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No measurability is required here. 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The definition is exact, not an efficient evaluation algorithm.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.KServer.optimalCost", "observation": "Infimum over costs of the finite label-string set, attained when k>0. The selected theorem requires k>=2.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.KServer.MainStatement", "observation": "Positive universal coefficient, all eligible metrics and starts, one policy and nonnegative finite additive constant for all finite words. B=0 for injective starts belongs to the existence theorem; the separate uniform implementation has unrestricted finite B.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" } ], "reviewed_source_files": [ { "path": "lean/ComparatorChallenges/KServer.json", "sha256": "e1d596679fa3adb7bc8be4d09c8e8219602df6a15ca0d8610989ae0021ad1dee" }, { "path": "lean/ComparatorChallenges/KServer.lean", "sha256": "e6ae7349a69c21a8466e6c8e02fe5572dba7ea9eaece17133041d1c2495daa6f" }, { "path": "lean/OAI/Combinatorics/KServer/Basic.lean", "sha256": "1b809bcf2b48b373766be41f4c907f343ebef67af92233c61e4fb0052b2878a3" }, { "path": "lean/docs/110.md", "sha256": "398ad379c334661bdba0c43c96f500483c18f73efb94123e79a79cd7b76c8afc" }, { "path": "lean/OAI/Combinatorics/KServer/Main.lean", "sha256": "dbaf015559def63f8331aaaf00e26bcde9e04f1b62b4241786265ecee425f04d" }, { "path": "lean/ComparatorChallenges/UniformKServer.lean", "sha256": "5defbe05414f2769784983a55aeb30ccc94c692e700f0772579febbf7a7b78cb" } ], "review_limit": "Definition and selected statement inspection only; imported dependency semantics, whole proof, kernel and executable program correspondence are not certified." }, { "config": "lean/ComparatorChallenges/LogspaceEquality.json", "challenge_module": "ComparatorChallenges.LogspaceEquality", "solution_module": "OAI.Computability.Logspace.Equality", "definition_names": [ "OAI.ExactDerandomization.Word", "OAI.ExactDerandomization.Language", "OAI.ExactDerandomization.CoinTape", "OAI.ExactDerandomization.Direction.move", "OAI.ExactDerandomization.Direction.moveInput", "OAI.ExactDerandomization.readInput", "OAI.ExactDerandomization.Machine.initial", "OAI.ExactDerandomization.Machine.step", "OAI.ExactDerandomization.Machine.run", "OAI.ExactDerandomization.Machine.spaceThrough", "OAI.ExactDerandomization.Machine.LogSpace", "OAI.ExactDerandomization.Machine.Deterministic", "OAI.ExactDerandomization.Machine.HaltsBy", "OAI.ExactDerandomization.Machine.Decides", "OAI.ExactDerandomization.Machine.extendCoins", "OAI.ExactDerandomization.Machine.acceptanceProbability", "OAI.ExactDerandomization.polynomialClock", "OAI.ExactDerandomization.L", "OAI.ExactDerandomization.RL", "OAI.ExactDerandomization.BPL" ], "theorem_names": [ "OAI.ExactDerandomization.exact_logarithmic_space_derandomization" ], "semantic_review_status": "selected_source_definitions_compared", "kernel_check_status": "not_run", "family_id": "103", "definition_reviews": [ { "name": "OAI.ExactDerandomization.Word", "observation": "Finite binary input words.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Language", "observation": "Sets of those binary words, hence language decision.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.CoinTape", "observation": "Infinite sequence of bits, with finite prefixes enumerated for probabilities.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Direction.move", "observation": "Local left/stay/right movement on signed work coordinates.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Direction.moveInput", "observation": "Input-head movement saturates at both endmarkers.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.readInput", "observation": "Left marker, indexed input bit, or right marker.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Machine.initial", "observation": "Initial finite state, all heads at origins/left marker, all work cells false.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Machine.step", "observation": "Halted configurations are absorbing; otherwise read one fresh bit, update scanned work cells, and move local heads.