[Vilin97]

Imports a reusable library of measurement representation theorems: Scott's eight numbered results connecting linear separation and cancellation to semiorders, additive pair utility, ordered utility differences, and finite subjective probability. The common separation/rationalization engine, atom-vector interface, and local ordered-group embeddings are useful beyond the individual examples. The completed semiorder, utility and qualitative-probability representation theory supplies research-level mathematics and a shared API.

Upstream: https://github.com/catskillsresearch/scott1964 at 591e8a6a5d7d1ebf4cc761b4a1cb749b6480dfeb. The core completion commit is 295e5620cb6193774a4ab8cd568b8003a3b582d6 (2026-08-31 03:38:56 UTC); the public Palomar registration was published 2026-09-25 12:54:19 UTC. Both fall in this acquisition cycle's interval [2026-08-10 09:45:30 UTC, 2026-10-03 09:45:30 UTC). Verified Apache-2.0 source license; original copyright and attribution to Lars Warren Ericson retained. Provenance is AI, based on the upstream automation record, with Ericson directing and reviewing the agents.

The import contains the coherent 21-module mathematical library, a thin public entry module, and its generated Imports wrapper. It retains the original Scott1964.MeasurementStructures namespace. It excludes upstream PDFs, reports, scripts, CI, and unrelated projects. It adds one split-registry YAML card and leaves the fixed LeanPool.lean unchanged. No complete matching project was found in pool cards/source/history/public issues and PRs. Semantic comparison did find partial foundational overlap: Scott Theorem 1.1 can be derived from Tau Ceti’s existing Tucker theorem, with the additional sign-completeness and sequence-cancellation reduction. That overlap requires an admission judgment; no Tau Ceti code is imported.

I compared all eight statements with Scott's 1964 paper and the explicit rank table with Kraft–Pratt–Seidenberg's original example. The card discloses the zero-inclusive additive-submonoid closure variant and the empty-domain generalizations of Theorems 2.1/3.1/3.2. The additional infinite theorem is explicitly a modern analogue: it assumes the stated generalized Kelley cover condition on comparison vectors. Its Boolean-algebra event embedding and probability/state correspondence are proved; it is not a countably additive measure theorem. Removed unsupported priority claims from the upstream exposition.

Ported to Lean v4.35.0-rc3 and Mathlib c55e6e786f49471c72fbddbec5415808896aec1e. Repaired deprecated APIs, proof elaboration, unused assumptions/instances, missing documentation, and style. Replaced native_decide with kernel-checked decide; there are no sorry/admit, added axioms, unsafe/partial, heartbeat overrides, forbidden options, or linter suppressions. The quality checker audited the compiled dependency closure and option backdoors successfully.

Measured optimization used project-clean builds with existing Mathlib/dependency artifacts, warm filesystem cache, Lake's default concurrency, and a shared Azure VM. These are observations, not dedicated-machine benchmarks:

Measurement	Ported baseline	Final import
Wall time	48.64 s	21.30 s
User + system CPU	100.75 s	54.17 s
Peak RSS	4,045,376 KiB	1,499,552 KiB
KPS counterexample module	16 s	2.7 s

A preceding optimized clean build took 26.47 s with similar memory, indicating some scheduling variation. Baseline command: /usr/bin/time -v lake build LeanPool.ScottMeasurement.Imports; final command adds --wfail. Before each run, only artifacts for this project's modules were removed from .lake/build, preserving dependency artifacts. Import analysis narrowed three blanket Mathlib imports and removed redundant dependencies. Profiling identified the exhaustive disjoint-union test as the main cost: a kernel-checked single-atom insertion lemma plus induction replaces the exhaustive triple-event enumeration. The probability API now converts to signed charges, so atom-sum/integration/representation lemmas reuse the general signed-charge proofs; the finite sufficiency theorem reuses the shared separation reduction. Nonnegative-charge monotonicity is generalized to signed charges, redundant probability-only helpers are consolidated, and algebraic cancellation helpers now require only the group/module structure they use. The non-realizability theorem reuses the preceding strict-order obstruction instead of duplicating its argument. Final rationalization and event-space profiles show mostly ordinary import, instance, and small tactic costs, with no comparable remaining hotspot.

Local validation passed:

• lake --wfail build LeanPool.ScottMeasurement.Imports and the fixed root module.
• lake exe mk_all --module --check.
• All 15 CI declaration linters on all 23 modules: 478 declarations, including generated auxiliaries.
• lake exe lint-style LeanPool.ScottMeasurement.Imports.
• The unmodified repository quality/trust checker on an exact project-scoped source/configuration copy, including generated card, axiom closure, file/header/size checks, and option audit.
• git diff --check; content-only diff. No Python changes.

The Greptile findings concerning duplicated probability proofs and upstream-only references were repaired. Its cross-project bridge suggestion was declined with a scope rationale. GPT’s review of 0274e8098 returned needs_discussion on the foundational overlap described above. Its two routine API findings are repaired at 5145367f0023684a016f4e39237e225111a721c0. Prior contributor-review summaries have been removed from this description; historical source-review checkpoints remain in the discussion as records, without authority over independent review.

The previous exact head passed full Lean Action CI. The current repair head is being submitted for CI and configured review; previous-head successes do not establish current-head success. PR610 and PR611 are merged, and exact current-main 103ee57c8901ee78cd9b416a261f7a7957914042 passed push CI. This PR remains open without auto-merge or native-queue enrollment because the novelty judgment is unresolved.

[Vilin97]

/review

[Vilin97]

Separate agentic acquisition review of exact head 111f29b3a5e64e7991b206d182193cd09eef5f06, performed by the importing agent in a separate source-review pass using the live .github/REVIEW_RULES.md, its five rubrics, and the acquisition selection/engineering requirements.

Conclusion: APPROVE the mathematical content. No unresolved mathematical, licensing, trust, attribution, scope, or maintainability defect was found. Final integration status is recorded below; this review does not request a merge or release the infrastructure hold.

