JUDGE_EVIDENCE_SCORECARD.md

# Judge-facing evidence scorecard

- Paper ID: `HMyCBL2yMV`
- Registered claims: 5
- Assessments: 5 verified
- Source matrix: `EVIDENCE_MATRIX.json`
- Prose-local artifact references: validated

## Claim summary

| # | Literal claim | Assessment | Decisive quantitative result |
| ---: | --- | --- | --- |
| 1 | Theorem 4.2 establishes a central limit theorem for the empirical KL_inf statistic, showing sqrt(n)(KL_inf(q_hat_n, m_o) - KL_inf(q, m_o)) converges in distribution to N(0, sigma^2(q, m_o)) (Theorem 4.2). | VERIFIED | VERIFIED with the paper's exact 5,000-path cells. Bernoulli standardized variance is 1.006 and KS falls from 0.148 at n=100 to 0.023 at n=2000; Beta(3,2) reaches variance 0.969 and KS 0.012 at n=2000. |
| 2 | Theorem 4.4 extends this result to the stopping time tau_alpha, proving sqrt(log(1/alpha))(tau_alpha/log(1/alpha) - 1/KL_inf(q,m_o)) converges to a Gaussian limit N(0, sigma^2_bd(q,m_o)) as alpha to 0 (Theorem 4.4). | VERIFIED | VERIFIED over 20,000 literal stopping paths. With the practical boundary, standardized variance is 0.995/1.022 and KS improves from 0.086 at alpha=1e-4 to 0.058 at alpha=1e-8; the theoretical boundary reproduces the paper's stronger finite-sample skew. |
| 3 | The proof decomposes the normalized KL_inf statistic into a term from the dual optimization (shown to vanish in probability) and a standard empirical-mean term that converges to Gaussian, combined with verification of Anscombe's condition to transfer the CLT to the stopping time (Section 4). | VERIFIED | VERIFIED directly. Across n=100,500,1000,2000, the dual decomposition reconstructs the statistic with maximum residual 1.11e-16; the optimization-term RMS shrinks 0.0856->0.0194, while the fixed-lambda leading term reaches Gaussian KS 0.014. |
| 4 | Proposition 4.5 constructs asymptotically valid confidence intervals for the stopping time using only a single simulation run, without requiring multiple independent replicates (Proposition 4.5). | VERIFIED | VERIFIED using 20,000 independently stopped paths, with every interval computed only from its own path. Empirical 95% coverage rises from 0.790 at alpha=1e-4 to 0.946 at alpha=1e-128, and the associated Gaussian KS falls to 0.023. |
| 5 | Numerical experiments on synthetic Beta and Bernoulli distributions and on real crop-yield data show empirical stopping-time distributions converging to the theoretical Gaussian limit, with stronger agreement at smaller significance levels alpha (Section 5). | VERIFIED | VERIFIED on all three registered families. The 5,000-path Beta and Bernoulli cells reach final KS 0.012 and 0.023. A 3,000-path bootstrap over 44 pinned primary DSSAT HWAM yields gives standardized mean -0.093, variance 0.975, and Gaussian KS 0.090. |

## Claim 1 — VERIFIED

> Theorem 4.2 establishes a central limit theorem for the empirical KL_inf statistic, showing sqrt(n)(KL_inf(q_hat_n, m_o) - KL_inf(q, m_o)) converges in distribution to N(0, sigma^2(q, m_o)) (Theorem 4.2).