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Machine.run", "observation": "Iterates step using the next bit at each time.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Machine.spaceThrough", "observation": "Sums distinct visited writable positions per tape through time t, including initially visited blank cells.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Machine.LogSpace", "observation": "One positive coefficient bounds traversed cells by ceil(log2(n+2)) on every input, coin tape and finite time.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Machine.Deterministic", "observation": "Transition action independent of the coin bit for every possible scanned state/symbol tuple.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Machine.HaltsBy", "observation": "Every coin tape has a halting output by the supplied time.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Machine.Decides", "observation": "For each word one finite time and correct Boolean output, common to all coin tapes.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Machine.extendCoins", "observation": "Finite fair-bit prefix followed by false; later bits cannot affect a t-step run.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.Machine.acceptanceProbability", "observation": "Exact count of accepting t-bit prefixes divided by 2^t. Direct enumeration is not the claimed low-space estimator.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.polynomialClock", "observation": "c*(n+2)^k time clock, with constants fixed for the machine.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.L", "observation": "Exists a deterministic logspace machine deciding the binary language. No separate polynomial clock in this definition; total deterministic logspace implies polynomial time by the finite-configuration argument described by the paper.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.RL", "observation": "Logspace machine, polynomial worst-case clock for all coin tapes, zero no-instance acceptance and at least one-half yes-instance acceptance.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.ExactDerandomization.BPL", "observation": "Logspace machine, polynomial worst-case clock for all coin tapes, at most one-third no-instance and at least two-thirds yes-instance acceptance.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" } ], "reviewed_source_files": [ { "path": "lean/ComparatorChallenges/LogspaceEquality.json", "sha256": "80a22fecb8d68504a00419c12de7d83f9a6556f01d512ef7607c1acff61118cc" }, { "path": "lean/ComparatorChallenges/LogspaceEquality.lean", "sha256": "5c9ed4d04a778b61b33693eff64227a9c5b8162bf53c0b3e3938fb505831d817" }, { "path": "lean/OAI/Computability/Logspace/Deterministic.lean", "sha256": "f51289517dc00b6f843e6f408f393c1bcac7d25e78eb162c0c629618875d252b" }, { "path": "lean/docs/103.md", "sha256": "21e0be3e46468655991435570d83521e12ab9c83ad76fa6f484c88edcbc0e139" } ], "review_limit": "Definition and selected statement inspection only; imported dependency semantics, whole proof, kernel and executable program correspondence are not certified." }, { "config": "lean/ComparatorChallenges/Naimark.json", "challenge_module": "ComparatorChallenges.Naimark", "solution_module": "OAI.Analysis.Naimark.Tracial", "definition_names": [ "OAI.NaimarkZFC.IsSimpleCStar", "OAI.NaimarkZFC.IsState", "OAI.NaimarkZFC.IsFaithfulTracialState", "OAI.NaimarkZFC.IsIrreducible", "OAI.NaimarkZFC.UnitarilyEquivalent", "OAI.NaimarkZFC.HasUniqueIrreducibleRepresentation", "OAI.NaimarkZFC.IsIsomorphicToCompacts" ], "theorem_names": [ "OAI.NaimarkZFC.main" ], "semantic_review_status": "selected_source_definitions_compared", "kernel_check_status": "not_run", "family_id": "297", "definition_reviews": [ { "name": "OAI.NaimarkZFC.IsSimpleCStar", "observation": "Nontrivial C*-algebra and only bottom/top norm-closed two-sided ideals; not the absence of a selected finite list of ideals.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.NaimarkZFC.IsState", "observation": "Continuous complex-linear functional of norm one, real and nonnegative on star(a)*a.