{ "accepted_cores": 29, "difficulty_calibrated": false, "items": { "sogb-001": { "editorial": "accepted", "formal_alignment": "conclusion-only", "issues": [], "remaining_unformalized": [ "The target states only reversibility, not the natural-language explanations of why division/cancellation are unnecessary or explicit counterexamples to normalization, irreducibility and convergence implications.", "No normalization, mixing, query-cost or empirical difficulty claim is formalized by this view." ], "report_sha256": "43a84923d0675442f1001dab29d2821a8472e08d0ca01a005dabbaf2ccc73baa", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-002": { "editorial": "accepted", "formal_alignment": "conclusion-only", "issues": [], "remaining_unformalized": [ "The target is the final objective-gap inequality. The reference Lean proof contains the sign split, but the target does not separately state the global-zero characterization for q<0 or the parameter interpretation of genuine geometric decay.", "No iterate convergence, distance rate, uniqueness, derivation of the upper model from smoothness, or empirical difficulty assertion is certified." ], "report_sha256": "43a84923d0675442f1001dab29d2821a8472e08d0ca01a005dabbaf2ccc73baa", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-003": { "editorial": "accepted-after-repair", "formal_alignment": "conclusion-only", "issues": [], "prior_review_report_sha256": "43a84923d0675442f1001dab29d2821a8472e08d0ca01a005dabbaf2ccc73baa", "remaining_unformalized": [ "The finite-dimensional Lebesgue-measure Gaussian domination argument, evaluation of the Gaussian integral, measurability, and positivity of the Gibbs normalizer are explanatory mathematics, not conclusions of the supplied Lean reference.", "The convexity of V(x)=|x| at k=0, its failure to have a positive global strong-convexity modulus, and the explicit integral of exp(-|x|) equal to 2 are not proved by the supplied Lean reference.", "Any separate derivation of the k/2 envelope remains outside the supplied midpoint proof and its formal conclusion." ], "report_sha256": "914be5d38d8804bab08c15730b870661f9d016b8f7b04dff7515e4fa6616175b", "reviewer": "agent-task:root/sog_exact_repair_reviewer_round1" }, "sogb-004": { "editorial": "accepted", "formal_alignment": "no-aligned-view", "issues": [], "remaining_unformalized": [ "This batch admits no aligned Lean view. The finite-dimensional finite-second-moment specialization, product-coupling cost bound, real-valued interpretation and explanatory boundary statements are reviewed here as mathematics, not as a checked translation of the full QA." ], "report_sha256": "43a84923d0675442f1001dab29d2821a8472e08d0ca01a005dabbaf2ccc73baa", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-005": { "editorial": "accepted", "formal_alignment": "no-aligned-view", "issues": [], "remaining_unformalized": [ "No aligned formal view is admitted. The weaker single-point regularity formulation, nonunit counterexample/correction and explanatory identification with the sphere's induced metric are not certified as a full QA translation by the stronger bundled local theorem." ], "report_sha256": "43a84923d0675442f1001dab29d2821a8472e08d0ca01a005dabbaf2ccc73baa", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-006": { "editorial": "accepted", "formal_alignment": "no-aligned-view", "issues": [], "remaining_unformalized": [ "There is no admitted equivalent Lean task. The arbitrary-kernel explanation, 00/11 nonirreducibility example and convergence discussion are NL obligations beyond the cited local reversibility declaration." ], "report_sha256": "43a84923d0675442f1001dab29d2821a8472e08d0ca01a005dabbaf2ccc73baa", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-007": { "editorial": "accepted", "formal_alignment": "no-aligned-view", "issues": [], "remaining_unformalized": [ "No aligned Lean view is admitted for the entire QA. Constructing a consistent algorithmic sequence of adjacent hybrids/history laws, and any adapters identifying the abstract kernels with a concrete recursive algorithm, remain outside the component theorems.", "The TV/expected-cost counterexample, uniform-integrability or tail-control discussion, recursion/stopping/cap