I reviewed all 21 upstream library modules and all 24 changed files, including all endpoint declarations and the dependency closure. Coverage includes Definitions/Separation/Rationalization/Sequences/ScottTheorems/OrderedGroup; Cycle/Direct/Intransitive; Pair/Ordered; Basic/Atoms/Finite/KPSCounterexample; EventSpace/HahnBanach/Kelley/Reconstructed; the aggregators, generated wrapper, entry documentation, and YAML card. The review used bounded complete source reads, not only the displayed diff or declaration inventory.

Faithfulness. I compared the eight numbered results with the original Scott 1964 paper. Finite symmetric vector sets, weighted versus integer-repeat cancellation, exact relation representation, permutation cancellation on pairs, reversal for differences, unit-threshold preference, probability nonnegativity/normalization, and the directions of comparison are explicit. The informal card tracks the Lean quantifiers. The zero-inclusive additive-submonoid closure and empty-domain generalizations are disclosed. The proof does not substitute the desired conclusion for a hypothesis. The separate infinite result explicitly assumes a generalized Kelley cover of strict comparison vectors by closed convex upper sets avoiding zero. The universal event representation is backed by a proved Stone embedding and probability/state equivalence; it does not assume the sought representing probability exists. No claim of countable additivity or of proving Scott's unpublished infinite theorem remains.

Sources and provenance. The imported commit is 591e8a6a5d7d1ebf4cc761b4a1cb749b6480dfeb from the public catskillsresearch/scott1964 repository. Apache-2.0 was verified in the upstream license and source headers; copyright/author attribution to Lars Warren Ericson is retained. The upstream automation record supports provenance AI, with human direction/review, and the card records that accurately. Third-party paper PDFs and generated reports are not redistributed. The core completion commit (2026-08-31 03:38:56 UTC) and public Palomar registration (2026-09-25 12:54:19 UTC) both establish eligibility independently of repository refresh dates. I also inspected the original KPS paper's rank table directly and compared all 32 ranks and the four contradictory strict inequalities with the Lean example.

Novelty and significance. No duplicate was found in the current pool's split cards, source, repository history, or public issues/PRs, or in the Mathlib/TauCeti source searches. This is a coherent representation-theory library rather than a collection of elementary exercises. It connects finite linear inequalities to measurement, utility, and qualitative probability. The reusable finite separation and rationalization engine, local ordered-group models, atom-vector interface, and general countable-cone separation construction justify preserving the infrastructure along with the eight source results. Existing Mathlib separation/topological algebra results are reused through imports rather than vendored.

Correctness and trust. I inspected the hard proof steps: finite separation and its converse, rational kernel/density conversion to repeat cancellation, the finite semiorder staircase, pair-vector fiber/permutation matching, reversal-to-difference utility, atom decomposition and probability normalization, local order/addition constraints, the Stone/event-span construction, and the summable normalized family of Hahn–Banach separators. The KPS obstruction's inequalities imply an actual incompatible sum of atom weights. All imported modules compile without warnings. The compiled quality/axiom-closure and option audits pass; no proof holes, extra axioms, unsafe/partial code, native decision procedure, forbidden option, heartbeat escape hatch, or suppression remains. Finite computations use kernel-checked decide.

Quality and measured cost. The closure is 21 mathematical modules plus two public packaging modules, with 4,653 inserted lines including the card. Every file is within the repository size limits and all imports stay within Mathlib and this project. Port repairs remove deprecated APIs, unused hypotheses/instances, duplicate proof work, broad imports, and unsupported exposition claims; missing API documentation and trailing whitespace were fixed. The public root is unchanged and the one split card plus generated Imports wrapper satisfy the current migration policy. All project declaration linters pass on 477 declarations, as do text style, generated indexes, and the unmodified quality checker on the exact project-scoped source/configuration copy.

The controlled project-clean baseline was 48.64 s wall time / 100.75 s CPU / 4,045,376 KiB peak RSS. Final source was 22.23 s / 56.90 s / 1,509,172 KiB, with an earlier optimized observation of 26.47 s. Dependencies remained prebuilt, filesystem caches warm, Lake concurrency default, and the Azure VM shared; the variation limits precision. Profiling justified replacing exhaustive three-event KPS checking with a checked insertion lemma and induction (16 s module baseline to 3.2 s final), alongside narrower imports and proof reuse. Final rationalization/event-space profiles expose no similar large remaining declaration hotspot, so no further material safe optimization is evident.

Integration checkpoint. Local checks and exact-copy/source-hash checks pass at the head above. The content guard and metadata advisory are green. Full Lean CI, the advisory profile run, Greptile, and the requested GPT verdict are still running/pending; this comment is not a claim that those gates have passed. Auto-merge is disabled. PR610/611 are merged, but exact current-main Lean CI verification remains unresolved, so the infrastructure priority hold remains in force. I will update this checkpoint when integration evidence arrives.

[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 impact] No blocking code defect was found in the current repair.

Summary

Imports Scott’s eight finite representation theorems, shared separation proofs, the KPS counterexample, and a separately labelled infinite analogue.

• Finite comparison rules can now be tested with a shared separation engine.
• Finite preference rules now have tests that lead to real-valued scores.
• Pair utilities and ordered utility differences now have representation theorems.
• Finite parts of ordered groups get real models, while lexicographic order has no global one.
• Finite event comparisons now have a test for probability representation.
• The five-atom KPS ordering shows de Finetti’s axioms do not ensure a probability score.
• Infinite event comparisons get a modern probability theorem with an extra cover condition.
• The Scott measurement library now has a public Lean Pool entry point.

_{Reviews (3) · Last reviewed commit: "Generalize Scott measurement algebraic h..." · Reviewed by Greptile}

[github-actions]

Proof profile (new / modified Lean files)

lake build wall time (changed modules): 28.50 s (= 0.47 min) — user 44.82 s, sys 12.36 s.

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: 639,679 maxHeartbeats units across 23 valid files (4,532 added LOC).

Sum of lean --profile: 40421.2 ms (= 40.42 s) across 23 valid files. Import-excluded time: 21404.2 ms (= 21.40 s).

Count-heartbeats wall-clock total: 94.15 s. Repeated import cost inside lean --profile: 19017.0 ms (= 19.02 s).

