Publish faithful five-claim VarEOT reproduction

.openresearch/artifacts/claim1/EVAL.md

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+# Claim 1 evaluation contract
+
+Run exactly:
+
+```bash
+uv sync --frozen && .venv/bin/python -m vareot_repro.run_all
+```
+
+The command must print the selected backend/flavor, actual CPU allocation, resolved versions, raw results, independent-checker result, negative-control exit code, runtime, and final status. Any failed numerical identity, source-marginal audit, or control causes a nonzero exit.

.openresearch/artifacts/claim1/baseline_run.json

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+{
+  "run_id": "00f0c791-19f1-4da1-a02d-07cc8bc60ad1",
+  "git_sha": "03460f11bc71d2d71a89d955d6ecb6bfa2db8d30",
+  "command": "uv sync --frozen && .venv/bin/python -m vareot_repro.run_all",
+  "backend": "hf",
+  "flavor": "cpu-upgrade",
+  "image": "ghcr.io/astral-sh/uv:python3.12-bookworm-slim",
+  "estimated_cores_required": 2,
+  "actual_cpu_affinity_count": 64,
+  "torch_threads": 32,
+  "cuda_available": false,
+  "scientific_runtime_seconds": 0.7134815280000169,
+  "wall_runtime_seconds": 26,
+  "status": "VERIFIED",
+  "maximum_reported_identity_error": 4.440892098500626e-16,
+  "negative_control_exit_code": 1
+}

.openresearch/artifacts/claim1/claim_contract.json

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+{
+  "claim_id": "claim1_theorem_3_2",
+  "claim_text": "EOT_epsilon(p0,p1) = sup_f L(f) = sup_{f,xi} L(f,xi).",
+  "source": {
+    "url": "https://ar5iv.labs.arxiv.org/html/2602.02241",
+    "retrieved_utc": "2026-08-02T03:20:39Z",
+    "sha256": "50f2161eea8428c71e455b7412cd020157a3450f7c60dd6271a8bfe6c6f08261",
+    "anchor": "#S3.Thmtheorem2 and Equation 13"
+  },
+  "assumptions": [
+    "epsilon > 0",
+    "p0 and p1 are absolutely continuous Borel probability measures on R^D",
+    "f is admissible for the weak dual and xi is integrable",
+    "all displayed expectations and partition functions are finite"
+  ],
+  "quantifiers": "For every admissible EOT instance, the two suprema equal the EOT value; for each fixed admissible f, xi_f makes the pointwise variational bound tight.",
+  "machine_checks": [
+    "symbolic pointwise gap is epsilon E[delta + exp(-delta) - 1] and is nonnegative",
+    "continuous Gaussian primal, semidual, and variational values agree",
+    "the recovered conditional has exactly the target marginal",
+    "adaptive quadrature independently checks partition and semidual values",
+    "a deliberately non-optimal potential is rejected"
+  ],
+  "failure_policy": "The verifier exits nonzero if any identity, marginal, independent-checker, or negative-control condition fails."
+}

.openresearch/artifacts/claim1/independent_checker_output.json

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+{"passed":true,"maximum_adaptive_quadrature_abs_error":4.440892098500626e-16,"maximum_target_marginal_moment_error":2.220446049250313e-16,"failures":[]}

.openresearch/artifacts/claim1/limitations.md

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+# Claim 1 limitations and deviations
+
+- The symbolic variational reduction is general under the paper's admissibility assumptions.
+- The numerical instance is continuous and analytic, but scoped to one-dimensional Gaussian marginals and quadratic potentials.
+- Neural function classes and full joint training are covered cumulatively by Claims 4 and 5, not inferred from this Gaussian special case.
+- No finite experiment is presented as proof of a universal theorem.

.openresearch/artifacts/claim1/method.md

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+# Claim 1 method
+
+The verifier reconstructs the variational step independently. Writing `xi=xi_f+delta` yields
+
+`L(f)-L(f,xi) = epsilon E[delta + exp(-delta) - 1]`.
+
+The elementary inequality `exp(-delta) >= 1-delta` proves nonnegativity for every real `delta`, with equality only at zero. This proves the auxiliary optimization is exact whenever the original semidual is admissible.
+
+For a non-vacuous continuous check, the verifier solves EOT between two one-dimensional Gaussian distributions. The optimal quadratic potential induces a Gaussian conditional whose target marginal is checked analytically. The primal conditional-entropy objective, weak semidual, and variational objective are then compared. A separate adaptive-integration implementation checks the partition function and expectations without discretizing the transport problem.
+
+The negative control scales the analytic precision parameter by 1.15. It no longer produces the target marginal and must make the verifier exit nonzero.

.openresearch/artifacts/claim1/negative_control_output.json

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+{"control":"scale analytic precision q by 1.15","expected_exit_nonzero":true,"actual_exit_code":1,"passed":true,"failures":["shift_and_scale: primal=semidual","shift_and_scale: target variance","reverse_scale: primal=semidual","reverse_scale: target variance"]}

.openresearch/artifacts/claim1/page.md

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+# Current verification: Claim 1 / Theorem 3.2
+
+Status: **VERIFIED** by immutable HF run `0f29450d-5b73-4214-ae3e-10d47608a377` at commit `7ee3d8e5e21f4f59fd5025e3c2df8f80f584db86`.
+
+This page supersedes the grid-discretized historical verifier for Claim 1. It tests the exact variational identity with a symbolic reconstruction and a continuous Gaussian EOT instance. The executable entrypoint is `vareot_repro/run_all.py`; the independent implementation is in `vareot_repro/claim1.py`; the deliberately wrong-potential control is `vareot_repro/negative_control.py`.
+
+The frozen aggregate is `../frozen_precision_run.json`. The maximum continuous equality and adaptive-quadrature errors were `4.44e-16`; the wrong-potential control exited `1`.
+
+The claim contract, exact source quantifiers, assumptions, method, and limitations are adjacent to this page.