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.NaimarkZFC.IsFaithfulTracialState", "observation": "State plus cyclic trace and strictly positive value on every nonzero square; not just positive on a finite probe set.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.NaimarkZFC.IsIrreducible", "observation": "Nonzero *-representation on a complex Hilbert space whose closed invariant subspaces are only zero/all.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.NaimarkZFC.UnitarilyEquivalent", "observation": "Surjective linear isometric equivalence intertwining the two representations, not merely matching spectra on sampled operators.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.NaimarkZFC.HasUniqueIrreducibleRepresentation", "observation": "Every pair of irreducible representations in the stated Hilbert universes is unitarily equivalent. This predicate alone does not assert existence; the selected nontrivial C*-algebra framework supplies the separate existence context.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.NaimarkZFC.IsIsomorphicToCompacts", "observation": "Injective *-homomorphism whose range is exactly the compact operators on the Hilbert space. The source counterexample is outside the separable regime and gives no finite-dimensional numerical construction.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" } ], "reviewed_source_files": [ { "path": "lean/ComparatorChallenges/Naimark.json", "sha256": "a657509ed81bd3769754cb2a5c3fa0f6bf7504935c46660b3a6fe8400bbbde5d" }, { "path": "lean/ComparatorChallenges/Naimark.lean", "sha256": "68b364f0998bd30cd0ebf8c87c591267df29b97f183204e93396bda7befe86e0" }, { "path": "lean/docs/297.md", "sha256": "5d0717736953a9833486896e53d80a456b63d4ce530a2b7888a8ad374e452fe4" }, { "path": "lean/OAI/Analysis/Naimark/Basic.lean", "sha256": "4b7fffb6c31cde6f4c53f18588a56c419508e4fdecd7d55a6b5d01b6dc35c0a6" } ], "review_limit": "Definition and selected statement inspection only; imported dependency semantics, whole proof, kernel and executable program correspondence are not certified." }, { "config": "lean/ComparatorChallenges/OccupiedOverlap.json", "challenge_module": "ComparatorChallenges.OccupiedOverlap", "solution_module": "OAI.RepresentationTheory.RowColumn.Occupied", "definition_names": [ "OAI.CubeShuffle.UnitaryFinite.IsUnitary", "OAI.CubeShuffle.Specht.hilbertSpace", "OAI.CubeShuffle.Specht.unitaryRepresentation", "OAI.CubeShuffle.Specht.relabelledUnitary", "OAI.RowColumn.OccupiedOverlapEndpoint" ], "theorem_names": [ "OAI.RowColumn.occupied_overlap_endpoint", "OAI.RowColumn.occupied_overlap" ], "semantic_review_status": "selected_source_definitions_compared", "kernel_check_status": "not_run", "family_id": "238", "definition_reviews": [ { "name": "OAI.CubeShuffle.UnitaryFinite.IsUnitary", "observation": "Finite-group representation preserves the complex inner product for every group element and vector pair.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.CubeShuffle.Specht.hilbertSpace", "observation": "Actual Young-diagram Specht polytabloid orbit span embedded in the complex Euclidean tabloid space, not an arbitrary vector space with a supplied dimension.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.CubeShuffle.Specht.unitaryRepresentation", "observation": "Actual Specht action conjugated through the Hilbert-space equivalence.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.CubeShuffle.Specht.relabelledUnitary", "observation": "Pullback of that genuine action along the permutation equivalence induced by occupied-board/Young-cell relabeling, which enforces equal cardinalities.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.RowColumn.OccupiedOverlapEndpoint", "observation": "Absolute constant for every eligible occupied board, actual Young shape, hook cutoff, genuine row/column unitary irreducibles and complete orthogonal isometric multiplicity-copy families. Sums squared operator norms over every pair of copies; a single chosen copy or Frobenius surrogate is insufficient. 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Sending every gap to infinity separates the ordered k observations.