comparisons and source-paper noncompletion explanation are NL-reviewed obligations, not certified by the local telescope declaration." ], "report_sha256": "43a84923d0675442f1001dab29d2821a8472e08d0ca01a005dabbaf2ccc73baa", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-008": { "editorial": "accepted", "formal_alignment": "no-aligned-view", "issues": [], "remaining_unformalized": [ "This QA has no aligned Lean view. Borel measurability bookkeeping, the numerical normalization criterion and its probability-density verification, positivity of the Lebesgue integral, and the infinite-volume V=0 example are independently checked prose obligations beyond the cited log-concavity leaf." ], "report_sha256": "eab27df13f595a7778c7ba0d0cae82af0e9745fd85eee509d104e2bdab6e6204", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-009": { "editorial": "accepted", "formal_alignment": "no-aligned-view", "issues": [], "remaining_unformalized": [ "There is no aligned Lean certification of the full terminology comparison, the choice of an algorithmic run/input law, any invariant distribution or actual-output-law identification, or any expected-cost bound." ], "report_sha256": "eab27df13f595a7778c7ba0d0cae82af0e9745fd85eee509d104e2bdab6e6204", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-010": { "editorial": "accepted", "formal_alignment": "no-aligned-view", "issues": [], "remaining_unformalized": [ "The full explanatory answer has no equivalent Lean task. In particular the ordinary differentiable-function interpretation, terminology distinctions and warnings against inferring an unprovided algorithmic rate are prose review findings, not an alignment certificate." ], "report_sha256": "eab27df13f595a7778c7ba0d0cae82af0e9745fd85eee509d104e2bdab6e6204", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-011": { "editorial": "accepted", "formal_alignment": "no-aligned-view", "issues": [], "remaining_unformalized": [ "No aligned Lean view is admitted for the general smooth-function sphere-gradient definition, tangent-space construction, uniqueness argument, dependence only on the restriction, or the explanatory ambient-versus-tangent comparison. The local feature identities are supporting instances, not certification of the entire QA." ], "report_sha256": "eab27df13f595a7778c7ba0d0cae82af0e9745fd85eee509d104e2bdab6e6204", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-012": { "editorial": "accepted", "formal_alignment": "no-aligned-view", "issues": [], "remaining_unformalized": [ "The complete explanatory QA has no aligned Lean view. The rectangle-language interpretation, general discussion of dependence and distinction between feasibility and cost optimality are prose-reviewed here; no optimal-plan or metric certification is claimed." ], "report_sha256": "eab27df13f595a7778c7ba0d0cae82af0e9745fd85eee509d104e2bdab6e6204", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-013": { "editorial": "accepted", "formal_alignment": "no-aligned-view", "issues": [], "remaining_unformalized": [ "There is no aligned proof-completion task for this QA. The verbal random-site interpretation, sweep/time-unit conventions, self-transition explanation and absence of mixing/query-cost conclusions are editorially checked rather than certified as an equivalent Lean statement.", "Neither the cited mixture definition nor the supplementary coordinate-retention evidence implements a conditional sampler or proves a target-specific null-fiber conditional law, ergodicity, mixing time or cost theorem." ], "report_sha256": "eab27df13f595a7778c7ba0d0cae82af0e9745fd85eee509d104e2bdab6e6204", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-014": { "editorial": "accepted", "formal_alignment": "no-aligned-view", "issues": [], "remaining_unformalized": [ "No aligned Lean view is admitted for the row-vector/matrix formulation, detailed-balance-to-invariance summation under stochastic normalization, event-TV convergence definition, or identity-matrix illustration. No irreducibility, aperiodicity, rate or general-state ergodic theorem is certified." ], "report_sha256": "eab27df13f595a7778c7ba0d0cae82af0e9745fd85eee509d104e2bdab6e6204", "reviewer": "agent-task:root/sog_source_reviewer_round1" }, "sogb-015": { "editorial": "accepted", "formal_alignment": "conclusion-only", "issues": [], "remaining_unformalized": [ "The natural-language account of measurable projection, inverse images, and why the second conjunct is unused is reviewed here against definitions and proof dependencies, not certified as a separate proposition by the conclusion-only Lean target.", "The explanation that no additional probability premise on nu is needed, and the distinction between such a premise and its derivability, are not separate Lean results in this task. The signature and displayed source proof support that explanation.", "The exclusions of optimality, arbitrary unbounded integrability, and moment guarantees are scope explanations rather than theorem statements proved by this target. No new production theorem, Registry leaf, or canonical VERIFIED publication is supplied or inferred.", "Rubric appropriateness and the provisional foundation/L2 difficulty assessment remain independent AI editorial judgments. They are not empirical calibration, human expert consensus, or a claim that every explanatory component has been formalized." ], "report_sha256": "4fac2c04ddb23f8b79d84b600616c7d994ab6c78f29f002b4132ecbdd3934abe", "reviewer": "agent-task:root/sog_paired_review_3" }, "sogb-016": { "editorial": "accepted", "formal_alignment": "conclusion-only", "issues": [], "remaining_unformalized": [ "Conclusion-only coverage means the exact displayed representation equivalence is the artifact being checked. Natural-language pedagogical completeness, the four separate rubric awards and provisional difficulty labels are not additional Lean propositions; local derivative and chain-rule mechanisms are nevertheless formally present in the proof and inspected dependencies.", "The separate stationarity/eigenvector equivalences, arbitrary-manifold or arbitrary-metric generalizations, textbook-wide alignment, optimization algorithms and convergence rates are not established by this QA. The packet explicitly excludes these, so this is a scope boundary rather than a repair request." ], "report_sha256": "49829567e1d3cc6672b3449ac3e47dbd2f696589ebf774ab06723e8d7bd96c31", "reviewer": "agent-task:root/sog_paired_review_5" }, "sogb-017": { "editorial": "accepted", "formal_alignment": "conclusion-only", "issues": [], "remaining_unformalized": [ "Only the displayed one-step event discrepancy proposition is the formal conclusion of this QA. Its prose explanation, independent pedagogical assessment and four-point rubric are not separately formalized scoring theorems, although the integrability and conversion mechanisms appear in the checked reference proof.", "Common-suffix data processing and finite telescoping are separate local results; recursively constructed adaptive history kernels, measurable paper error quantities, stopping/cap adapters, uncapped/capped comparisons and expected query-cost guarantees remain outside this QA. The packet explicitly acknowledges these limits and does not claim full alignment of the earlier hybrid/cost question or a whole paper theorem." ], "report_sha256": "49829567e1d3cc6672b3449ac3e47dbd2f696589ebf774ab06723e8d7bd96c31", "reviewer": "agent-task:root/sog_paired_review_5" }, "sogb-018": { "editorial": "accepted", "formal_alignment": "conclusion-only", "issues": [], "remaining_unformalized": [ "The fixed target certifies only the conditional strict endpoint bound. It does not separately formalize the new explanatory Bernoulli construction, its discrepancy probability, edge norm or shortcut-failure diagnosis.", "The proof invokes original gluing, marginal and Minkowski ancestors rather than reproving the conditional-kernel existence theorem, its almost-everywhere uniqueness, or the full measure-theoretic explanation in the prose answer. The relevant interfaces and source obligations were inspected, but these are not separately graded conclusions of this example.", "The exact non-strict triangle inequality belongs to the separate WassersteinTriangleExact consumer. This task neither imports it as a shortcut nor constructs a full Wasserstein metric-space instance, proves optimal-plan attainment, or proves a theorem about all arbitrary metric spaces.", "L4 