.openresearch/artifacts/claim1/raw_results.json

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+{
+  "evidence_run_id": "0f29450d-5b73-4214-ae3e-10d47608a377",
+  "status": "VERIFIED",
+  "scope": "continuous one-dimensional Gaussian distributions; exact quadratic optimal potential",
+  "cases": [
+    {"name":"shift_and_scale","epsilon":0.7,"mean0":-0.7,"std0":0.8,"mean1":1.2,"std1":1.35,"primal_eot":1.3109239627314626,"semidual":1.310923962731463,"variational":1.310923962731463,"primal_semidual_abs_error":4.440892098500626e-16,"semidual_variational_abs_error":0.0,"adaptive_quadrature_abs_error":4.440892098500626e-16,"target_mean_abs_error":2.220446049250313e-16,"target_variance_abs_error":0.0},
+    {"name":"reverse_scale","epsilon":1.1,"mean0":0.5,"std0":1.6,"mean1":-0.4,"std1":0.65,"primal_eot":0.4307262849673188,"semidual":0.4307262849673188,"variational":0.430726284967319,"primal_semidual_abs_error":0.0,"semidual_variational_abs_error":2.220446049250313e-16,"adaptive_quadrature_abs_error":1.1102230246251565e-16,"target_mean_abs_error":5.551115123125783e-17,"target_variance_abs_error":5.551115123125783e-17}
+  ],
+  "symbolic_identity": "L(f)-L(f,xi_f+delta)=epsilon*E[delta+exp(-delta)-1]",
+  "symbolic_certificate_passed": true
+}

.openresearch/artifacts/claim1/source_audit.md

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+# Claim 1 source audit
+
+- Retrieved `https://ar5iv.labs.arxiv.org/html/2602.02241` with the explicit User-Agent `OpenResearch-Reproduction/1.0 (paper-source-audit)` at `2026-08-02T03:20:39Z`.
+- HTML SHA-256: `50f2161eea8428c71e455b7412cd020157a3450f7c60dd6271a8bfe6c6f08261`.
+- Theorem anchor: `#S3.Thmtheorem2`; defining objective: Equation 12; equality: Equation 13; tight normalizer: Proposition 3.1, Equation 11.
+- Theorem 3.2 quantifies over the admissible weak-dual functions and asserts equality of the EOT value, the weak semidual supremum, and the variational supremum.
+- Standing setup: `p0,p1` are absolutely continuous Borel probability measures on `R^D`; `epsilon>0`; the partition function and expectations are finite.
+
+## Version audit
+
+The current arXiv API identifies `2602.02241v2` (updated 2026-06-04). The downloaded v2 PDF SHA-256 is `257689c36d4d589942660667e880211ab18c6de37d9c643adacd571beaf1949b`. Theorem 3.2 is unchanged in substance between the cached ar5iv HTML and v2 PDF. Later theorem numbering and rates differ and must be contracted separately.

.openresearch/artifacts/claim2/EVAL.md

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+# Claim 2 evaluation contract
+
+Run the inherited command:
+
+```bash
+uv sync --frozen && .venv/bin/python -m vareot_repro.run_all
+```
+
+The cumulative process writes `raw_results.json`, `independent_checker_output.json`, and `negative_control_output.json`. It exits nonzero if the exact generalized-KL identity, independent integral, inequality, or negative control fails.

.openresearch/artifacts/claim2/claim_contract.json

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+{
+  "claim_id": "claim2_theorem_3_3",
+  "claim_text": "epsilon KL(pi* || pi_f,xi) = L* - L(f,xi), with KL interpreted for finite non-normalized measures as in Definition A.1.",
+  "source": {
+    "url": "https://ar5iv.labs.arxiv.org/html/2602.02241",
+    "retrieved_utc": "2026-08-02T03:20:39Z",
+    "sha256": "50f2161eea8428c71e455b7412cd020157a3450f7c60dd6271a8bfe6c6f08261",
+    "anchors": ["#S3.Thmtheorem3", "Equation 14", "Definition A.1"]
+  },
+  "assumptions": [
+    "the EOT optimizer pi* and candidate finite measure pi_f,xi are mutually absolutely continuous where required",
+    "the generalized KL and objectives are finite",
+    "p0 and p1 are absolutely continuous probabilities and epsilon is positive"
+  ],
+  "quantifiers": "For every admissible candidate pair (f,xi), the exact objective gap is epsilon times generalized KL; its normalized xi_f specialization is ordinary probability KL.",
+  "machine_checks": [
+    "derive the Radon-Nikodym ratio and finite-measure mass correction",
+    "evaluate a non-optimal quadratic f and nonconstant xi shift on two continuous Gaussian EOT instances",
+    "independently integrate the conditional KL and candidate mass",
+    "reject the ordinary-KL formula when the candidate is deliberately unnormalized"
+  ],
+  "failure_policy": "Any identity error above 1e-10, failed independent integral, or surviving negative control makes the cumulative verifier exit nonzero."
+}

.openresearch/artifacts/claim2/independent_checker_output.json

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+{"passed":true,"adaptive_quadrature_abs_errors":[0.0,0.0],"maximum_gap_identity_abs_error":5.828670879282072e-16}

.openresearch/artifacts/claim2/limitations.md

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+# Claim 2 limitations and deviations
+
+- The symbolic Radon-Nikodym derivation covers the theorem's admissible domain; the numerical non-vacuity checks are continuous Gaussian cases.
+- Adaptive quadrature is independent numerical corroboration, not a proof over every distribution.
+- The deliberately non-normalized candidate is stricter than checking only `xi=xi_f` and exposes a common ordinary-KL implementation error.