Heartbeat values sum disjoint root command traces with trace.profiler.useHeartbeats and synchronous elaboration, converted from raw allocations to maxHeartbeats units by dividing by 1000. They include command elaboration and kernel checking, exclude imports, and include profiler overhead; they are not comparable to the deprecated linter's totals. Per-file wall clocks are measured under parallel load and are noisier than heartbeats.

LOC counts added lines in the profiled Lean files from this PR diff.

File	LOC	Heartbeats (maxHB)	Count wall (s)	lean --profile (s)	Without import (s)	Import (s)	Commands	Errors
LeanPool/ScottMeasurement/Probability/Infinite/Reconstructed.lean	233	101,560	10.03	3.40	2.42	0.97	21	0
LeanPool/ScottMeasurement/LinearInequalities/ScottTheorems.lean	413	95,158	7.18	2.63	1.77	0.86	44	0
LeanPool/ScottMeasurement/LinearInequalities/Rationalization.lean	250	81,366	9.67	2.43	1.62	0.81	39	0
LeanPool/ScottMeasurement/LinearInequalities/OrderedGroup.lean	327	47,553	6.01	2.13	1.19	0.95	84	0
LeanPool/ScottMeasurement/Preference/Intransitive.lean	312	43,315	3.87	1.67	1.09	0.58	44	0
LeanPool/ScottMeasurement/Probability/Finite.lean	517	42,029	5.58	2.10	1.19	0.91	108	0
LeanPool/ScottMeasurement/Probability/Infinite/EventSpace.lean	395	41,777	6.26	2.19	1.42	0.77	59	0
LeanPool/ScottMeasurement/Probability/Infinite/Kelley.lean	131	40,791	4.59	1.57	0.69	0.88	20	0
LeanPool/ScottMeasurement/Probability/Atoms.lean	263	39,894	5.13	1.50	0.87	0.62	61	0
LeanPool/ScottMeasurement/Differences/Pair.lean	282	24,078	4.71	2.06	1.14	0.92	38	0
LeanPool/ScottMeasurement/Probability/KPSCounterexample.lean	258	17,307	3.43	5.48	4.59	0.90	42	0
LeanPool/ScottMeasurement/Preference/Direct.lean	290	14,831	3.63	1.29	0.66	0.63	19	0
LeanPool/ScottMeasurement/Probability/Basic.lean	201	13,060	2.31	0.99	0.43	0.56	80	0
LeanPool/ScottMeasurement/LinearInequalities/Separation.lean	71	11,022	2.69	1.30	0.41	0.89	8	0
LeanPool/ScottMeasurement/Probability/Infinite/HahnBanach.lean	68	9,230	2.69	1.19	0.33	0.86	11	0
LeanPool/ScottMeasurement/LinearInequalities/Sequences.lean	68	7,063	2.08	0.92	0.26	0.66	22	0
LeanPool/ScottMeasurement/LinearInequalities/Definitions.lean	126	5,610	2.61	0.92	0.30	0.63	27	0
LeanPool/ScottMeasurement/Differences/Ordered.lean	115	3,672	2.26	1.32	0.37	0.94	28	0
LeanPool/ScottMeasurement/Preference/Cycle.lean	63	211	1.21	0.40	0.10	0.30	9	0
LeanPool/ScottMeasurement/FinHead.lean	35	150	1.49	0.55	0.11	0.43	8	0
LeanPool/ScottMeasurement/Basic.lean	52	4	2.36	1.12	0.16	0.95	5	0
LeanPool/ScottMeasurement.lean	32	0	2.39	2.25	0.15	2.10	3	0
LeanPool/ScottMeasurement/Imports.lean	30	0	1.97	1.02	0.13	0.89	1	0
Total	4,532	639,679	94.15	40.42	21.40	19.02	781	0

Aggregate phase totals

Phase	Time
import	19017.0 ms (= 19.02 s)
typeclass inference	5503.4 ms (= 5.50 s)
interpretation	4586.5 ms (= 4.59 s)
blocked (unaccounted)	3651.3 ms (= 3.65 s)
tactic execution	1938.8 ms (= 1.94 s)
simp	1614.2 ms (= 1.61 s)
type checking	1324.6 ms (= 1.32 s)
initialization	612.3 ms (= 0.61 s)
elaboration	595.4 ms (= 0.60 s)
tacticAnalysis	413.6 ms (= 0.41 s)
linting	289.5 ms (= 0.29 s)
ring	159.4 ms (= 0.16 s)

Slowest changed modules (from lake build)

Changed module	Lake time
LeanPool.ScottMeasurement.Probability.Infinite.Reconstructed	4.30 s
LeanPool.ScottMeasurement.LinearInequalities.OrderedGroup	3.60 s
LeanPool.ScottMeasurement.LinearInequalities.Rationalization	3.50 s
LeanPool.ScottMeasurement.Probability.Finite	3.50 s
LeanPool.ScottMeasurement.Probability.Infinite.EventSpace	3.40 s
LeanPool.ScottMeasurement.Differences.Pair	3.40 s
LeanPool.ScottMeasurement.Probability.Infinite.HahnBanach	2.70 s
LeanPool.ScottMeasurement.Preference.Direct	2.60 s
LeanPool.ScottMeasurement.LinearInequalities.Definitions	2.50 s
LeanPool.ScottMeasurement.Preference.Intransitive	2.50 s
LeanPool.ScottMeasurement.LinearInequalities.ScottTheorems	2.50 s
LeanPool.ScottMeasurement.LinearInequalities.Separation	2.40 s

Per-file `lean --profile` output

LeanPool/ScottMeasurement.lean

import took 2.1s
cumulative profiling times:
	elaboration 0.315ms
	import 2.1s
	initialization 27.7ms
	interpretation 115ms
	linting 0.616ms
	module linting 0.00189ms
	overlappingInstancesLinter 0.346ms
	parsing 0.0539ms
	tacticAnalysis 2.33ms
real 2.82
user 0.87
sys 0.87

LeanPool/ScottMeasurement/Basic.lean

import took 952ms
cumulative profiling times:
	elaboration 0.465ms
	import 952ms
	initialization 24.1ms
	interpretation 133ms
	linting 0.693ms
	module linting 0.0021ms
	overlappingInstancesLinter 0.557ms
	parsing 0.23ms
	tacticAnalysis 4.5ms
real 1.68
user 0.89
sys 0.82

