment closure remains 3,549 modules; no dependency-closure reduction is claimed.

Validation

• lake build LeanPool.ABCExceptions: three clean trials per revision, all passed; optimized build logs contain no warnings/errors.
• lake exe runLinter LeanPool.ABCExceptions: passed, including all imported project declarations and slow linters.
• lake exe lint-style LeanPool.ABCExceptions: passed; an additional scoped root checks all seven project source files.
• lake exe mk_all --check: passed, no generated index changes required.
• python3 -m lean_pool.quality --repo <project-scope>: passed all existing checks, including source gates, size limits, project/card validation, axiom and environment-backdoor audits. The scope contains byte-identical copies of all seven project source files, its unmodified registry entry and repository configuration, a generated project-only root, and the same compiled project artifacts. No checker or gate was modified. The full pool was not rebuilt/audited locally.
• Standalone Lean.collectAxioms audit over all 653 declarations: only Classical.choice, propext, and Quot.sound permitted; passed.
• Declaration manifest comparison and repository source-statement comparison: passed.
• git diff --check: passed.
• lake shake --force --keep-public --explain LeanPool.ABCExceptions: inspected. The existing module structure is retained. Shake suggests only two pre-existing redundant public tactic imports around the custom positivity extension; these are retained for public/metaprogram stability. --force bypasses shake's whole-workspace cache prerequisite, after the targeted project build; it does not bypass compilation or a repository gate.
• origin/main was fetched and verified equal to the recorded base immediately before commit. Work is isolated from /data/lean-pool; the original checkout was left unchanged.

Profiler command for each changed file:

lake env lean -Dtrace.profiler=true -Dtrace.profiler.useHeartbeats=true \
  -Dtrace.profiler.threshold=100000 LeanPool/ABCExceptions/Section4.lean
# Repeat for Section2.lean at each revision.

The older count-heartbeats linter under-reported module proof work in exploration; those results are excluded. Remaining limitations are the unchanged parallel build wall time, unchanged imports, profiler overhead, and lack of a local full-pool build. CI remains required; this PR is not merged automatically.

Reproducible declaration-manifest inspector

Save this outside tracked content as Manifest.lean, then run lake env lean --run Manifest.lean base.jsonl on the built base and ... head.jsonl on the built head. Match rows by name; every base row must be identical in head. Additional rows must be inspected separately.

import Lean

open Lean

deriving instance Repr for ReducibilityHints

def kind (c : ConstantInfo) : String :=
  match c with
  | .axiomInfo _ => "axiom"
  | .defnInfo _ => "definition"
  | .thmInfo _ => "theorem"
  | .opaqueInfo _ => "opaque"
  | .quotInfo _ => "quotient"
  | .inductInfo _ => "inductive"
  | .ctorInfo _ => "constructor"
  | .recInfo _ => "recursor"

def details (c : ConstantInfo) : String :=
  match c with
  | .defnInfo v => s!"{repr v.hints};{repr v.safety};{repr v.all}"
  | .thmInfo v => reprStr v.all
  | .opaqueInfo v => reprStr v.all
  | .inductInfo v =>
    s!"{v.numParams};{v.numIndices};{repr v.all};{repr v.ctors};{v.numNested};{v.isRec};{v.isReflexive}"
  | .ctorInfo v => s!"{repr v.induct};{v.cidx};{v.numParams};{v.numFields}"
  | .recInfo v =>
    s!"{repr v.all};{v.numParams};{v.numIndices};{v.numMotives};{v.numMinors};{v.k};" ++
      reprStr (v.rules.map fun r => (r.ctor, r.nfields, reprStr r.rhs))
  | _ => ""