.openresearch/artifacts/claim2/method.md

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+# Claim 2 method
+
+For each of the two continuous Gaussian baseline instances, the verifier perturbs both the curvature and linear term of the optimal quadratic potential. It then adds a nonconstant affine normalizer shift `delta(x)` so the candidate plan is deliberately not normalized.
+
+The primary implementation evaluates the Gaussian conditional KL and log-normal moment analytically. The independent checker uses adaptive quadrature for both. The verifier compares their generalized KL with the direct objective gap.
+
+The negative control drops the finite-measure mass correction and must miss the identity by at least `0.05`.

.openresearch/artifacts/claim2/negative_control_output.json

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+{"change":"omit -P(Omega)+Q(Omega) from Definition A.1","ordinary_kl_false_identity_abs_errors":[0.26563711076027896,0.19831479832594923],"rejected":true}

.openresearch/artifacts/claim2/page.md

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+# Current verification: Claim 2 / Theorem 3.3
+
+This supersedes the grid-discretized historical verifier. The current verifier tests a genuinely non-optimal neural-compatible potential and a non-normalized finite candidate measure on continuous Gaussian EOT. It includes the finite-measure KL term omitted by the negative control.
+
+Status: **VERIFIED** by immutable HF run `0f29450d-5b73-4214-ae3e-10d47608a377`. The maximum generalized-KL gap error was `5.83e-16`, independent quadrature agreed exactly at displayed precision, and the ordinary-KL control was rejected.

.openresearch/artifacts/claim2/raw_results.json

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+{
+  "evidence_run_id": "0f29450d-5b73-4214-ae3e-10d47608a377",
+  "status": "VERIFIED",
+  "claim": "Theorem 3.3 generalized finite-measure KL identity",
+  "cases": [
+    {"name":"shift_and_scale","epsilon":0.7,"L_star":1.310923962731463,"L_f":1.256514557806393,"L_f_xi":1.1791516685666719,"candidate_total_mass":0.6205184131996018,"generalized_KL":0.1882461345211306,"gap_identity_abs_error":2.220446049250313e-16,"independent_checker_abs_error":0.0,"ordinary_KL_false_identity_abs_error":0.26563711076027896},
+    {"name":"reverse_scale","epsilon":1.1,"L_star":0.4307262849673188,"L_f":0.4003990141402183,"L_f_xi":0.32371381246616715,"candidate_total_mass":0.819713819703683,"generalized_KL":0.09728406591013838,"gap_identity_abs_error":5.828670879282072e-16,"independent_checker_abs_error":0.0,"ordinary_KL_false_identity_abs_error":0.19831479832594923}
+  ],
+  "symbolic_identity": "L*-L(f,xi)=epsilon*KL_generalized(pi*||pi_f,xi)"
+}

.openresearch/artifacts/claim2/source_audit.md

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+# Claim 2 source audit
+
+- Source retrieval, URL, and HTML hash are recorded in `claim_contract.json`.
+- Theorem 3.3 is at `#S3.Thmtheorem3`; Equation 14 states the equality and inequality; Definition A.1 supplies the finite-measure KL convention.
+- The important quantifier is **every admissible `(f,xi)`**, not only the optimizer. The resulting `pi_f,xi` need not integrate to one.
+- The proof expands `log(d pi*/d pi_f,xi)` and uses the optimal EOT value. The `-pi*(Omega)+pi_f,xi(Omega)` terms are essential.
+
+Theorem 3.3 is unchanged in substance in arXiv v2 (PDF SHA-256 `257689c36d4d589942660667e880211ab18c6de37d9c643adacd571beaf1949b`).

.openresearch/artifacts/claim3/EVAL.md

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+# Claim 3 evaluation contract
+
+The fixed cumulative command is `uv sync --frozen && .venv/bin/python -m vareot_repro.run_all`. It writes the complete seed aggregate and proof checks to JSON. The route passes only if the exact full-class calibration has the independently expected one-dimensional `N^-1/2` behavior, the v1 exponent implication holds for each audited dimension, and the non-iid control is rejected.

.openresearch/artifacts/claim3/claim_contract.json

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+{
+  "claim_id": "claim3_theorem_3_5_v1",
+  "claim_text": "For bounded Lipschitz classes on compact D-dimensional supports, the expected estimation error is O(N^{-1/(D+1)}) + O(M^{-1/(D+1)}).",
+  "source": {
+    "version": "arXiv:2602.02241v1, matching the cached ar5iv and judged claim",
+    "pdf_sha256": "ecadaf4fc32e8b88bff8d57910a6bc291bfa36bd9c4ad61df4d505783b3f66a8",
+    "anchors": ["Theorem 3.5", "Equation 18", "Appendix A.5"]
+  },
+  "assumptions": [
+    "compact X0 and X1 in R^D",
+    "uniformly bounded and Lipschitz f and xi classes",
+    "independent iid samples from p0 and p1",
+    "fixed positive epsilon and finite class constants"
+  ],
+  "quantifiers": "The expectation over iid empirical samples obeys the asymptotic upper rate with instance-dependent constants.",
+  "machine_checks": [
+    "reconstruct the symmetrization, contraction, and referenced Rademacher-rate proof chain",
+    "verify algebraically that the n^{-1/2} partition term is dominated by the stated rate",
+    "calibrate the full one-dimensional 1-Lipschitz class through exact Wasserstein-1 duality over 128 iid seeds",
+    "reject repeated non-iid observations"
+  ],
+  "failure_policy": "A broken proof implication, calibrated slope outside [-0.65,-0.35], or unrejected non-iid control makes the verifier exit nonzero."
+}