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.Rokhlin.MixingOfOrder", "observation": "For every k-tuple of measurable sets, the translated intersection measure tends to the product along all diverging gaps. The source is asymptotic and supplies no finite waiting-time rate; one-step pairwise-independent finite data is not its hypothesis.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" } ], "reviewed_source_files": [ { "path": "lean/ComparatorChallenges/Rokhlin.json", "sha256": "a0421a77acd1ebe5a01865b0aed6c19fcb35cd6fd0c5a8d5614e9c7ec1e723a9" }, { "path": "lean/ComparatorChallenges/Rokhlin.lean", "sha256": "f1cb24d9b04f86273fd9895eef73da12dcda912a6c9e1fb90956ed6af2a8383d" }, { "path": "lean/docs/145.md", "sha256": "ea72c0ad0646b0b425402ab4a0ccaa7f4aab5df3c1e0c71101f3ae5411fe04d9" }, { "path": "lean/OAI/Dynamics/MultipleMixing/HilbertCodes.lean", "sha256": "1ea71195ab9acb5de95eba35b68a9d7e679d8aad7f40b5b4352be11dbde6b4f5" } ], "review_limit": "Definition and selected statement inspection only; imported dependency semantics, whole proof, kernel and executable program correspondence are not certified." }, { "config": "lean/ComparatorChallenges/SpinAngle.json", "challenge_module": "ComparatorChallenges.SpinAngle", "solution_module": "OAI.RepresentationTheory.SpinAngle.TypeAngle", "definition_names": [ "OAI.SpinAngle.TypeAngle.row", "OAI.SpinAngle.TypeAngle.column", "OAI.SpinAngle.TypeAngle.phi" ], "theorem_names": [ "OAI.SpinAngle.TypeAngle.one_sided_type_angle" ], "semantic_review_status": "selected_source_definitions_compared", "kernel_check_status": "not_run", "family_id": "238", "definition_reviews": [ { "name": "OAI.SpinAngle.TypeAngle.row", "observation": "Row index of an actual occupied cell in W.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.SpinAngle.TypeAngle.column", "observation": "Column index of an actual occupied cell in W.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" }, { "name": "OAI.SpinAngle.TypeAngle.phi", "observation": "Product over rows of (m/s)^s for positive occupied row count s, with empty-row factor one, equivalently the missing-cell factors; bounded by exp(total missing cells). The angle theorem also requires actual signed tensor type projections and matching global/line type sizes. A geometry factor alone does not certify a computed projection or sweep speed.", "comparison": "No intended-model mismatch detected in this selected source-level comparison", "status": "source_level_review_only", "independent_kernel_status": "not_run" } ], "reviewed_source_files": [ { "path": "lean/ComparatorChallenges/SpinAngle.json", "sha256": "c1f18b2fe4b0d069ea22ceb5b3840e1eb8ae0bd12121748bebe4a89757acf1b9" }, { "path": "lean/ComparatorChallenges/SpinAngle.lean", "sha256": "d78fd35b20a9ff932f70739cea90fcc98cd1960e9e117b1c6f47217ee632620a" }, { "path": "lean/docs/238.md", "sha256": "90935144b3f4346476ff852911ad709fe354446bc383e291db4afb90a98aaa49" }, { "path": "lean/OAI/RepresentationTheory/SpinAngle/TypeAngle.lean", "sha256": "2d3210c1388eee9a2cc2eaf004c2c53a20715115a003bffc9cf653a5ac503a78" }, { "path": "lean/OAI/RepresentationTheory/SpinAngle/Core.lean", "sha256": "91def13f821665924acfb5fc0ec405142cffe031b478e8095ade1743111217ee" } ], "review_limit": "Definition and selected statement inspection only; imported dependency semantics, whole proof, kernel and executable program correspondence are not certified." } ], "primary_documentation": "https://github.com/leanprover/comparator", "interpretation": "All ten queued configurations/65 declared entries received selected source-level observations. No intended-model mismatch detected there. This finite queue does not establish full source semantics, imported trust closure, theorem proof, kernel acceptance or executable program correspondence.", "generated_at_utc": "2026-10-08T21:29:44.999821+00:00", "reviewed_configs": 10, "source_level_definition_entries_reviewed": 65, "pending_configs": 0, "pending_definition_entries": 0, "textual_control": { "config": "LogspaceEquality", "challenge_definition_prefix_matches_solution_after_whitespace_comment_removal": true, "interpretation": "A lexical control over the displayed definitions/structures, not Lean elaboration, definitional-equivalence proof or independent kernel acceptance." } }