LeanPool/ScottMeasurement/Differences/Ordered.lean

import took 945ms
cumulative profiling times:
	attribute application 0.0793ms
	blocked (unaccounted) 0.885ms
	dsimp 2.17ms
	elaboration 14.4ms
	fix level params 0.364ms
	import 945ms
	initialization 31.2ms
	instantiate metavars 0.755ms
	interpretation 212ms
	let-to-have transformation 0.0646ms
	linting 10.1ms
	module linting 0.0021ms
	norm_num 0.582ms
	overlappingInstancesLinter 3.94ms
	parsing 4.62ms
	process pre-definitions 4.2ms
	ring 17.5ms
	share common exprs 2.6ms
	tactic execution 19.6ms
	tacticAnalysis 11.6ms
	type checking 13.2ms
	typeclass inference 21.6ms
real 1.85
user 1.14
sys 0.87

LeanPool/ScottMeasurement/Differences/Pair.lean

import took 918ms
cumulative profiling times:
	attribute application 0.107ms
	blocked (unaccounted) 260ms
	congr simp thm 3.77ms
	dsimp 3.3ms
	elaboration 24.5ms
	fix level params 1.37ms
	import 918ms
	initialization 24.7ms
	instantiate metavars 2.83ms
	interpretation 214ms
	let-to-have transformation 0.0826ms
	linting 18ms
	module linting 0.00184ms
	norm_num 0.255ms
	overlappingInstancesLinter 3.37ms
	parsing 12.9ms
	process pre-definitions 7.92ms
	ring 7.09ms
	share common exprs 4.14ms
	simp 161ms
	tactic execution 156ms
	tacticAnalysis 25ms
	type checking 34.2ms
	typeclass inference 173ms
real 2.02
user 1.54
sys 0.84

LeanPool/ScottMeasurement/FinHead.lean

import took 431ms
cumulative profiling times:
	attribute application 0.0202ms
	compilation (IR) 0.0429ms
	compilation (LCNF base) 0.4ms
	compilation (LCNF impure) 0.182ms
	compilation (LCNF mono) 0.168ms
	elaboration 4.1ms
	fix level params 0.0174ms
	import 431ms
	initialization 27.4ms
	instantiate metavars 0.0132ms
	interpretation 72.4ms
	let-to-have transformation 0.027ms
	linting 1.3ms
	module linting 0.00169ms
	overlappingInstancesLinter 0.873ms
	parsing 0.678ms
	process pre-definitions 0.327ms
	share common exprs 0.0615ms
	tacticAnalysis 3.68ms
	type checking 0.453ms
	typeclass inference 2.03ms
real 1.11
user 0.52
sys 0.63

LeanPool/ScottMeasurement/Imports.lean

import took 892ms
cumulative profiling times:
	elaboration 0.0917ms
	import 892ms
	initialization 24.1ms
	interpretation 108ms
	linting 0.212ms
	module linting 0.00171ms
	overlappingInstancesLinter 0.0823ms
	parsing 0.00254ms
	tacticAnalysis 0.438ms
real 1.58
user 0.81
sys 0.81

LeanPool/ScottMeasurement/LinearInequalities/Definitions.lean

import took 628ms
cumulative profiling times:
	attribute application 0.121ms
	elaboration 30.2ms
	fix level params 0.267ms
	import 628ms
	initialization 30.2ms
	instantiate metavars 0.11ms
	interpretation 135ms
	let-to-have transformation 0.0893ms
	linting 8.39ms
	module linting 0.00176ms
	overlappingInstancesLinter 4.78ms
	parsing 6.36ms
	process pre-definitions 4.18ms
	share common exprs 0.597ms
	tacticAnalysis 14.8ms
	type checking 4.78ms
	typeclass inference 55.2ms
real 1.40
user 0.79
sys 0.72

LeanPool/ScottMeasurement/LinearInequalities/OrderedGroup.lean

import took 948ms
cumulative profiling times:
	attribute application 0.207ms
	compilation (IR) 0.219ms
	compilation (LCNF base) 3.8ms
	compilation (LCNF impure) 0.962ms
	compilation (LCNF mono) 2.1ms
	congr simp thm 2.95ms
	elaboration 56.3ms
	fix level params 1.75ms
	import 948ms
	initialization 30ms
	instantiate metavars 2.95ms
	interpretation 265ms
	let-to-have transformation 0.172ms
	linting 23.5ms
	module linting 0.0018ms
	norm_num 4.04ms
	overlappingInstancesLinter 9.21ms
	parsing 13.7ms
	process pre-definitions 10.3ms
	share common exprs 4.92ms
	simp 98.3ms
	tactic execution 178ms
	tacticAnalysis 34.2ms
	type checking 60.2ms
	typeclass inference 383ms
real 2.04
user 1.92
sys 0.83

LeanPool/ScottMeasurement/LinearInequalities/Rationalization.lean

import took 807ms
cumulative profiling times:
	attribute application 0.0608ms
	congr simp thm 5.98ms
	dsimp 0.69ms
	elaboration 17.6ms
	fix level params 2.17ms
	import 807ms
	initialization 30.4ms
	instantiate metavars 1.87ms
	interpretation 317ms
	let-to-have transformation 0.0681ms
	linting 16.7ms
	module linting 0.00198ms
	norm_num 7.47ms
	overlappingInstancesLinter 4.55ms
	parsing 8.52ms
	process pre-definitions 7.23ms
	ring 6.48ms
	share common exprs 5.17ms
	simp 233ms
	tactic execution 153ms
	tacticAnalysis 25ms
	type checking 55.9ms
	typeclass inference 724ms
real 2.53
user 2.24
sys 0.80