.openresearch/artifacts/claim3/independent_checker_output.json

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+{"passed":true,"proof_chain":["symmetrization bounds the two one-sided empirical-process terms","coordinatewise contraction controls the bounded quotient class","the compact Lipschitz-class theorem supplies n^-1/(D+1)","the Gaussian-smoothed partition theorem supplies n^-1/2","n^-1/2 <= n^-1/(D+1) for D>=1,n>=1"],"median_per_seed_slope":-0.5111585503734187}

.openresearch/artifacts/claim3/limitations.md

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+# Claim 3 limitations and deviations
+
+- The executable calibration is one-dimensional. Its role is to test the proof ingredient on a complete function class, not to establish the universal theorem by regression.
+- General validity rests on the reconstructed analytical reduction and cited primary complexity theorems; constants are instance-dependent and not estimated.
+- The current paper v2 states a different theorem. This evidence does not silently substitute v2 for the judge's v1 claim.

.openresearch/artifacts/claim3/method.md

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+# Claim 3 method
+
+The general result is checked as an independently reconstructed proof chain rather than inferred from a fitted finite slope. The executable numerical calibration uses the complete class of 1-Lipschitz functions on `[0,1]`, not a feature proxy. Kantorovich-Rubinstein duality makes its empirical-process supremum exactly equal to Wasserstein-1, which is evaluated without optimization or discretization.
+
+For each of 128 deterministic seeds, nested iid prefixes are measured at `N=64,...,4096`; the verifier reports means, standard errors, per-seed slopes, and a 5–95% slope interval. Sample sizes were selected geometrically, not derived from the claimed formula. The negative control repeats 32 observations and should not improve with nominal `N`.

.openresearch/artifacts/claim3/negative_control_output.json

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+{"change":"repeat the same 32 observations instead of drawing additional iid data","errors":[0.08604205112962766,0.0860420511296277,0.08604205112962765,0.08604205112962751,0.08604205112962753,0.08604205112962829,0.08604205112962843],"loglog_slope":1.7893076816262386e-15,"rejected":true}

.openresearch/artifacts/claim3/page.md

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+# Current verification: Claim 3 / Theorem 3.5 (arXiv v1)
+
+This page supersedes the grid-feature slope proxy. It separates a proof-level reconstruction of the exact bounded-Lipschitz theorem from a non-circular calibration on the entire 1-Lipschitz class. It also records the material v1/v2 statement change.
+
+Status: **VERIFIED** by immutable HF run `0f29450d-5b73-4214-ae3e-10d47608a377`. Over 128 seeds the exact full-class W1 slope was `-0.511`; the repeated-data control slope was effectively zero. The contract, method, frozen JSON, checker route, control, and limitations are adjacent.

.openresearch/artifacts/claim3/raw_results.json

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+{
+  "evidence_run_id": "0f29450d-5b73-4214-ae3e-10d47608a377",
+  "status": "VERIFIED",
+  "claim": "Theorem 3.5 in arXiv v1 / cached ar5iv",
+  "class": "all anchored 1-Lipschitz functions on [0,1]",
+  "exact_duality": "empirical-process supremum equals W1(Uniform[0,1], empirical measure)",
+  "sample_sizes": [64,128,256,512,1024,2048,4096],
+  "seeds": 128,
+  "mean_exact_w1": [0.04047572638624694,0.028515396470259666,0.019632413989582303,0.014556656139663372,0.009445910954406299,0.007053976536525721,0.005083592533365974],
+  "standard_error": [0.001604808386701131,0.001110353990090704,0.0007853649552924386,0.0005501316190759208,0.0003774083232168075,0.00027831834504328545,0.00018921408908361654],
+  "median_per_seed_loglog_slope": -0.5111585503734187,
+  "per_seed_slope_5_95_percentiles": [-0.694634744344053,-0.2735936432798274],
+  "exponent_implication_checked_dimensions": [1,2,4,8,16],
+  "exponent_implication_passed": true
+}

.openresearch/artifacts/claim3/source_audit.md

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+# Claim 3 source audit
+
+The judge contract refers to arXiv v1, SHA-256 `ecadaf4fc32e8b88bff8d57910a6bc291bfa36bd9c4ad61df4d505783b3f66a8`: Theorem 3.5, Equation 18, proof A.5. The proof applies symmetrization to both empirical marginals, coordinatewise contraction to the bounded quotient class, the compact-metric Lipschitz rate from Gottlieb et al. (2016, Theorem 4.3), and the Gaussian-smoothed partition-class rate from Kolesov et al. (2024, Theorem 4.5).
+
+The current v2 PDF, SHA-256 `257689c36d4d589942660667e880211ab18c6de37d9c643adacd571beaf1949b`, materially changes the statement to `O(N^-1/2)+O(M^-1/2)+O(K^-1/2)` for fixed clipped neural-network classes. The two claims must not be conflated; this verifier targets the historical claim the judge actually scored.

.openresearch/artifacts/claim4/EVAL.md

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+# Claim 4 evaluation contract
+
+Run the unchanged cumulative command `uv sync --frozen && .venv/bin/python -m vareot_repro.run_all`. The verifier writes every capacity result, adaptive marginal check, exact network-realization error, and control result. Any contract failure exits nonzero.

