Repository navigation
feat: preserve the completed zeta(5) irrationality formalization - #540
Conversation
|
Advisory cross-file review against Lean Pool's supervisory rubric. This is not by itself a significance, source-verification, or merge verdict. [Low risk] Adds a mathematical formalization library for zeta function irrationality. No outstanding finding from this review prevents merging this PR. SummaryThis PR adds a completed Lean formalization of the irrationality of
Reviews (7) · Last reviewed commit: "Merge remote-tracking branch 'origin/mai..." |
|
/review The current head is 73fe1f4. Local project build, style, all slow linters, complete axiom/option audits, and original-type compatibility checks pass; full repository CI is still running and remains required before merge. Please review the complete source in bounded portions. The tested certificate-regeneration companion is #541; the unused reference-only normalizer identified by Greptile has been removed. The PR body records the quantitative deviation from the paper and the measured 979.67 s → 580.80 s clean-build improvement. |
|
{ |
🤖 LLM review (
|
| Rubric | Verdict | Bottom line |
|---|---|---|
| Faithfulness | ✅ pass |
All three headline results match the card, including unconditional irrationality of Mathlib’s riemannZeta 5. |
| Novelty | ✅ pass |
Searches of pinned Mathlib and existing pool sources found no duplicate of the ζ(5) irrationality theorem or its determinant-polynomial estimate. |
| Significance | ✅ pass |
Worth pooling: substantial research mathematics with maintainable certificates; generated tables occupy 327,764 of 347,381 implementation lines (94.4%), use ordinary arithmetic tactics and project analytic lemmas, and all 118 modules reproduce byte-for-byte using the archived tooling in companion #541. |
| Sources | ✅ pass |
Fauzan’s Theorem 1.1 supports the irrationality claim, numerical variants are explicitly labelled, and Firsching’s prior formalization is credited. |
| Code quality (advisory) | ✅ pass |
The development is competently modularized around reusable valuation, energy, and certificate lemmas; no material code-quality issue warrants maintainer discussion. |
| Aspect | Value |
|---|---|
| Proves the claim | ✅ proves_it |
| Assumed, not proved | The irrationality theorem and main estimate have no extra hypotheses. The reusable criterion assumes eventual positive polynomial evaluations and decay for every positive natural denominator, exactly as disclosed in the card. |
| Matches cited source | ✅ matches |
| Fit | ✅ good_fit |
| Level | research |
| Branch | analytic number theory |
| Mode | mixed |
| Code quality | 3 / 5 |
Statement check: The Lean proves that riemannZeta 5 equals the complex coercion of an irrational real, and establishes the stated eventual degree-37n polynomial estimate with a positive decay constant.
The project establishes irrationality of ζ(5), supported by substantial developments in polynomial approximation, Hankel determinants, logarithmic energy, and prime-adic bounds.
Tokens: 5,366,532 in / 36,288 out across 5 model calls · Tier: codex-subscription · Effort: xhigh · Billing: Codex subscription quota (no API credits) · Estimated cost: $110.0522 (Standard API equivalent; uncached input)
Each rubric is an independent review against .github/review-rubrics/ on top of .github/REVIEW_RULES.md. Disagree? Reply on the PR; rules can be updated in a PR of their own.
CI was not green for this commit at review time; this review does not replace CI.