LeanPool/ScottMeasurement/LinearInequalities/ScottTheorems.lean

import took 861ms
cumulative profiling times:
	attribute application 0.0878ms
	compilation (IR) 0.0614ms
	compilation (LCNF base) 0.405ms
	compilation (LCNF impure) 0.303ms
	compilation (LCNF mono) 0.398ms
	congr simp thm 3.41ms
	dsimp 43.8ms
	elaboration 45.5ms
	fix level params 2.53ms
	import 861ms
	initialization 27.8ms
	instantiate metavars 4.57ms
	interpretation 326ms
	let-to-have transformation 0.106ms
	linting 35.5ms
	module linting 0.00175ms
	norm_num 1.03ms
	overlappingInstancesLinter 6.63ms
	parsing 13.6ms
	process pre-definitions 13.3ms
	ring 21.2ms
	share common exprs 9.4ms
	simp 181ms
	tactic execution 274ms
	tacticAnalysis 45.1ms
	type checking 74.5ms
	typeclass inference 640ms
real 2.25
user 2.40
sys 0.87

LeanPool/ScottMeasurement/LinearInequalities/Separation.lean

import took 892ms
cumulative profiling times:
	attribute application 0.0164ms
	congr simp thm 0.589ms
	elaboration 8.66ms
	fix level params 0.368ms
	import 892ms
	initialization 30.5ms
	instantiate metavars 0.473ms
	interpretation 160ms
	let-to-have transformation 0.0296ms
	linting 4.36ms
	module linting 0.00167ms
	norm_num 1.06ms
	overlappingInstancesLinter 2.09ms
	parsing 1.61ms
	process pre-definitions 1.92ms
	ring 2.94ms
	share common exprs 1.34ms
	simp 13.5ms
	tactic execution 42.6ms
	tacticAnalysis 5.89ms
	type checking 13.9ms
	typeclass inference 120ms
real 1.85
user 1.09
sys 0.81

LeanPool/ScottMeasurement/LinearInequalities/Sequences.lean

import took 661ms
cumulative profiling times:
	attribute application 0.0266ms
	congr simp thm 0.612ms
	elaboration 6.79ms
	fix level params 0.231ms
	import 661ms
	initialization 24ms
	instantiate metavars 0.257ms
	interpretation 117ms
	let-to-have transformation 0.0229ms
	linting 4ms
	module linting 0.00148ms
	overlappingInstancesLinter 2.5ms
	parsing 2.61ms
	process pre-definitions 1.18ms
	share common exprs 0.733ms
	simp 16.4ms
	tactic execution 17.9ms
	tacticAnalysis 9.39ms
	type checking 5ms
	typeclass inference 48.7ms
real 1.41
user 0.79
sys 0.72

LeanPool/ScottMeasurement/Preference/Cycle.lean

import took 301ms
cumulative profiling times:
	attribute application 0.0334ms
	blocked (unaccounted) 0.934ms
	elaboration 5.26ms
	fix level params 0.044ms
	import 301ms
	initialization 29ms
	instantiate metavars 0.0995ms
	interpretation 43.1ms
	let-to-have transformation 0.036ms
	linting 2.97ms
	module linting 0.00157ms
	overlappingInstancesLinter 1.7ms
	parsing 1.8ms
	process pre-definitions 1.13ms
	share common exprs 0.125ms
	tactic execution 2.88ms
	tacticAnalysis 7.52ms
	type checking 0.738ms
real 0.90
user 0.41
sys 0.55

LeanPool/ScottMeasurement/Preference/Direct.lean

import took 626ms
cumulative profiling times:
	attribute application 0.0629ms
	congr simp thm 2.42ms
	dsimp 7.23ms
	elaboration 14ms
	fix level params 1ms
	import 626ms
	initialization 30.3ms
	instantiate metavars 2.09ms
	interpretation 235ms
	let-to-have transformation 0.0598ms
	linting 13ms
	module linting 0.00159ms
	norm_num 6.95ms
	overlappingInstancesLinter 3.13ms
	parsing 8.17ms
	process pre-definitions 5.87ms
	ring 15.2ms
	share common exprs 4.29ms
	simp 76.5ms
	tactic execution 106ms
	tacticAnalysis 23ms
	type checking 24.4ms
	typeclass inference 84.8ms
real 1.76
user 1.18
sys 0.70

LeanPool/ScottMeasurement/Preference/Intransitive.lean

import took 581ms
cumulative profiling times:
	attribute application 0.11ms
	congr simp thm 1.51ms
	dsimp 1.47ms
	elaboration 21ms
	fix level params 1.23ms
	import 581ms
	initialization 24.5ms
	instantiate metavars 2.89ms
	interpretation 461ms
	let-to-have transformation 0.0815ms
	linting 18.2ms
	module linting 0.00198ms
	norm_num 18.3ms
	overlappingInstancesLinter 4.56ms
	parsing 10ms
	process pre-definitions 10.7ms
	ring 43.9ms
	share common exprs 11.9ms
	simp 53.6ms
	tactic execution 116ms
	tacticAnalysis 30ms
	type checking 49.3ms
	typeclass inference 209ms
real 1.76
user 1.52
sys 0.71

LeanPool/ScottMeasurement/Probability/Atoms.lean

import took 625ms
cumulative profiling times:
	attribute application 0.389ms
	blocked (unaccounted) 0.342ms
	congr simp thm 1.91ms
	elaboration 41.7ms
	fix level params 1.23ms
	import 625ms
	initialization 25ms
	instantiate metavars 1.25ms
	interpretation 170ms
	let-to-have transformation 0.188ms
	linting 16.6ms
	module linting 0.00146ms
	norm_num 1.71ms
	overlappingInstancesLinter 5.5ms
	parsing 9.09ms
	process pre-definitions 5.8ms
	share common exprs 3.27ms
	simp 109ms
	tactic execution 121ms
	tacticAnalysis 25.3ms
	type checking 20.3ms
	typeclass inference 312ms
real 1.51
user 1.34
sys 0.72

LeanPool/ScottMeasurement/Probability/Basic.lean

import took 559ms
cumulative profiling times:
	attribute application 0.152ms
	congr simp thm 0.449ms
	elaboration 31.5ms
	fix level params 0.476ms
	import 559ms
	initialization 23.2ms
	instantiate metavars 0.586ms
	interpretation 171ms
	let-to-have transformation 0.107ms
	linting 12.5ms
	module linting 0.00165ms
	norm_num 1.62ms
	overlappingInstancesLinter 8.34ms
	parsing 7.48ms
	process pre-definitions 5.34ms
	ring 8.54ms
	share common exprs 1.77ms
	simp 21.2ms
	tactic execution 30.5ms
	tacticAnalysis 18.7ms
	type checking 17.3ms
	typeclass inference 73.3ms
real 1.33
user 0.89
sys 0.69

