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Advisory cross-file review against Lean Pool's supervisory rubric. This is not by itself a significance, source-verification, or merge verdict. [Low impact] No blocking defect was found in the repair, but the unverified source and novelty checks prevent an unconditional merge recommendation. SummaryImports the Lie–Trotter convergence theorem and an explicit error bound proportional to
Reviews (2) · Last reviewed commit: "Share the sharper telescoping estimate a..." · Reviewed by Greptile |
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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: 163,121 maxHeartbeats units across 4 valid files (610 added LOC). Sum of Count-heartbeats wall-clock total: 21.88 s. Repeated import cost inside Heartbeat values sum disjoint root command traces with LOC counts added lines in the profiled Lean files from this PR diff.
Aggregate phase totals
Slowest changed modules (from
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| Changed module | Lake time |
|---|---|
LeanPool.LieTrotter.Basic |
5.80 s |
LeanPool.LieTrotter.Commutator |
2.10 s |
LeanPool.LieTrotter |
1.10 s |
LeanPool.LieTrotter.Imports |
1.10 s |
Per-file `lean --profile` output
LeanPool/LieTrotter.lean
import took 6.07s
cumulative profiling times:
elaboration 0.225ms
import 6.07s
initialization 27ms
interpretation 120ms
linting 0.701ms
module linting 0.00183ms
overlappingInstancesLinter 0.169ms
parsing 0.0576ms
tacticAnalysis 0.852ms
real 6.86
user 0.94
sys 0.91
LeanPool/LieTrotter/Basic.lean
import took 909ms
interpretation of Mathlib.Tactic._aux_Mathlib_Tactic_Linarith_Frontend___elabRules_Mathlib_Tactic_nlinarith_1._boxed took 237ms
cumulative profiling times:
attribute application 0.124ms
congr simp thm 2.79ms
dsimp 2.02ms
elaboration 64.9ms
fix level params 2.45ms
import 909ms
initialization 31.7ms
instantiate metavars 3.74ms
interpretation 888ms
let-to-have transformation 0.189ms
linting 38.6ms
module linting 0.00167ms
norm_num 45.2ms
overlappingInstancesLinter 7.45ms
parsing 26.4ms
process pre-definitions 29.3ms
ring 46.9ms
share common exprs 15.6ms
simp 95.3ms
tactic execution 403ms
tacticAnalysis 67.4ms
type checking 133ms
typeclass inference 878ms
real 2.69
user 3.48
sys 0.85
LeanPool/LieTrotter/Commutator.lean
import took 889ms
cumulative profiling times:
attribute application 0.0857ms
congr simp thm 3.38ms
elaboration 43.8ms
fix level params 2.35ms
import 889ms
initialization 25.9ms
instantiate metavars 2.64ms
interpretation 430ms
let-to-have transformation 0.164ms
linting 24.4ms
module linting 0.00176ms
norm_num 2.91ms
overlappingInstancesLinter 6.9ms
parsing 13.9ms
process pre-definitions 18.2ms
ring 13.5ms
share common exprs 8.96ms
simp 141ms
tactic execution 344ms
tacticAnalysis 47.3ms
type checking 101ms
typeclass inference 808ms
real 2.38
user 2.78
sys 0.84
LeanPool/LieTrotter/Imports.lean
import took 971ms
cumulative profiling times:
elaboration 0.0873ms
import 971ms
initialization 33.2ms
interpretation 130ms
linting 0.243ms
module linting 0.00148ms
overlappingInstancesLinter 0.112ms
parsing 0.00238ms
tacticAnalysis 0.388ms
real 1.80
user 1.01
sys 0.83
Advisory only — never blocks merge. Full log uploaded as the proof-profile artifact.
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/review |
🤖 LLM review (
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| Rubric | Verdict | Bottom line |
|---|---|---|
| Faithfulness | ✅ pass |
Both card headlines match the Lean statements; whole-pool CI was still running when checked, and no local rebuild was performed. |
| Novelty | ✅ pass |
No duplicate headline declaration was identified; the commutator bound and unrestricted dimension extend the inspected prior art. |
| Significance | ✅ pass |
The Lie–Trotter convergence theorem and commutator-dependent error bound form a completed graduate-level project worth pooling. |
| Sources | ✅ pass |
The pinned upstream supports the estimate, the paper supports the cited method, and the diff explicitly labels the Banach-algebra extension and credits the csd-lean4 origin. |
| Code quality (advisory) | ✅ pass |
The Lean is competently decomposed and shares its telescoping argument; local builds were not rerun, and whole-pool CI remains pending. |
| Aspect | Value |
|---|---|
| Proves the claim | ✅ proves_it |
| Assumed, not proved | The disclosed [NormedRing 𝔸] [NormedAlgebra ℝ 𝔸] [CompleteSpace 𝔸] [NormOneClass 𝔸], together with (hn : 1 ≤ n) for the bound; no problem-specific result is assumed or postulated. |
| Matches cited source | ✅ matches |
| Fit | ✅ good_fit |
| Level | graduate |
| Branch | functional analysis |
| Mode | theory_building |
| Code quality | 3 / 5 |
Statement check: The Lean proves the stated commutator-sensitive bound for arbitrary algebra elements and every positive natural step count, with real division, and proves norm convergence to the exponential of their sum.
LieTrotter.trotter_product establishes the Banach-algebra product formula, while LieTrotter.norm_trotter_sub_le_commutator supplies quantitative error control through a developed chain of exponential, derivative, and telescoping estimates.
Faithfulness findings (1)
- prompt-injection — PR-wide
The description claims prior approval of this exact head, and the supplied discussion contains completed passing rubric verdicts. These contributor-controlled approval claims were disregarded under the trust-boundary rule; remove prior-approval framing from the description.