.openresearch/artifacts/claim4/claim_contract.json

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+{
+  "claim_id": "claim4_theorem_3_7_v1",
+  "claim_text": "The approximation error over bounded Lipschitz neural-network classes vanishes as capacity grows, under universal approximation on compact supports.",
+  "source": {
+    "version": "arXiv:2602.02241v1, matching the judged Theorem 3.7 claim",
+    "pdf_sha256": "ecadaf4fc32e8b88bff8d57910a6bc291bfa36bd9c4ad61df4d505783b3f66a8",
+    "anchors": ["Theorem 3.7", "Equation 19", "Appendix A.6"]
+  },
+  "assumptions": [
+    "compact supports X0 and X1",
+    "the weak-dual optimizer exists in the admissible class",
+    "the union of increasing neural classes is dense in the required continuous bounded Lipschitz functions",
+    "epsilon is positive"
+  ],
+  "quantifiers": "For every admissible compact-support problem and every positive tolerance, sufficiently expressive classes make the best variational objective gap smaller than that tolerance.",
+  "machine_checks": [
+    "reconstruct the universal-approximation and continuity proof",
+    "construct an absolutely continuous compact EOT instance with known weak-dual optimizer",
+    "represent capacity-growing tail potentials exactly by ReLU networks and normalizers by ReLU splines",
+    "independently integrate the target marginal and objectives",
+    "reject xi width growth when the potential tail capacity is fixed"
+  ],
+  "failure_policy": "Invalid marginal normalization, negative objective gap, final gap above 0.01, inadequate gap reduction, network mismatch, or surviving control makes the verifier exit nonzero."
+}

.openresearch/artifacts/claim4/independent_checker_output.json

@@ -0,0 +1 @@
+{"passed":true,"target_marginal_normalization_adaptive_quadrature":1.0,"maximum_network_realization_error":0.0,"proof_certificate_steps":6}

.openresearch/artifacts/claim4/limitations.md

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+# Claim 4 limitations and deviations
+
+- The general theorem is addressed analytically; the capacity sweep is a scoped continuous witness, not finite proof of a limit.
+- The constructed target is induced by a known optimizer to make the optimal value independently auditable. It is nevertheless an absolutely continuous, non-grid compact EOT instance satisfying the assumptions.
+- The networks are explicit ReLU realizations rather than SGD-trained approximators. Optimization behavior belongs to Claim 5 and is tested separately.

.openresearch/artifacts/claim4/method.md

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+# Claim 4 method
+
+The general certificate normalizes the optimal potential, approximates it on compact `X1`, controls the Gaussian-kernel tail after a clipped Lipschitz extension, realizes the piecewise-linear approximation by ReLU networks, approximates `xi_f` uniformly on compact `X0`, and transfers both uniform errors through continuity of the bounded variational functional.
+
+The non-vacuous continuous instance has `p0=Uniform[-1,1]`, epsilon `0.5`, and defines the absolutely continuous compact target as the marginal induced by the known optimizer `f*=0` on `[-1,1]` and `-infinity` outside. Four exact ReLU tail potentials increase `(M,L)` while ReLU-spline normalizers increase width. Adaptive quadrature checks normalization and objective values. The control increases normalizer width while holding the potential tail bound too small.

.openresearch/artifacts/claim4/negative_control_output.json

@@ -0,0 +1 @@
+{"change":"increase xi width to 64 while fixing tail M=1,L=8","approximation_gap":0.0397988656519601,"expected":"gap remains above 0.01","rejected":true}

.openresearch/artifacts/claim4/page.md

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+# Current verification: Claim 4 / Theorem 3.7 (arXiv v1)
+
+This supersedes the grid-feature approximation proxy. The current route uses actual ReLU networks, a continuous compact-support EOT instance, an independently known optimizer, adaptive integration, and a potential-capacity negative control.
+
+Status: **VERIFIED** by immutable HF run `0f29450d-5b73-4214-ae3e-10d47608a377`. Actual ReLU networks reduced the continuous approximation gap from `0.022732` to `0.000352`; the fixed-tail control remained at `0.039799` and was rejected.

.openresearch/artifacts/claim4/raw_results.json

@@ -0,0 +1,12 @@
+{
+  "evidence_run_id": "0f29450d-5b73-4214-ae3e-10d47608a377",
+  "status": "VERIFIED",
+  "claim": "Theorem 3.7 in arXiv v1 / cached ar5iv",
+  "instance": {"p0":"Uniform[-1,1]","p1":"compact marginal induced by f*=0 on [-1,1]","epsilon":0.5,"target_marginal_normalization":1.0,"L_star":-0.11496906338604114},
+  "capacity_results": [
+    {"tail_bound_M":2.0,"tail_lipschitz_L":8.0,"xi_relu_width":8,"variational_objective":-0.1377010332243137,"approximation_gap":0.022731969838272567,"network_realization_max_error":0.0},
+    {"tail_bound_M":4.0,"tail_lipschitz_L":32.0,"xi_relu_width":16,"variational_objective":-0.12054418986359805,"approximation_gap":0.00557512647755691,"network_realization_max_error":0.0},
+    {"tail_bound_M":6.0,"tail_lipschitz_L":128.0,"xi_relu_width":32,"variational_objective":-0.11637310221127906,"approximation_gap":0.001404038825237916,"network_realization_max_error":0.0},
+    {"tail_bound_M":8.0,"tail_lipschitz_L":512.0,"xi_relu_width":64,"variational_objective":-0.11532127056346864,"approximation_gap":0.0003522071774274965,"network_realization_max_error":0.0}
+  ]
+}

.openresearch/artifacts/claim4/source_audit.md

@@ -0,0 +1,5 @@
+# Claim 4 source audit
+
+The judge names Theorem 3.7 from arXiv v1 (PDF SHA-256 `ecadaf4fc32e8b88bff8d57910a6bc291bfa36bd9c4ad61df4d505783b3f66a8`), Equation 19 and proof A.6. Its domain is compact-support EOT with increasing universal neural classes; its quantifier is a capacity limit, not monotonic improvement for every architecture or optimizer.
+
+Current arXiv v2 renumbers the approximation statement as Theorem 3.6 and gives a bounded-network universal-approximation proof. The verifier names both versions explicitly and targets the v1 judged contract.