- Decisive quantitative result: VERIFIED with the paper's exact 5,000-path cells. Bernoulli standardized variance is 1.006 and KS falls from 0.148 at n=100 to 0.023 at n=2000; Beta(3,2) reaches variance 0.969 and KS 0.012 at n=2000.
- Native scale: The computation uses the paper's literal KL_inf dual and thresholds, its Beta(3,2)/Bernoulli settings, 5,000 paths per synthetic cell, and 3,000 bootstrap paths over pinned primary DSSAT maize-yield observations.
- Source locator: source/paper/icml_final_submission.tex Theorem 1 and Experiment 1; reproduce.py claim 1
- Upstream pin:
  - digest: `sha256:27ca92473d1ca2e37c227850717f771cbfd820e7db0ab3459a868ecb7bcea220`
  - dssat_commit: `a4f95d3ef36f1358bdeb5db49d498d5db373ba7a`
  - version: `arXiv:2606.04520 accepted source`
- Independent evidence:
  - `outputs/claim1.json`
  - `replay_a/claim1.json`
  - `replay_b/claim1.json`
- Executed outputs:
  - `outputs/claim1.json`
  - `outputs/results.json`
- Independent oracle paths:
  - `replay_a/claim1.json`
  - `replay_b/claim1.json`
- Control paths:
  - `outputs/claim1.json`
  - `outputs/results.json`
- Destructive or boundary control: Forcing lambda=0 makes every empirical objective exactly zero and destroys the positive KL signal; n=100 is the pre-asymptotic boundary against the n=2000 result.
- Rate relation: claim-consistent; mode `empirical_scaling`; measured slope `-0.617`.
  - Horizons: 100, 500, 1000, 2000
  - Repetitions per horizon: 5000
  - Measurement: Bernoulli Gaussian KS decreases 0.148406->0.023374; Beta reaches 0.011989
  - Rate artifact: `outputs/claim1.json`
- Limitation: The verdict is limited to the literal statistic, distributions, thresholds, and primary-data realization executed here; no neighboring theorem, proxy statistic, or source narration is counted.
- Scope boundary: The verdict resolves the registered statement at the accepted paper's stated synthetic scale and through a pinned official DSSAT primary-data realization.

## Claim 2 — VERIFIED

> Theorem 4.4 extends this result to the stopping time tau_alpha, proving sqrt(log(1/alpha))(tau_alpha/log(1/alpha) - 1/KL_inf(q,m_o)) converges to a Gaussian limit N(0, sigma^2_bd(q,m_o)) as alpha to 0 (Theorem 4.4).

- Decisive quantitative result: VERIFIED over 20,000 literal stopping paths. With the practical boundary, standardized variance is 0.995/1.022 and KS improves from 0.086 at alpha=1e-4 to 0.058 at alpha=1e-8; the theoretical boundary reproduces the paper's stronger finite-sample skew.
- Native scale: The computation uses the paper's literal KL_inf dual and thresholds, its Beta(3,2)/Bernoulli settings, 5,000 paths per synthetic cell, and 3,000 bootstrap paths over pinned primary DSSAT maize-yield observations.
- Source locator: source/paper/icml_final_submission.tex Theorem 2, Equations 5/13/14 and Experiment 2; reproduce.py claim 2
- Upstream pin:
  - digest: `sha256:27ca92473d1ca2e37c227850717f771cbfd820e7db0ab3459a868ecb7bcea220`
  - dssat_commit: `a4f95d3ef36f1358bdeb5db49d498d5db373ba7a`
  - version: `arXiv:2606.04520 accepted source`
- Independent evidence:
  - `outputs/claim2.json`
  - `replay_a/claim2.json`
  - `replay_b/claim2.json`
- Executed outputs:
  - `outputs/claim2.json`
  - `outputs/results.json`
- Independent oracle paths:
  - `replay_a/claim2.json`
  - `replay_b/claim2.json`
- Control paths:
  - `outputs/claim2.json`
  - `outputs/results.json`
- Destructive or boundary control: The matched theoretical versus constant boundaries change only beta(n,alpha); the alpha=1e-4 cells expose the registered finite-sample distortion while alpha=1e-8 moves deeper into the limit.
- Rate relation: claim-consistent; mode `empirical_scaling`; measured slope `-0.385`.
  - Horizons: 4, 8, 32, 128
  - Repetitions per horizon: 5000
  - Measurement: Constant-boundary Gaussian KS decreases 0.086339->0.022754 as -log10(alpha) increases 4->128
  - Rate artifact: `outputs/claim2.json`
- Limitation: The verdict is limited to the literal statistic, distributions, thresholds, and primary-data realization executed here; no neighboring theorem, proxy statistic, or source narration is counted.
- Scope boundary: The verdict resolves the registered statement at the accepted paper's stated synthetic scale and through a pinned official DSSAT primary-data realization.

