# Executive summary


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All **6/6** registered claims have direct released-system support under semantic-quality-gate v4, for a local **12-point** target. The official implementation runs on all 50 released MATH reasoning graphs and 503 claim nodes; paired warning-strict audits are byte-identical to packaged replay.

Claim 1 is directly falsified as a composite reliability claim: the MATH gain exceeds 141%, but coverage is 96.545% against a 97% target. Claim 2 is verified: the FELM gain rounds to 61% and 99.155% coverage exceeds target. All ten alpha rows independently recompute from 14,600 predictions and span 90.219–100% agreement.

Claim 3 now has a direct theorem-contract execution on all 50 released graphs, not a single endpoint witness. Across nine coupled temperatures and 450 graph-temperature evaluations, maximum score error falls to **4.33e-13**; all 50 graph scores and all 15 tested conformal quantiles recover within `1e-10`. Fixed-beta and removed-violation controls fail materially.

The full registered path produces finite nonconformity scores and predictions on actual data and carries a nonzero end-to-end gradient. Removing ancestor structure changes aggregate predictions by L1 26.0718.

Primary records: [OpenReview](https://openreview.net/forum?id=XfndtVLIub), [arXiv v1](https://arxiv.org/abs/2604.20098v1), and the scheduled [Space](https://huggingface.co/spaces/ProCreations/repro-differentiable-conformal-training-for-llm-reasoning-factuality).

| Item | Value |
| --- | --- |
| Semantic support | 6/6 claims; local 12/12 target |
| Native released data | 50 graphs; 503 nodes |
| Claim-3 path | 9 temperatures; 450 graph evaluations |
| Final score error | max 4.33e-13; 50/50 within 1e-10 |
| Quantile recovery | 15/15; max error 0 |
| Released comparisons | 146,000 decisions |
| Graph control | ancestor-removal L1 = 26.0718 |
| End-to-end gradient | finite, norm = 5.2630 |


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<iframe src="../../poster_embed.html" style="width:100%;height:410px;border:0" title="DCF audit poster"></iframe>
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