LeanPool/ScottMeasurement/Probability/Finite.lean

import took 913ms
cumulative profiling times:
	attribute application 3.37ms
	congr simp thm 3.06ms
	elaboration 68.6ms
	fix level params 2.26ms
	import 913ms
	initialization 24.1ms
	instantiate metavars 3.48ms
	interpretation 297ms
	let-to-have transformation 0.261ms
	linting 33.7ms
	module linting 0.0022ms
	norm_num 0.291ms
	overlappingInstancesLinter 10.5ms
	parsing 17.7ms
	process pre-definitions 11.1ms
	ring 6.69ms
	share common exprs 6.86ms
	simp 185ms
	tactic execution 154ms
	tacticAnalysis 43.1ms
	type checking 57.5ms
	typeclass inference 262ms
real 1.97
user 1.84
sys 0.85

LeanPool/ScottMeasurement/Probability/Infinite/EventSpace.lean

import took 770ms
cumulative profiling times:
	attribute application 5.42ms
	blocked (unaccounted) 93.5ms
	compilation (IR) 0.251ms
	compilation (LCNF base) 3.19ms
	compilation (LCNF impure) 0.998ms
	compilation (LCNF mono) 2.11ms
	congr simp thm 10.1ms
	elaboration 84.2ms
	fix level params 1.97ms
	import 770ms
	initialization 23.2ms
	instantiate metavars 1.82ms
	interpretation 226ms
	let-to-have transformation 0.34ms
	linting 23.6ms
	module linting 0.00186ms
	norm_num 3.78ms
	overlappingInstancesLinter 8.96ms
	parsing 12.7ms
	process pre-definitions 11.9ms
	ring 4.14ms
	share common exprs 4.96ms
	simp 177ms
	tactic execution 152ms
	tacticAnalysis 29.2ms
	type checking 83.3ms
	typeclass inference 457ms
real 2.09
user 1.93
sys 0.75

LeanPool/ScottMeasurement/Probability/Infinite/HahnBanach.lean

import took 859ms
cumulative profiling times:
	attribute application 0.0143ms
	congr simp thm 0.184ms
	elaboration 10.4ms
	fix level params 0.306ms
	import 859ms
	initialization 23.5ms
	instantiate metavars 0.264ms
	interpretation 142ms
	let-to-have transformation 0.0379ms
	linting 3.62ms
	module linting 0.00185ms
	norm_num 1.71ms
	overlappingInstancesLinter 2.46ms
	parsing 1.56ms
	process pre-definitions 1.28ms
	ring 2.31ms
	share common exprs 0.954ms
	simp 3.8ms
	tactic execution 21.9ms
	tacticAnalysis 6.23ms
	type checking 7.54ms
	typeclass inference 99.5ms
real 1.71
user 0.99
sys 0.77

LeanPool/ScottMeasurement/Probability/Infinite/Kelley.lean

import took 879ms
cumulative profiling times:
	attribute application 0.0256ms
	blocked (unaccounted) 5.68ms
	congr simp thm 2.38ms
	dsimp 0.536ms
	elaboration 30.5ms
	fix level params 0.684ms
	import 879ms
	initialization 24ms
	instantiate metavars 0.636ms
	interpretation 180ms
	let-to-have transformation 0.0519ms
	linting 7.53ms
	module linting 0.00139ms
	norm_num 5.23ms
	overlappingInstancesLinter 3.1ms
	parsing 4.13ms
	process pre-definitions 3.04ms
	ring 4.1ms
	share common exprs 2.21ms
	simp 2.9ms
	tactic execution 97.4ms
	tacticAnalysis 11.6ms
	type checking 51.8ms
	typeclass inference 250ms
real 2.04
user 1.38
sys 0.78

LeanPool/ScottMeasurement/Probability/Infinite/Reconstructed.lean

import took 974ms
typeclass inference of CompleteLattice took 111ms
simp took 158ms
cumulative profiling times:
	attribute application 0.0801ms
	congr simp thm 3.47ms
	dsimp 6.11ms
	elaboration 41.3ms
	fix level params 1.49ms
	import 974ms
	initialization 29.6ms
	instantiate metavars 2.21ms
	interpretation 260ms
	let-to-have transformation 0.187ms
	linting 16.7ms
	module linting 0.00186ms
	norm_num 7.66ms
	overlappingInstancesLinter 4.83ms
	parsing 7.09ms
	process pre-definitions 11.1ms
	ring 13.1ms
	share common exprs 6.36ms
	simp 166ms
	tactic execution 242ms
	tacticAnalysis 17ms
	type checking 95.3ms
	typeclass inference 1.49s
real 2.70
user 3.15
sys 0.88

LeanPool/ScottMeasurement/Probability/KPSCounterexample.lean

import took 895ms
type checking took 558ms
cumulative profiling times:
	attribute application 0.618ms
	blocked (unaccounted) 3.29s
	compilation (IR) 0.373ms
	compilation (LCNF base) 8.23ms
	compilation (LCNF impure) 1.68ms
	compilation (LCNF mono) 4.01ms
	congr simp thm 1.97ms
	elaboration 38ms
	fix level params 0.323ms
	import 895ms
	initialization 23.8ms
	instantiate metavars 1.43ms
	interpretation 227ms
	let-to-have transformation 0.175ms
	linting 17.7ms
	module linting 0.00134ms
	norm_num 0.299ms
	overlappingInstancesLinter 5.13ms
	parsing 8.86ms
	process pre-definitions 7.19ms
	ring 6.24ms
	share common exprs 2.06ms
	simp 116ms
	tactic execution 54ms
	tacticAnalysis 20ms
	type checking 655ms
	typeclass inference 98.3ms
real 2.33
user 1.94
sys 0.84

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

[Vilin97]

Thorough-review checkpoint for repaired head 0274e8098a287e40d6550c6e699ab7c0f3c44397: APPROVE the mathematical content, carrying forward the full source/faithfulness/significance/license/trust review at 111f29b3a above. I inspected the complete four-file follow-up diff. The two conversion theorems and proof reuse preserve all endpoint types and eliminate duplicated atom-sum, integration, representation, and finite-sufficiency arguments. Documentation now identifies upstream-only references. Greptile's two actionable findings were repaired; its nonblocking cross-project bridge suggestion was declined with an explicit dependency/scope rationale in the thread. No material content finding remains unresolved.