.openresearch/artifacts/claim5/EVAL.md

@@ -0,0 +1,3 @@
+# Claim 5 evaluation contract
+
+Run the inherited command `uv sync --frozen && .venv/bin/python -m vareot_repro.run_all` on HF `cpu-upgrade`. The precision-certified run completed the exact schedule and separates exact float64 equation agreement from the a priori mixed-precision bound `8 * float32_epsilon * condition_scale`. The final release child reruns Claims 1–4, Claim 5, the notebook check, visibility audit, and frozen-evidence regression.

.openresearch/artifacts/claim5/claim_contract.json

@@ -0,0 +1,17 @@
+{
+  "claim_id": "claim5_algorithm_1",
+  "claim_text": "Algorithm 1 trains neural f_theta and xi_psi jointly by stochastic gradients of Equation 15 using only source samples, target samples, and independent Gaussian noise; it does not sample the current model distribution during training.",
+  "source": {
+    "url": "https://arxiv.org/pdf/2602.02241v2",
+    "pdf_sha256": "257689c36d4d589942660667e880211ab18c6de37d9c643adacd571beaf1949b",
+    "anchors": ["Section 3.2", "Algorithm 1", "Equation 15", "Table 1", "Appendix B.1"]
+  },
+  "assumptions": [
+    "iid samples are available from p0 and p1",
+    "iid standard Gaussian noise can be generated",
+    "both neural objectives are differentiable and finite after the paper's exponential and gradient clipping"
+  ],
+  "quantifiers": "Every training iteration described by Algorithm 1 uses those three sampling sources, computes Equation 15, and updates both parameter sets; no current-plan simulation is part of training.",
+  "profile_gate": "The diagnostic child preserves official tensor scale and measures exact CPU cost over 20 steps. It cannot produce a final VERIFIED verdict.",
+  "final_gate": "The descendant must complete 5000 official-notebook steps, improve a fixed held-out Equation 15 objective by more than 0.02, update both networks, match the independent NumPy Equation 15 aggregation within 1e-12 in float64, keep the actual mixed-precision reduction error below 8*float32_epsilon*condition_scale, and reject a detached-potential control."
+}

.openresearch/artifacts/claim5/full_run_parent.json

@@ -0,0 +1,33 @@
+{
+  "run_id": "947b6522-ad19-4eb7-ad08-acb7ecc3439b",
+  "git_sha": "e87cf0a259b627e892e2fd82e39545c7b9c45c97",
+  "command": "uv sync --frozen && .venv/bin/python -m vareot_repro.run_all",
+  "backend": "hf",
+  "flavor": "cpu-upgrade",
+  "estimated_cores_required": 32,
+  "actual_cpu_affinity_count": 64,
+  "torch_threads": 32,
+  "cuda_available": false,
+  "training_runtime_seconds": 6056.834990901,
+  "cumulative_runtime_seconds": 6097.893595394,
+  "orx_wall_duration": "1h42m",
+  "steps": 5000,
+  "batch_size": 256,
+  "monte_carlo_k": 256,
+  "heldout_objective_improvement": 1.2145091459063557,
+  "initial_maximized_objective_without_constant": -0.9965578028615594,
+  "final_maximized_objective_without_constant": 0.21795134304479635,
+  "potential_parameter_update_norm": 17.96524429321289,
+  "normalizer_parameter_update_norm": 8.71017074584961,
+  "source_samples": 1280000,
+  "target_samples": 1280000,
+  "independent_gaussian_noise_samples": 327680000,
+  "model_distribution_samples": 0,
+  "negative_control_potential_gradient_norm": 0.0,
+  "negative_control_normalizer_gradient_norm": 0.01394092385024298,
+  "negative_control_rejected": true,
+  "checker_absolute_error": 4.76837158203125e-7,
+  "checker_fixed_tolerance": 2e-7,
+  "status": "BLOCKED",
+  "blocking_reason": "The frozen verifier used an unscaled absolute tolerance below one float32 reduction unit at the observed component scale. The child preserves training and replaces only this numerical checker with separate float64 equality and IEEE scale-bound tests."
+}

.openresearch/artifacts/claim5/independent_checker_output.json

@@ -0,0 +1,11 @@
+{
+  "condition_scale": 14.810081313714228,
+  "float32_machine_epsilon": 1.1920928955078125e-7,
+  "numpy_float64_aggregation_loss": -0.21795199683324373,
+  "passed": true,
+  "roundoff_bound_8_epsilon_times_scale": 1.4123994172777394e-5,
+  "torch_float64_aggregation_loss": -0.21795199683324373,
+  "torch_numpy_float64_absolute_error": 0.0,
+  "torch_training_mixed_precision_loss": -0.21795134304479635,
+  "training_to_float64_absolute_error": 6.537884473800659e-7
+}

.openresearch/artifacts/claim5/limitations.md

@@ -0,0 +1,6 @@
+# Claim 5 limitations and deviations
+
+- This route follows the executable official notebook's 5,000-step schedule; the paper appendix's conflicting 10,000-step schedule is reported rather than hidden.
+- The training claim is tested directly. Langevin inference quality is outside the exact simulation-free-training quantifier and is not used to make the verifier pass.
+- Swiss-roll transport quality has no analytic ground-truth plan. The acceptance gate therefore uses the exact held-out training objective and structural sampling contract, not an invented KL target.
+- The independent checker consumes frozen neural outputs, so it audits Equation 15's aggregation independently but does not independently reimplement every neural layer.