## Claim 3 — VERIFIED

> The proof decomposes the normalized KL_inf statistic into a term from the dual optimization (shown to vanish in probability) and a standard empirical-mean term that converges to Gaussian, combined with verification of Anscombe's condition to transfer the CLT to the stopping time (Section 4).

- Decisive quantitative result: VERIFIED directly. Across n=100,500,1000,2000, the dual decomposition reconstructs the statistic with maximum residual 1.11e-16; the optimization-term RMS shrinks 0.0856->0.0194, while the fixed-lambda leading term reaches Gaussian KS 0.014.
- Native scale: The computation uses the paper's literal KL_inf dual and thresholds, its Beta(3,2)/Bernoulli settings, 5,000 paths per synthetic cell, and 3,000 bootstrap paths over pinned primary DSSAT maize-yield observations.
- Source locator: source/paper/icml_final_submission.tex proof sketch and Anscombe decomposition; reproduce.py claim 3
- Upstream pin:
  - digest: `sha256:27ca92473d1ca2e37c227850717f771cbfd820e7db0ab3459a868ecb7bcea220`
  - dssat_commit: `a4f95d3ef36f1358bdeb5db49d498d5db373ba7a`
  - version: `arXiv:2606.04520 accepted source`
- Independent evidence:
  - `outputs/claim3.json`
  - `replay_a/claim3.json`
  - `replay_b/claim3.json`
- Executed outputs:
  - `outputs/claim3.json`
  - `outputs/results.json`
- Independent oracle paths:
  - `replay_a/claim3.json`
  - `replay_b/claim3.json`
- Control paths:
  - `outputs/claim3.json`
  - `outputs/results.json`
- Destructive or boundary control: The lambda=0 destructive branch eliminates the KL evidence, while the n sweep tests rather than assumes the optimization remainder's disappearance.
- Rate relation: claim-consistent; mode `empirical_scaling`; measured slope `-0.496`.
  - Horizons: 100, 500, 1000, 2000
  - Repetitions per horizon: 5000
  - Measurement: Optimization-remainder RMS decreases 0.085607->0.019365
  - Rate artifact: `outputs/claim3.json`
- Limitation: The verdict is limited to the literal statistic, distributions, thresholds, and primary-data realization executed here; no neighboring theorem, proxy statistic, or source narration is counted.
- Scope boundary: The verdict resolves the registered statement at the accepted paper's stated synthetic scale and through a pinned official DSSAT primary-data realization.

## Claim 4 — VERIFIED

> Proposition 4.5 constructs asymptotically valid confidence intervals for the stopping time using only a single simulation run, without requiring multiple independent replicates (Proposition 4.5).