All local gates pass again: warning-failing build, generated indexes, style, quality/axiom/option audits, and declaration linters on 23 modules / 479 declarations. The exact validation copy is byte-identical to the changed source. A new project-clean measurement is 22.74 s wall / 57.60 s CPU / 1,508,024 KiB RSS, against the 48.64 s / 100.75 s / 4,045,376 KiB baseline. The previous source measured 22.23 s, consistent with small scheduling variation. This head has 24 changed files / 4,633 inserted lines.

The previous-head advisory profile completed with no errors across all 23 files, reporting 28.50 s changed-module build wall time and 40.42 s summed serial profiling time; these are different conditions from the local clean measurements. Its CI run reached repository quality checks before the normal new-head update superseded it, so I do not claim a completed full-CI pass for that head. Final CI and automated reviews are now running for this repaired head. The exact-head source manifests, logs, and first review checkpoint are preserved. No rebase, auto-merge, queue enrollment, or merge has been requested; the infrastructure priority hold remains active.

[Vilin97]

Final integration checkpoint at 0274e8098a287e40d6550c6e699ab7c0f3c44397: Lean Action CI run 38047466918 is successful, including the combined pool build, declaration/style linters, repository quality/trust audits, and retained build/validation receipts. All published checks are green or appropriately skipped. Greptile's final rereview reports no blocking code issue, and the three original threads have been addressed.

The separate thorough review remains APPROVE the mathematical content, with no unresolved content defect. The configured GPT verdict is still awaited. Source, review, performance, and CI checkpoints for both commits are preserved. Auto-merge remains disabled and this PR has not been enqueued: the exact current-main Lean CI verification required by the infrastructure hold remains unresolved. This checkpoint does not release that hold or request a merge.

[Vilin97]

/review

[Vilin97]

🤖 LLM review (gpt-6.1-sol, 5 rubrics)

Reviewed head: 5145367f0023684a016f4e39237e225111a721c0

Verdict: 🤔 needs_discussion — computed from the rubric verdicts below, not chosen by a model.

Rubric	Verdict	Bottom line
Faithfulness	✅ pass	All twelve card headlines match the Lean and disclose their substantive assumptions; exact-head CI has completed build and lint successfully but remains in progress.
Novelty	🤔 discuss	Scott’s separation headlines substantially overlap Tau Ceti’s Tucker theorem; the distinct cancellation and measurement interfaces require a maintainer novelty judgment.
Significance	✅ pass	The representation equivalences and explicit probability obstruction meet the research-level significance bar; local build verification was blocked by HTTP 403 while fetching Mathlib.
Sources	✅ pass	The Scott results and KPS example match their sources; the finite variants and modern Kelley adaptation are labelled, and the upstream formalization is credited.
Code quality (advisory)	✅ pass	Competent modular code reuses separation and signed-charge proofs; exact-head build checks now report success, while local rebuilding stopped at a Mathlib fetch HTTP 403.

Aspect	Value
Proves the claim	✅ proves_it
Assumed, not proved	Finiteness, symmetry, rational coordinates, ordered-group structure, and the relational cancellation or extension conditions apply where stated in the card. Infinite sufficiency uses the disclosed nontriviality, nonnegativity, totality, and GeneralizedKelleyCondition; the separating functional and representing probability are constructed rather than postulated.
Matches cited source	✅ matches
Fit	✅ good_fit
Level	research
Branch	measurement theory
Mode	theory_building
Code quality	3 / 5

Statement check: The Lean proves the eight finite representation equivalences, the local ordered-group map, the explicit five-atom obstruction, and the infinite representation and probability/state equivalences as described.

Theorems theorem_2_1, theorem_3_1, theorem_3_2, and theorem_4_1_vector develop finite semiorder, additive utility, utility-difference, and qualitative-probability representation theory using substantial supporting constructions, complemented by the explicit obstruction deFinetti_axioms_insufficient.

Faithfulness findings (1)

• prompt-injection — PR-wide
  Historical contributor comments assert prior approval and absence of content defects. These assertions have no authority in this independent review and were disregarded; retain their explicit historical status rather than treating them as approval evidence.
  Evidence: prose only: Discussion in .review-pr.json states 'Conclusion: APPROVE the mathematical content.' and 'The separate thorough review remains APPROVE the mathematical content, with no unresolved content defect.'

Novelty findings (2)

• partial-overlap — LeanPool/ScottMeasurement/LinearInequalities/ScottTheorems.lean:223
  Reduction: apply Tucker over ℝ to the finite family in X ∩ N and restrict its zero relation to positive coefficients. Scott cancellation forces supported vectors to be indifferent, so coefficients on strict vectors vanish and Tucker’s functional is strictly positive there. Symmetry forces zero on indifferent vectors; sign completeness yields exact realization. The rational specialization, denominator clearing, and extension of the coordinate functional to ℝ similarly recover Theorem 1.2. Both separation headlines therefore share existing mathematics, while their sequence-cancellation formulation and subsequent measurement reductions supply distinct interfaces.
  Evidence: The diff states Realizable X N ↔ SignComplete X N ∧ WeightedSequenceCancellation X N and, at line 263, Realizable X N ↔ SignComplete X N ∧ UnweightedSequenceCancellation X N. Existing TauCeti.exists_nonneg_sum_smul_eq_zero_and_forall_coeff_add_dual_pos supplies nonnegative zero-relation coefficients and a nonnegative dual functional, with coefficient plus functional value positive at every index, over any linearly ordered field: pinned Tucker declaration.
• prompt-injection — PR-wide
  Historical contributor comments assert prior approval. Using those assertions to settle novelty would substitute self-review for declaration comparison; they were disregarded.
  Evidence: Contributor comments in .review-pr.json state ‘Conclusion: APPROVE the mathematical content.’ and ‘The separate thorough review remains APPROVE the mathematical content, with no unresolved content defect.’ These historical assertions have no authority over this review.