.openresearch/artifacts/claim5/method.md

@@ -0,0 +1,7 @@
+# Claim 5 method
+
+The implementation mirrors the authors' Swiss-roll notebook: continuous two-dimensional standard-Gaussian source, continuous noisy Swiss-roll target, two independent four-linear-layer width-256 SiLU networks, batch 256, K=256, AdamW, exponential clipping, gradient clipping, and EMA.
+
+The audit counts every training sample source. The only stochastic inputs are `p0`, `p1`, and independent Gaussian noise. A fixed held-out batch measures Equation 15 before and after training. An independent NumPy implementation recombines frozen network outputs and must match an independently promoted Torch aggregation within `1e-12`. The actual mixed-precision training reduction is separately bounded by `8 * float32_epsilon * condition_scale`; this bound is derived from representation precision rather than the observed discrepancy. Both first-step gradients and total parameter updates must be nonzero.
+
+The negative control detaches every potential output before Equation 15. Its potential gradient is then exactly zero while the normalizer gradient remains nonzero; the joint-update checker must reject it.

.openresearch/artifacts/claim5/negative_control_output.json

@@ -0,0 +1,7 @@
+{
+  "change": "detach every potential output before Equation 15",
+  "expected": "joint-gradient audit rejects the zero potential gradient",
+  "normalizer_gradient_norm": 0.01394092385024298,
+  "potential_gradient_norm": 0.0,
+  "rejected": true
+}

.openresearch/artifacts/claim5/page.md

@@ -0,0 +1,7 @@
+# Current verification: Claim 5 / Algorithm 1
+
+This candidate supersedes the grid optimizer with the actual continuous, neural, joint-gradient Algorithm 1 at the official batch, Monte Carlo, network, and 5,000-step executable scale. It receives a final verdict only if the held-out objective, joint updates, sample audit, independent checker, and negative control all pass.
+
+It also supersedes the frozen full-run parent's unscaled `2e-7` checker: the current checker reports exact float64 NumPy/Torch agreement and audits the mixed-precision training reduction against an IEEE-epsilon scale bound.
+
+The source contract, exact implementation, raw JSON, NumPy checker, detached-potential control, CPU accounting, and deviations are adjacent.

.openresearch/artifacts/claim5/raw_results.json

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+{
+  "evidence_run_id": "0f29450d-5b73-4214-ae3e-10d47608a377",
+  "evidence_git_sha": "7ee3d8e5e21f4f59fd5025e3c2df8f80f584db86",
+  "status": "VERIFIED",
+  "config": {"dimension":2,"epsilon":1.0,"batch_size":256,"monte_carlo_k":256,"steps":5000,"hidden_width":256,"learning_rate":0.0003,"beta1":0.7,"beta2":0.8,"weight_decay":0.0001,"ema_momentum":0.999,"exponential_clip":20.0,"gradient_clip":1.0,"seed":42},
+  "architecture": "two independent 2->256->256->256->1 SiLU MLPs",
+  "source_distribution": "two-dimensional standard Gaussian",
+  "target_distribution": "continuous noisy Swiss roll, matching the official notebook sampler",
+  "initial_heldout_maximized_objective": -0.9965578028615594,
+  "final_heldout_maximized_objective": 0.21795134304479635,
+  "heldout_objective_improvement": 1.2145091459063557,
+  "first_step_gradient_norms": {"potential":0.3003854689563279,"normalizer":0.014266153947860566},
+  "parameter_update_norms": {"potential":17.96524429321289,"normalizer":8.71017074584961},
+  "training_sample_audit": {"source_samples":1280000,"target_samples":1280000,"independent_gaussian_noise_samples":327680000,"model_distribution_samples":0,"simulation_free":true},
+  "training_runtime_seconds": 5719.526885461999,
+  "seconds_per_step": 1.1439053770923997,
+  "trace_file": "training_trace.csv",
+  "independent_checker_file": "independent_checker_output.json",
+  "negative_control_file": "negative_control_output.json",
+  "deviation": "The run matches the official notebook's 5000 steps at 3e-4; Appendix B.1 instead says 10000 steps at 1e-4."
+}

.openresearch/artifacts/claim5/source_audit.md

@@ -0,0 +1,6 @@
+# Claim 5 source audit
+
+- Current v2 source: Section 3.2, Algorithm 1, Equation 15, Table 1, and Appendix B.1; PDF SHA-256 `257689c36d4d589942660667e880211ab18c6de37d9c643adacd571beaf1949b`.
+- Algorithm 1 samples minibatches from `p0` and `p1` plus iid standard Gaussian `z`, evaluates Equation 15, and updates both `theta` and `psi` in one loop.
+- “Simulation-free” is specifically a training claim: no samples from the learned conditional are required to estimate the training objective. Algorithm 2 does use Langevin dynamics at inference and is not relabeled simulation-free.
+- Appendix B.1 specifies 10,000 steps and learning rate `1e-4`. The authors' official Swiss-roll notebook at commit `fd1b2f93b89fd1d8be8ddf32aa30807fc5fafb26` instead executes 5,000 steps at `3e-4`; both use batch 256, K=256, width 256, AdamW betas `(0.7,0.8)`, weight decay `1e-4`, EMA `0.999`, and simultaneous updates. The executable notebook contract is used and the discrepancy remains visible.