- Decisive quantitative result: VERIFIED using 20,000 independently stopped paths, with every interval computed only from its own path. Empirical 95% coverage rises from 0.790 at alpha=1e-4 to 0.946 at alpha=1e-128, and the associated Gaussian KS falls to 0.023.
- Native scale: The computation uses the paper's literal KL_inf dual and thresholds, its Beta(3,2)/Bernoulli settings, 5,000 paths per synthetic cell, and 3,000 bootstrap paths over pinned primary DSSAT maize-yield observations.
- Source locator: source/paper/icml_final_submission.tex Proposition 1; reproduce.py claim 4
- Upstream pin:
  - digest: `sha256:27ca92473d1ca2e37c227850717f771cbfd820e7db0ab3459a868ecb7bcea220`
  - dssat_commit: `a4f95d3ef36f1358bdeb5db49d498d5db373ba7a`
  - version: `arXiv:2606.04520 accepted source`
- Independent evidence:
  - `outputs/claim4.json`
  - `replay_a/claim4.json`
  - `replay_b/claim4.json`
- Executed outputs:
  - `outputs/claim4.json`
  - `outputs/results.json`
- Independent oracle paths:
  - `replay_a/claim4.json`
  - `replay_b/claim4.json`
- Control paths:
  - `outputs/claim4.json`
  - `outputs/results.json`
- Destructive or boundary control: The alpha sweep from 1e-4 to 1e-128 is the boundary control: it exposes low-alpha convergence rather than reporting one favorable path or one favorable confidence level.
- Rate relation: claim-consistent; mode `empirical_scaling`; measured slope `-1.05`.
  - Horizons: 4, 8, 32, 128
  - Repetitions per horizon: 5000
  - Measurement: Single-path interval coverage converges 0.7904->0.9458 toward 0.95
  - Rate artifact: `outputs/claim4.json`
- Limitation: The verdict is limited to the literal statistic, distributions, thresholds, and primary-data realization executed here; no neighboring theorem, proxy statistic, or source narration is counted.
- Scope boundary: The verdict resolves the registered statement at the accepted paper's stated synthetic scale and through a pinned official DSSAT primary-data realization.

## Claim 5 — VERIFIED

> Numerical experiments on synthetic Beta and Bernoulli distributions and on real crop-yield data show empirical stopping-time distributions converging to the theoretical Gaussian limit, with stronger agreement at smaller significance levels alpha (Section 5).

- Decisive quantitative result: VERIFIED on all three registered families. The 5,000-path Beta and Bernoulli cells reach final KS 0.012 and 0.023. A 3,000-path bootstrap over 44 pinned primary DSSAT HWAM yields gives standardized mean -0.093, variance 0.975, and Gaussian KS 0.090.
- Native scale: The computation uses the paper's literal KL_inf dual and thresholds, its Beta(3,2)/Bernoulli settings, 5,000 paths per synthetic cell, and 3,000 bootstrap paths over pinned primary DSSAT maize-yield observations.
- Source locator: source/paper/icml_final_submission.tex Experiments 1-3; source/dssat-maize official primary observations; reproduce.py claim 5
- Upstream pin:
  - digest: `sha256:27ca92473d1ca2e37c227850717f771cbfd820e7db0ab3459a868ecb7bcea220`
  - dssat_commit: `a4f95d3ef36f1358bdeb5db49d498d5db373ba7a`
  - version: `arXiv:2606.04520 accepted source`
- Independent evidence:
  - `outputs/claim5.json`
  - `replay_a/claim5.json`
  - `replay_b/claim5.json`
- Executed outputs:
  - `outputs/claim5.json`
  - `outputs/results.json`
- Independent oracle paths:
  - `replay_a/claim5.json`
  - `replay_b/claim5.json`
- Control paths:
  - `outputs/claim5.json`
  - `outputs/results.json`
- Destructive or boundary control: The synthetic distributions, two sample sizes, two alpha levels, two boundary forms, and real nonparametric pool are mutually destructive boundary controls against a distribution-specific or source-only result.
- Rate relation: claim-consistent; mode `empirical_scaling`; measured slope `-0.617`.
  - Horizons: 100, 500, 1000, 2000
  - Repetitions per horizon: 5000
  - Measurement: Synthetic KS improves with n/smaller alpha and the 3,000-path DSSAT cell achieves KS 0.090239
  - Rate artifact: `outputs/claim5.json`
- Limitation: The verdict is limited to the literal statistic, distributions, thresholds, and primary-data realization executed here; no neighboring theorem, proxy statistic, or source narration is counted.
- Scope boundary: The verdict resolves the registered statement at the accepted paper's stated synthetic scale and through a pinned official DSSAT primary-data realization.