labels, rubric adequacy and license/family placement are editorial judgments on the inspected frozen slice, not Lean propositions, human consensus, authenticated model execution or empirical difficulty measurements.", "This report supplies independent paired-QA editorial review only. It does not publish a canonical source theorem, approve a repair overlay, advance Registry/frontier status or establish completion of the continuing benchmark Goal." ], "report_sha256": "99966a8ea0a7ed065b3442784dee703570afbc6906762f515a76a4dc29f2cb7a", "reviewer": "agent-task:root/sog_paired_review_6" }, "sogb-019": { "editorial": "accepted-after-repair", "formal_alignment": "conclusion-only", "issues": [], "prior_review_report_sha256": "bc22cf3d4349a8f7ad608a38cc57da4c6ad2faaed70725d1bd0506276746e289", "remaining_unformalized": [ "The constrained-support counterexample and diagnosis are prose claims, not additional conclusions of the unchanged Lean norm-bound task.", "Acceptance is an exact mathematical/rubric review, not a compiler execution receipt, empirical calibration, model-evaluation result or theorem-publication certificate." ], "report_sha256": "01e79bb99d9749d690f38dc2c7ddb3ac07d93969fa85b6385c7285ab28297819", "reviewer": "agent-task:/root/sog_exact_repair_7" }, "sogb-020": { "editorial": "accepted-after-repair", "formal_alignment": "no-aligned-view", "issues": [], "prior_review_report_sha256": "63d89203fd5e49b40e2b2e5d1e450ee5f7907aa2858355a740d3bda780cc7f21", "remaining_unformalized": [ "This core has no aligned Lean QA. Its unchanged supporting module is evidence for the norm, weighted telescope and finite-iterate witness, not certification of the entire prose exercise.", "The explicit constant-step optimization and degenerate-case prose are not separate matching formal conclusions in this core.", "This exact-proposal review does not certify compiler execution, model or human performance, empirical difficulty calibration, theorem publication or whole-Goal completion." ], "report_sha256": "67c87571a96f9649c98b1a34ee6dc8f0d8f8084c2c2b6e822381986c86bdf3d5", "reviewer": "agent-task:/root/sog_exact_repair_7" }, "sogb-021": { "editorial": "accepted-after-repair", "formal_alignment": "conclusion-only", "issues": [], "prior_review_report_sha256": "bc22cf3d4349a8f7ad608a38cc57da4c6ad2faaed70725d1bd0506276746e289", "remaining_unformalized": [ "The finite-state counterexample and persistent-discrepancy calculation remain prose rather than additional Lean conclusions. The formal target asserts only invariance of the supplied finite target.", "This review provides no irreducibility, uniqueness, convergence or mixing theorem, no compiler execution receipt, and no empirical calibration, publication or whole-Goal completion certification." ], "report_sha256": "01e79bb99d9749d690f38dc2c7ddb3ac07d93969fa85b6385c7285ab28297819", "reviewer": "agent-task:/root/sog_exact_repair_7" }, "sogb-022": { "editorial": "accepted-after-repair", "formal_alignment": "conclusion-only", "issues": [], "prior_review_report_sha256": "1004de0d5767c4fd5fa3d9727c5303bf9816e2d8dfb4099bfd1b30ac2f9b52e2", "remaining_unformalized": [ "Formal coverage remains the supplied selected-curve scalar endpoint inequality only. Curve existence for arbitrary endpoints, constant-speed geodesicity, and identification of the scalar derivative with a Riemannian or Wasserstein gradient pairing are not supplied by this target.", "The explanatory audit of totalized derivatives and any possible one-sided replacement API is prose rather than an additional formal conclusion; the actual HasDerivAt premise is retained unchanged.", "The sign comparison and negative-alpha example used to assess this wording repair are mathematical review evidence, not additional Lean theorems or evidence of empirical difficulty calibration. No compiler replay or publication status is asserted." ], "report_sha256": "e3f95a1b798d4dd375e96e668afc2a216084ac594bd51a91b13bd3adc0b64f7e", "reviewer": "agent-task:/root/sog_exact_repair_8" }, "sogb-023": { "editorial": "accepted", "formal_alignment": "conclusion-only", "issues": [], "remaining_unformalized": [ "The aligned target certifies only the finite, nonnegative objective-gap inequality at 0