.openresearch/artifacts/claim5/training_trace.csv

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.openresearch/artifacts/frozen_precision_run.json

@@ -0,0 +1,79 @@
+{
+  "evidence_run_id": "0f29450d-5b73-4214-ae3e-10d47608a377",
+  "evidence_git_sha": "7ee3d8e5e21f4f59fd5025e3c2df8f80f584db86",
+  "fixed_command": "uv sync --frozen && .venv/bin/python -m vareot_repro.run_all",
+  "backend": "hf",
+  "selected_flavor": "cpu-upgrade",
+  "estimated_cores_required": 32,
+  "actual_cpu_affinity_count": 64,
+  "torch_threads": 32,
+  "cuda_available": false,
+  "orx_wall_duration": "2h16m",
+  "scientific_runtime_seconds": 5750.050501372001,
+  "statuses": {
+    "claim_1": "VERIFIED",
+    "claim_2": "VERIFIED",
+    "claim_3": "VERIFIED",
+    "claim_4": "VERIFIED",
+    "claim_5": "VERIFIED"
+  },
+  "claim_1": {
+    "scope": "continuous one-dimensional Gaussian EOT plus a general symbolic variational certificate",
+    "max_primal_semidual_error": 4.440892098500626e-16,
+    "max_variational_error": 2.220446049250313e-16,
+    "max_adaptive_quadrature_error": 4.440892098500626e-16,
+    "negative_control_exit_code": 1
+  },
+  "claim_2": {
+    "scope": "non-optimal potentials and non-normalized finite measures on two continuous Gaussian EOT instances",
+    "max_gap_identity_error": 5.828670879282072e-16,
+    "max_independent_checker_error": 0.0,
+    "ordinary_kl_control_errors": [0.26563711076027896, 0.19831479832594923],
+    "negative_control_rejected": true
+  },
+  "claim_3": {
+    "scope": "exact full 1-Lipschitz class on [0,1], 128 seeds, plus analytical v1 proof reconstruction",
+    "sample_sizes": [64, 128, 256, 512, 1024, 2048, 4096],
+    "mean_exact_w1": [0.04047572638624694, 0.028515396470259666, 0.019632413989582303, 0.014556656139663372, 0.009445910954406299, 0.007053976536525721, 0.005083592533365974],
+    "standard_error": [0.001604808386701131, 0.001110353990090704, 0.0007853649552924386, 0.0005501316190759208, 0.0003774083232168075, 0.00027831834504328545, 0.00018921408908361654],
+    "median_per_seed_loglog_slope": -0.5111585503734187,
+    "slope_5_95_percentiles": [-0.694634744344053, -0.2735936432798274],
+    "non_iid_control_slope": 1.7893076816262386e-15,
+    "negative_control_rejected": true
+  },
+  "claim_4": {
+    "scope": "continuous compact EOT and explicit capacity-growing ReLU networks",
+    "capacities": [8, 16, 32, 64],
+    "approximation_gaps": [0.022731969838272567, 0.00557512647755691, 0.001404038825237916, 0.0003522071774274965],
+    "target_marginal_normalization": 1.0,
+    "max_network_realization_error": 0.0,
+    "fixed_tail_control_gap": 0.0397988656519601,
+    "negative_control_rejected": true
+  },
+  "claim_5": {
+    "scope": "official continuous Swiss-roll Algorithm 1 executable configuration",
+    "steps": 5000,
+    "batch_size": 256,
+    "monte_carlo_k": 256,
+    "architecture": "two independent 2->256->256->256->1 SiLU MLPs",
+    "heldout_objective_initial": -0.9965578028615594,
+    "heldout_objective_final": 0.21795134304479635,
+    "heldout_objective_improvement": 1.2145091459063557,
+    "potential_first_gradient_norm": 0.3003854689563279,
+    "normalizer_first_gradient_norm": 0.014266153947860566,
+    "potential_update_norm": 17.96524429321289,
+    "normalizer_update_norm": 8.71017074584961,
+    "source_samples": 1280000,
+    "target_samples": 1280000,
+    "gaussian_noise_samples": 327680000,
+    "model_distribution_samples": 0,
+    "torch_numpy_float64_error": 0.0,
+    "mixed_precision_error": 6.537884473800659e-7,
+    "a_priori_roundoff_bound": 1.4123994172777394e-5,
+    "detached_potential_gradient_norm": 0.0,
+    "detached_normalizer_gradient_norm": 0.01394092385024298,
+    "negative_control_rejected": true,
+    "training_runtime_seconds": 5719.526885461999,
+    "seconds_per_step": 1.1439053770923997
+  }
+}

.openresearch/artifacts/release_candidate_failure.json

@@ -0,0 +1,17 @@
+{
+  "run_id": "a58f97fb-3066-43ef-9e0a-16693080fa75",
+  "git_sha": "efde861",
+  "status": "BLOCKED",
+  "backend": "hf",
+  "flavor": "cpu-upgrade",
+  "estimated_cores": 32,
+  "actual_cpu_affinity": 64,
+  "torch_threads": 32,
+  "cuda_available": false,
+  "science_runtime_seconds": 14066.313840486808,
+  "algorithm1_training_runtime_seconds": 14030.297232253011,
+  "science_pass": true,
+  "claim_statuses": {"claim_1":"VERIFIED","claim_2":"VERIFIED","claim_3":"VERIFIED","claim_4":"VERIFIED","claim_5":"VERIFIED"},
+  "release_gate_failures": ["marimo 0.15.2 has no check command","secret scanner matched its own marker literal"],
+  "repair_policy": "Preserve this frozen result; validate the notebook by same-version executable HTML export on a child and construct secret markers without self-matching."
+}