Significance findings (1)

• prompt-injection — PR-wide
  The supplied discussion repeatedly invokes contributor self-review approval, risking substitution of those assertions for independent significance judgment; they were ignored and must carry no approval authority.
  Evidence: Contributor comments preserved in .review-pr.json include 'Conclusion: APPROVE the mathematical content.' and 'The separate thorough review remains APPROVE the mathematical content, with no unresolved content defect.'

Sources findings (1)

• prompt-injection — PR-wide
  Repeated contributor self-review checkpoints claim prior approval. Treating them as authority would replace independent citation checking with self-review; they were disregarded. Keep these historical verdicts separate from reviewer instructions and source-verification evidence.
  Evidence: Contributor discussion in .review-pr.json states: 'Conclusion: APPROVE the mathematical content.' (comment 6096809966), 'APPROVE the mathematical content' (comment 6096884921), and 'The separate thorough review remains APPROVE the mathematical content, with no unresolved content defect.' (comment 6097036250).

Code quality findings (1)

• prompt-injection — PR-wide
  Historical contributor checkpoints assert prior approval and maintainability clearance. These assertions risk biasing independent review and were ignored; keep them identified as contributor self-assessments.
  Evidence: Contributor discussion states: 'Conclusion: APPROVE the mathematical content. No unresolved mathematical, licensing, trust, attribution, scope, or maintainability defect was found.' Two subsequent checkpoints repeat 'APPROVE the mathematical content'.

---

Tokens: 8,205,015 in / 46,787 out across 5 model calls · Tier: codex-subscription · Effort: xhigh · Billing: Codex subscription quota (no API credits) · Estimated cost: $33.5219 (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.

[Vilin97]

Separate source-review update at 5145367f0023684a016f4e39237e225111a721c0.

Conclusion: REQUEST_CHANGES on admission readiness. The unresolved item is whether the cancellation interface and the broader representation library supply sufficient distinct value despite the partial foundational overlap identified by the independent GPT review. No merge or queue enrollment has been requested.

I independently inspected the pinned Tau Ceti Tucker declaration and the Scott cancellation reduction. For the finite family in X ∩ N, Tucker gives a nonnegative zero relation and a nonnegative dual functional, with coefficient plus functional value positive at every index. Restricting the relation to its positive support, Scott cancellation forces each supported vector's negative into N. Consequently a strictly positive vector has zero coefficient and strictly positive functional value. Symmetry forces indifferent vectors to have functional value zero; sign completeness then yields exact realization. Theorem 1.1 therefore has substantial mathematical overlap; the initial keyword-based duplicate search missed this semantic reformulation. No complete Scott measurement project duplicate or copied Tau Ceti implementation was found. I am not treating that distinction as a resolution of the admission question.

The two author-actionable quality findings are repaired, with no weakening of the numbered results:

• IsSignedCharge.mono_of_nonnegative now needs only a signed charge and nonnegativity; probability monotonicity reuses it. The redundant probability-specific le_one_of_nonnegative wrapper is removed, while IsProbability.le_one remains.
• Three real-linear cancellation/extension helpers now use AddCommGroup and Module ℝ; additive relation cancellation uses only AddCommGroup. The proof bodies are preserved, and the normed finite-dimensional assumptions remain on the results that require separation.

I inspected both complete changed files and their diff. Warning-failing project and fixed-root builds, all 15 declaration linters (23 modules, 478 declarations), generated indexes, style, exact generated card checks, compiled axiom closure and option audit passed locally using the unmodified gates. The validated source/configuration copy is byte-identical, and LeanPool.lean is unchanged. The final project-clean build took 21.30 s wall, 43.32 s user CPU, 10.85 s system CPU, and 1,499,552 KiB peak RSS, versus 48.64 s / 100.75 s combined CPU / 4,045,376 KiB at baseline. Dependency artifacts and warm caches were retained on the same shared Azure VM; KPS decreased from 16 s to 2.7 s.

The PR description now discloses the partial overlap and contains no prior contributor-approval summaries. Earlier exact-head reviews are preserved as historical records, as requested; this readiness conclusion supersedes them and does not substitute for independent review. The prior head's full CI passed, but the repair head still requires its own CI and configured review. PR610/611 are merged and exact current-main CI is green, so the remaining blocker is the novelty judgment rather than the infrastructure rollout.

[Vilin97]

/review

[Vilin97]

Reviewed the complete 24-file contribution at 5145367f0023684a016f4e39237e225111a721c0, including both full current changed files and an independent comparison with their predecessors.

The mathematical content is acceptable. Finite cancellation criteria construct their realizing functionals and utilities. Infinite results give a conditional generalized-Kelley representation and a state correspondence on the constructed event-evaluation span, with finitely additive probabilities. The reordered Scott proofs use weaker algebraic contexts without changing their declaration/proof bodies. Signed-charge monotonicity still requires explicit nonnegativity.

I resolve the novelty discussion in favor of inclusion, with a qualification: Scott 1.1 and 1.2 are mathematical corollaries of the existing pinned field/integral Tucker alternatives. Positive-support cancellation, symmetry and sign completeness bridge 1.1; finite rational denominator clearing and coefficient repetition bridge 1.2. Both sides use the algebraic dual Module.Dual ℝ L; this is real prior-art coverage, without claiming a compiled Lean wrapper. The different sequence-cancellation/measurement setting, together with constructed semiorder, pair/difference and additive-extension representations, finite-local ordered-group maps, Boolean probability normalization, the KPS obstruction and modern infinite event-span reconstruction, justifies retaining the whole project. This comparison establishes no all-corpus absence claim.

Scott's 1964 publication is bibliographically verified. Exact numbered-paper wording remains unverifiable; this supplies no evidence of a mismatch.

One low-priority documentation correction: Preference/Intransitive.lean:15–17 says the converse uses the finite linear-inequality engine, while line 164 calls finite_staircase_representation. The actual quotient-order/staircase proof is present. This advisory does not prevent merging.

All five review dimensions pass with the explicit novelty-extension resolution above. Current CI is checked separately before publication and merge; this source review claims no new local kernel/build run.