…ized' into codex/daily-zeta5-20260927-optimized
|
/review Please refresh the completed review of 73fe1f4 to current head b00b44f. Both concrete quality findings are repaired:
The complete project rebuilt with zero warnings, generated indexes pass, all 210 source modules pass style/static quality. The fresh clean measurement, full slow-linter pass, and compiled trust audit are running; final CI remains mandatory. All table proof bodies are unchanged. Companion #541 is being refreshed to reproduce the final header changes byte-for-byte, retaining its tested renderer and exact certificate data. No policy or waiver changed. |
|
/review Please review exact head |
|
/review The current head adds only citation clarifications to the previously measured and audited proof. The parallel daily-review job's valid 715bb26 commit is preserved. I checked the primary PDF's Section 6 and added the remaining variant labels for (6.9) and (6.14): All five affected files have identical comment-stripped code to b00b44f. Full incremental project build is warning-free; all-module style, changed-module slow linters, static checks and indexes pass. The final clean measurement and paired profiles are recorded in the PR body, including the worse final wall time; no uniform wall-time improvement is claimed. Full compiled audits are being refreshed and current CI remains required. The 118 generated certificate files are unchanged, so companion #541 still reproduces them exactly. |
|
Disposition: needs-maintainer — protected merge operation. Reviewed exact head The unconditional ζ(5) irrationality theorem is complete and significant. All changed files, endpoint/dependency closure and bounded certificate slices were audited. The generator reproduced all 118 generated modules; trust/declaration checks passed. The source-variant constants are now explicitly disclosed, including the comment-only follow-up at this head. The stronger paper decay-rate/irrationality-exponent constants are not claimed. Repair validated: Labeled the different sum/integral, regularization and real-bound constants as source variants; the subsequent author follow-up extends those annotations, with executable Lean unchanged. The targeted build, declaration/style linters, and source-scoped trust/quality audit passed. Module profiles are recorded; shared-host timing is not treated as a deterministic performance guarantee. Protected-check snapshot: Build project: not reported; Content / non-content separation: SUCCESS; Documentation preflight: SUCCESS; GitHub merge state Exact maintainer decision: Authorize repository protected auto-merge, or arrange serialized current-main integration and normal protected merging. There is no remaining material mathematical/code blocker supporting requested changes or closure; current protection prevents immediate merge and automation cannot change repository settings under this task. Remove this label before merging. |
Proof profile (new / modified Lean files)
This build covers the changed modules and their dependency cones on top of the restored cache. The serial per-file sums below are useful for ranking slow files, not as a build budget. Total heartbeats: 62,978 maxHeartbeats units across 211 files (347,379 added LOC). Sum of Count-heartbeats wall-clock total: 9438.33 s. Repeated import cost inside Heartbeat values come from Mathlib's LOC counts added lines in the profiled Lean files from this PR diff.
Aggregate phase totals
Slowest changed modules (from
|
| Changed module | Lake time |
|---|---|
LeanPool.Zeta5Irrational.Growth.InnerTable |
863.00 s |
LeanPool.Zeta5Irrational.Table.Intervals |
249.00 s |
LeanPool.Zeta5Irrational.Growth.OuterTable |
239.00 s |
LeanPool.Zeta5Irrational.Table.U55 |
165.00 s |
LeanPool.Zeta5Irrational.Table.U54 |
165.00 s |
LeanPool.Zeta5Irrational.Table.U53 |
158.00 s |
LeanPool.Zeta5Irrational.Table.U51 |
152.00 s |
LeanPool.Zeta5Irrational.Table.U52 |
151.00 s |
LeanPool.Zeta5Irrational.Table.U50 |
146.00 s |
LeanPool.Zeta5Irrational.Table.U48 |
146.00 s |
LeanPool.Zeta5Irrational.Table.U49 |
145.00 s |
LeanPool.Zeta5Irrational.Table.U44 |
143.00 s |
Comment truncated to fit GitHub's 64 KB limit. This PR profiles 211 files; the per-file table shows only the 211 hottest by heartbeats. The full table and raw
lean --profileoutput for every file are in the run's step summary andproof-profileartifact.
Advisory only — never blocks merge.
Proves that Mathlib's
riemannZeta 5is an irrational real number. This imports Moritz Firsching's completed Zeta5 development, following Aabir Fauzan's September 17 preprint, together with its reusable polynomial irrationality criterion, Andréief identity, moment formulas, logarithmic-energy machinery, and prime-adic determinant bounds.2c80b320d06b4395605edbd413649d19094507afis dated September 23, 2026, 12:22:05 UTC; releasev4.34.0-rc1followed at 20:14:14 UTC. Public announcement: https://x.com/AlexKontorovich/status/2102870642555269554 (September 23, 21:20:05 UTC). The acquisition window is September 20, 10:56:43 UTC through September 27, 10:56:43 UTC, end exclusive. The September 17 paper alone would not qualify; the completed formalization does.mix: upstream explicitly declares manual formalization informalization.yaml; this port includes substantial AI proof refactoring. Moritz Firsching's authorship and copyright are retained.The dependency closure contains 208 upstream modules from the dependency closure of