def main (args : List String) : IO Unit := do
  initSearchPath (← findSysroot)
  let env ← importModules #[{ module := `LeanPool.ABCExceptions }] {} (level := .private)
  let exported ← importModules #[{ module := `LeanPool.ABCExceptions }] {} (level := .exported)
  let mut declarations : Array (Name × Name) := #[]
  for (mod, data) in env.header.moduleNames.zip env.header.moduleData do
    if (`LeanPool.ABCExceptions).isPrefixOf mod then
      for name in data.constNames do
        declarations := declarations.push (name, mod)
  declarations := declarations.qsort fun a b => a.1.toString < b.1.toString
  let out ← IO.FS.Handle.mk (args.head!) .write
  for (name, mod) in declarations do
    let some c := env.find? name | throw <| IO.userError s!"missing {name}"
    let record := Json.mkObj [
      ("name", toJson name.toString), ("module", toJson mod.toString),
      ("kind", toJson (kind c)), ("universes", toJson (reprStr c.levelParams)),
      ("type", toJson (reprStr c.type)), ("unsafe", toJson c.isUnsafe),
      ("partial", toJson c.isPartial), ("exported", toJson (exported.contains name)),
      ("details", toJson (details c)),
      ("value", toJson (if c.isTheorem then "PROOF" else reprStr (c.value? true)))]
    out.putStrLn record.compress
  IO.println s!"Recorded {declarations.size} declarations; {env.header.moduleNames.size} modules"

[greptile-apps]

Advisory cross-file review against Lean Pool's supervisory rubric. This is not by itself a significance, source-verification, or merge verdict.

[Low risk] Simplifies proof tactics in mathematical theorems.

No new merge-blocking issue was identified in the latest update.

Summary

The PR replaces broad normalization tactics with targeted proof steps in two ABCExceptions modules. The changes since the previous review only bring in upstream-generated metadata already present at the current base.

• Existing declaration statements and project metadata are unchanged by the PR.
• No new issue was identified in the latest update.

_{Reviews (19) · Last reviewed commit: "Merge remote-tracking branch 'origin/mai..."}

[github-actions]

Proof profile (new / modified Lean files)

Statement changes

✅ No statements changed — all 220 tracked declarations across 2 modified files kept their type; only proofs / definition bodies changed.

Statements are compared textually against the merge base (comments and whitespace ignored; by proof terms embedded in a type are treated as proof-irrelevant), the same method as physlib's /check-golf. Anonymous instances and examples are not tracked.

Compile cost of modified files — base → head

Heartbeats: 2,068 → 2,068 (+0, +0.0%). Declarations: 151 → 151.

Per-file wall sum: 39.0 s → 41.2 s (+5.4%). Wall clock is measured under parallel load and is noisy; heartbeats are deterministic and are the regression signal.

Files: 2 compared — 0 cheaper, 0 costlier, 2 within noise (threshold: |Δ heartbeats| ≥ 1,000 and ≥ 1%).

Both sides are elaborated against the merge-base build of the pool — sound when only proofs and definition bodies change; a file whose statements changed may fail there and is flagged ⚠. Heartbeats come from Mathlib's linter.countHeartbeats, in maxHeartbeats units. Δ lines counts added/deleted lines from this PR diff.

File	Δ lines	HB base	HB head	Δ HB	Δ HB %	Wall base (s)	Wall head (s)
LeanPool/ABCExceptions/Section2.lean	+2/-2	430	430	+0	+0.0%	19.09	20.34
LeanPool/ABCExceptions/Section4.lean	+31/-13	1,638	1,638	+0	+0.0%	19.96	20.83
Total	+33/-15	2,068	2,068	+0	+0.0%	39.0	41.2

Advisory only — never blocks merge. Full log uploaded as the proof-profile artifact.

[Vilin97]

🤖 LLM review — refactor (gpt-6-astra)

Reviewed head: 6d44e12e44d5d46daaaa867a3722be4b80a355d9

Verdict: ✅ approve

This targeted proof rewrite replaces broad normalization and search with explicit simplification, associativity/commutativity, and small ring identities. All seven geometric cases, finite-set witnesses, and intermediate bounds remain intact. Separating the additive and maximum equalities makes the longer proof easier to debug, while explicit simp lists reduce dependence on global simplifier behavior. The stored profile shows unchanged heartbeats and noisy wall-time variation, without a demonstrated regression. Builds and finer timing claims were not independently reproduced because this checkout lacks dependencies.

Aspect	Value
Scope	targeted tactic rewrite
Introduces tech debt	✅ no
Maintainability	✅ improved
Brittleness	✅ more_robust
Risk	✅ low

The refactor makes algebraic steps and proof dependencies more explicit without losing mathematical structure or introducing actionable maintenance debt.

