# Executive summary

## Setup

The package pins arXiv `2606.05689v1` and implements Definition 1, Definition 2, Algorithm 1's CPDAG interpretation, Theorem 3's multi-domain graph, and Algorithm 2's CDNOD run. It exhausts every labeled four-trait DAG crossed with every choice of parents of `S`: 543 DAGs times 16 selection-parent sets, or 8,688 source models. The selected unrolled graph is evaluated at `T=1,2,3` over all 55 disjoint `(A,B,C)` relations per model.

The finite experiments use the paper's native causal-learn PC, GES, and CDNOD implementations. The synthetic pipeline uses `N=5,000`, `d={10,15,20}`, `T={1,2,3,5,10}`, and 50 seeds per cell. PanTHERIA is pinned by SHA-256 and rerun at the paper's reported `626 x 8` shape.

## Correctness gates

| Gate | Result |
| --- | ---: |
| Bayes-ball vs `networkx.is_d_separator` | 0 disagreements / 11,984 queries |
| local CPDAG vs causal-learn DAG-to-CPDAG | 0 disagreements / 600 models |
| Verma–Pearl invariance enumeration | 543 DAGs, 185 MECs, 0 violations |
| Claim 3 destructive `S`-deleted control | 98,787 d-separation mismatches |
| Claim 4 reversed-edge control | 328/328 corruptions rejected |
| Claim 5 omitted-expansion control | 583,356 soundness violations |

## Findings

The exact core is exceptionally strong. Lemma 1 has zero violations and 17,712 converse-failure witnesses. Theorem 1 has exact agreement in all 1,433,520 cells. Theorem 2's three clauses pass across all 8,688 source models. Theorem 4 never loses a single-domain orientation and gives strict gains in 32.74% of 269,328 configurations.

The empirical headline is different. The native 750-run synthetic reproduction does not recover the paper's claim that oriented-only precision is consistently better: PC wins only 3/15 cell means and 0/5 at `d=20`; GES wins 14/15. The actual PanTHERIA rerun likewise gives lower oriented than unoriented precision in all four preprocessing/alpha sensitivity cells. This falsifies Claim 6 as a compound validation claim, without weakening the oracle-premise theorems.

## Reproducibility

`reproduce.py` generated two byte-identical trees, `outputs/` and `packaged_replay/`. `validate_evidence.py` checks the exact live claims, decisive scientific invariants, source/data hashes, destructive controls, paired replay, recursive manifest, and local-route audit.