Apery.Mainafter removing unused reference normalization scaffolding, renamed toZeta5Irrational, one new reusable upper-certificate helper, and the project entry module. It reusesMooreBound.chebyshev_asymptotic; no second PNT library, upstream challenge wrappers, numerical experiments, or CI code is imported. Registry/history and open/merged PR/issue checks found no duplicate. The existing zeta(3) project proves a different special value.The card explicitly distinguishes the proof from the preprint's stronger numerical claim: the formalization uses cutoff 400, full rank loss, direct class-wise partial fractions, and the positive decay rate
-800*(Aeff + U), rather than asserting the paper's rate 139/5. The unconditional final irrationality theorem has no extra hypotheses.Ported to the repository's exact Lean 4.34.0 and Mathlib
5ed2965256430c3649e86755f9576b54eca72435. Changes include module/public-import boundaries, targeted imports, removal of every resource override and diagnostic command, warning repairs, and proof decomposition to satisfy existing size limits. No gate, review rule, workflow, or waiver is changed.Measured optimization work:
b00b44fc5Command:
lake build LeanPool.Zeta5Irrational.Main, deleting every project module trace, with warm Mathlib/MooreBound and default Lake concurrency on the shared Azure VM. The final run compiled all 209 retained implementation modules without edits during execution; the removed obsolete module's trace was also cleared. The entry module was then rebuilt. Final user CPU is about 20% lower and maximum RSS about 22% lower than baseline, but the final wall time is worse. Shared VM load and parallel scheduling limit causal interpretation of wall time. GNU time's maximum RSS is a process maximum, not summed concurrent memory.An earlier optimized proof revision (
cb12fc3e5) measured 580.80 s wall / 8219.64 s user / 7677700 KiB. That remains historical evidence and is not presented as the final revision's timing. Earlier paired Common and 16-certificate profiles improved 4.12→2.84 s and 5.29→4.14 s, respectively.The final import cleanup was also checked with paired single-thread profiles (
lake env lean -j1 --profile) using identical proof bodies and warm dependencies. Constants improved 1.66→1.13 s wall, 0.98→0.65 s user, and 1752136→920028 KiB. The first three inner-table proofs stayed comparable: 18.98→18.51 s wall, 18.27→17.90 s user, and 1969664→1711136 KiB. No further material safe proof simplification was evident from those profiles.The optimization factors 6,396 arcsine certificates through two general lemmas without changing their statements; replaces repeated real-arithmetic expansions by exact rational certificates checked with
decide +kernel; splits large interval proofs; simplifies 1,242 interval-count branches; and removes thousands of irrelevant imports. The rational certificates use kernel reduction, not native execution.Generated tables account for approximately 94.4% of the 347,381 source lines after style wrapping (118 files). Merged companion tooling PR #541 preserves exact integer parameters and 461 shared proof templates that regenerate all 118 modules byte-for-byte. Every output hash matches this import. The tool reproduces the preserved certificates, not the original numerical search or stronger bounds. Its Python suite passes all 490 tests. The original upstream generators remain linked for search provenance; they do not reproduce this port. The imported Lean is the canonical certificate set. It uses ordinary arithmetic proofs and the project's analytic certificate interface, rather than serialized Lean terms or compiler internals. No external generator is needed to check the result.
Final review cleanup at
b00b44fc50beb974417bfdff2898aeedd83cfdderemoves the unusedNormalization/InnerDatasubsystem and recurring unrelated import bundles. The unchangedvSKdefinition now lives in Legendre;vS_eqstates its valuation formula directly, without the two redundantrflbridges. Every generated certificate proof body is unchanged.Final local validation:
lake exe mk_all --module --checkpasses.37c58c2b1reproduces all 118 files byte-for-byte at this commit; Ruff and all 490 Python tests pass. The content PR changes no Python.Upstream build and Comparator passed at the pinned revision. The upstream statement also matches the attributed Formal Conjectures benchmark; this import contains the completed proof closure, not its open challenge wrapper. The primary PDF's Theorem 1.1 and stronger numerical claim were checked directly; its separate bound on the irrationality exponent is not claimed here.
Current CI 36331168268 passes every required check on main-integrated head
c0b7f368f245292c8165fd86508ca73dc99e5b1d. Greptile reviewed 212 files with zero comments. GPT approved all five rubrics atf0a9f24e9; the complete PR diff is byte-identical after main integration. The separate thorough review approves the current head, all threads are resolved, and GitHub reports CLEAN. No gate or protection bypass is used.Citation follow-up: preserved the parallel reviewer’s
715bb2622corrections and added explicit (6.9)/(6.14) constants inf0a9f24e94702d0639775ed313b88c0ad4b8863d. The final five files differ from measuredb00b44fc5only in comments; the full compiled declaration inventory is identical. The warning-free rebuild, all 15 slow linters, static/style/index checks and full compiled trust audit pass again. All 118 archived generated files are unchanged. Content CI36327012420passed before main integration, and current CI36331168268also passes. Tooling CI36326982656passed before #541 merged as91d0ec39f. The complete before/after PR diff has SHA-256d6b32870e5b1d8eae7512723f9b8f5194bc6102ffe3539f5df13d1d7bc54d051. The automatic current-commit GPT refresh remains queued; the completed approval covers this identical content diff.