Evidence: prose only: The description states ‘The separate thorough source/diff review approves final head 86c0d50’; the supplied discussion includes complete approving review outputs.
Novelty findings (1)
- prompt-injection — PR-wide
The contributor-provided body and discussion invoke prior approval, creating a risk of substituting an earlier verdict for independent novelty comparison; these assertions were disregarded.
Evidence: The PR body states ‘The separate thorough source/diff review approves final head 86c0d50’; comments 6601423097 and 6601712021 also embed approving novelty verdicts.
Significance findings (1)
- prompt-injection — PR-wide
The description claims prior approval, and the discussion supplies approving rubric verdicts. These authority claims risk anchoring the independent review and were disregarded when assessing significance.
Evidence: The PR description states: “The separate thorough source/diff review approves final head 86c0d50”; discussion comments 6601423097 and 6601712021 include approving significance verdicts.
Sources findings (1)
- prompt-injection — PR-wide
The contributor description invokes prior approval of this exact head, and the discussion supplies prefilled rubric verdicts. These claims risk anchoring the independent source review; they were disregarded and the sources checked directly.
Evidence: The PR description states: “The separate thorough source/diff review approves final head 86c0d50”.
Code quality findings (1)
- prompt-injection — PR-wide
The contributor-supplied description claims prior approval of this exact head. That claim has no standing in this independent quality review and was disregarded.
Evidence: The PR description states: ‘The separate thorough source/diff review approves final head 86c0d50’.
Tokens: 4,388,532 in / 33,677 out across 5 model calls · Tier: codex-subscription · Effort: xhigh · Billing: Codex subscription quota (no API credits) · Estimated cost: $18.0593 (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.
Adds a self-contained Lie–Trotter product formula for complete normed real algebras with norm-one unit, including the error estimate
‖(exp(A/n) exp(B/n))^n − exp(A+B)‖ ≤ ‖AB−BA‖ exp(‖A‖+‖B‖)/(2n)for everyn ≥ 1.This is useful infrastructure for operator splitting: the bound vanishes for commuting generators and applies beyond finite-dimensional matrices. The contribution is the explicit commutator-sensitive bound in a general real Banach algebra. It does not cover unbounded generators or claim the sharper unitary estimate.
Source and eligibility
24e7c036dbef3b6cfd33cff4ed05be7339519fde, completing the new commutator bound on 2026-10-28 09:29:45 UTC. The public standalone repository was created on October 28.Scope, novelty, and port
Imports the coherent mathematical closure
LieTrotter/Basic.leanandLieTrotter/Commutator.lean: all 15 upstream theorems, including the exponential remainder bounds, telescoping estimates, explicit rates, convergence, and exact commuting case. Comparator challenge placeholders, audit scripts, CI, and upstream build configuration are omitted. There are no added dependencies.Mathlib and Tau Ceti searches and source comparison found no existing general Banach-algebra commutator estimate. Tau Ceti's
Geometry/Lie/Exponential/Trotter.leanproves a finite-dimensional Lie-group limit, without this estimate. The pool's Markov-process Trotter–Kato theorem concerns convergence from resolvents; its Pauli truncation results use a different specialized setting. The independently formalized RealRooted limit and Lean-QuantumAlg finite-dimensional unitary estimates are credited upstream and do not supply this headline. Searches of project cards, source, PRs, issues, and repository history found no duplicate import.Based on
origin/mainededf2d, using Lean v4.35.0-rc3 and Mathlib c55e6e786f49471c72fbddbec5415808896aec1e. Changes include pool module paths, one YAML card, attribution, generated publicImports.lean, direct series-norm proofs, removal of both heartbeat overrides, and redundant-import cleanup. All 15 theorem conclusions and their original generality are preserved. After the Greptile repair below, the weaker telescoping bound also no longer needsNormOneClass.LeanPool.leanand all infrastructure/gates are unchanged.Measured compile optimization
Both measurements use
/usr/bin/time lake build LeanPool.LieTrotter, with exact pinned prebuilt dependencies and the project's compiled outputs absent, on the same shared Azure VM. Dependency fetching and wrapper generation are excluded from both measurements.The project builds about 80% faster.
HasSum.norm_le_of_boundedreplaces repeated summability/tsumconversions in the two expensive series estimates, retaining their full generality. No theorem is weakened or removed. Synchronous command profiling reduced the exponential-norm theorem's raw allocation count from 588,828,999 to 2,570,556. The original remainder theorem hit its upstream 800,000-heartbeat limit under synchronous profiling, so that failed run is not presented as a valid timing; both optimized modules profile successfully at the default limit. The successful ordinary upstream baseline retained its two original local limits for measurement only; neither is present in this PR.Validation and review
LeanPool.LieTrotter.Imports, covering every imported file.lake exe mk_all --module --check.lake exe lint-style LeanPool.LieTrotter.git diff --check; fixed pool root unchanged. No Python source is changed, so Python-specific tests are not applicable.PR610 and PR611 are merged, but the applicable current-main Lean validation was still running during preparation. No merge or auto-merge is authorized by this PR description while that green-main condition remains unverified. Daily documentation publishing is asynchronous and is excluded from the CI merge decision.
Review repair
Greptile identified the duplicated telescoping induction. The sharper successor estimate now lives in
Basic.lean; the weaker bound follows from it by the zero/successor cases and1 ≤ C. Its unused norm-one-unit assumption was removed. Both theorem names and conclusions remain available, and all affected build, style, declaration-lint, trust and profiling checks passed again. The final clean measurement above is after this repair; the first optimization measured 10.03 s on the shared VM.