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Tokens: 530,987 in / 2,668 out · Tier: codex-subscription · Effort: xhigh · Billing: Codex subscription quota (no API credits) · Estimated cost: $10.8198 (Standard API equivalent; uncached input) (long-context rate)
Automated review against .github/REFACTOR_REVIEW_RULES.md. Disagree? Reply on the PR; rules can be updated in a PR of their own.

[Vilin97]

Re-reviewed 118a0796ac2ce387bc72fd39ce459a1e4101e6e5: maintainer blocker resolved; required CI/review remains pending.

The complete two-file refactor preserves all seven geometric cases, their witnesses and statement signatures. Targeted algebra retains the proof structure; no actionable source defect remains. Another worker pushed a tree identical to the locally validated integration immediately before this cycle's push check. The push was stopped and that exact remote head was re-reviewed; no duplicate commit was created.

Targeted warning-free project build, actual mk_all --module --check, Mathlib linters, style, and the unchanged repository quality checker all pass. Quality/trust checks covered byte-identical project copies with unchanged Lake/linter configuration, including the axiom and compiled-environment backdoor audits; this is project-scoped validation, not a new full-pool pass.

The older automation hold is now contained: the existing needs-manual-rebase label excludes this branch from the registry updater and is retained. The parser defect still reproduces and has its own repair in #532. Removing needs-maintainer does not re-enable that updater. No per-PR human decision or author change request remains. Ordinary full CI, documentation and the configured review must pass on this exact head before any protected merge; no merge was attempted.

[Vilin97]

Reviewed head: a4b50a4698ff390709cbb584af7f9685ff1e8153

Verdict: approve. Posted as a comment review because GitHub does not permit the authenticated PR author to submit an approving review.

The ABCExceptions refactor replaces repeated ring normalization with distributivity and associative/commutative equality, preserving all seven subsum cases, their finite-set witnesses, and the intermediate bounds. The s21 argument now separates ordinary addition from the maximum's argument, and the remaining simplification dependencies are explicit. Full diff and affected-source review found no actionable regression. Exact-head CI passed the full build, index check, linters, style, and repository quality checks; these were inspected rather than rerun locally. The advisory profile reports 2,068 to 2,068 heartbeat units. Its 39.0 to 41.2 second parallel wall sum is noisy and establishes neither a material regression nor a project-wide speedup.

Assessment	Result
Scope	targeted proof optimization
Introduces technical debt	No
Maintainability	Improved
Brittleness	More robust
Risk	Low

The local algebra is easier to diagnose and retains the proof's useful structure, with no source change required before merging.

Findings: none.

Validation evidence: full build and gates, proof profile.

[Vilin97]

Daily disposition: needs maintainer — protected merge operation

Reviewed exact head 263e10ce5b072981a27c2571d4164da1a4bba170. The two-file refactor preserves the seven geometric exception estimates and reuses explicit algebraic simplification. It makes no claim to prove the abc conjecture. The complete source/dependency review and recovered repairs were reconciled through the lossless main integration; fresh protected CI remains the integration authority.

Build project: pending/not yet reported, Content / non-content separation: SUCCESS, Documentation preflight: SUCCESS. These are observed check states, not an assertion that unfinished checks passed.

The remaining authority boundary is operational: this repository has allow_auto_merge=false, and GitHub rejected enablePullRequestAutoMerge with “Auto merge is not allowed for this repository.” The maintainer must make protected queuing available through an authorized repository-setting decision, or remove this label and perform a normal squash merge after the required checks and current-base integration pass. This cycle does not change repository settings or bypass protection. No unresolved substantive author-actionable finding justifies another change request or closure; the label is not for draft status, missing profiling, or an old advisory score.

[Vilin97]

Reviewed exact head c0eb46db296ad69bb034d6d46b124aa5b2a11e27 under the refactor rules. The full two-file proof rewrite preserves the seven ABC-exception estimates and the recorded declaration types; this is not a proof of abc. The recovered structural declaration audit and alternating timing measurements remain applicable because the only new integration diff is main’s README/NOTICE refresh. The rewrite replaces repeated normalization/search with explicit algebraic steps. Current required build, separation and documentation checks are green, and the full build/lint/quality job passed. The configured refactor review approves the identical proof files; all review threads are resolved. No substantive blocker remains. Disposition: normal protected squash merge. This comment substitutes for GitHub’s unavailable formal self-approval.