# Judge-facing evidence scorecard

- Paper ID: `mOcTXKawFY`
- Registered claims: 6
- Assessments: 5 verified, 1 falsified as literally registered
- Source matrix: `EVIDENCE_MATRIX.json`
- Prose-local artifact references: validated

## Claim summary

| # | Literal claim | Assessment | Decisive quantitative result |
| ---: | --- | --- | --- |
| 1 | Definition 1 formalizes an evolutionary selection model as a DAG G^(T) over trait variables X^(0)...X^(T), heritable factors epsilon^(0)...epsilon^(T), and reproduction/selection indicators S^(0)...S^(T-1), distinguishing it from one-shot static selection models (Section 2, Definition 1). | VERIFIED | 26,064/26,064 exhaustive constructions and 60/60 larger constructions are acyclic and match the exact node count, edge count, and required edge families. |
| 2 | Lemma 1 shows that repeated evolutionary selection induces conditional dependencies among variables that are absent under static selection models, so applying static-selection graphical models to evolutionary data can yield false causal discoveries (Section 2, Lemma 1). | VERIFIED | Lemma 1 has 0 violations in 1,433,520 exact relations and 17,712 strict converse-failure witnesses; paired PC finds 46 spurious adjacencies with evolution versus 8 without selection. |
| 3 | Theorem 1 proves that the clique-augmented DAG G^+ (Definition 2) fully captures all d-separation/conditional-independence constraints implied by the evolutionary selection model, without needing to explicitly model the selection variables (Section 3, Definition 2, Theorem 1). | VERIFIED | G^(T) and G^+ agree on all 1,433,520 exact d-separation relations with 0 violations; the naive S-deleted control mismatches 98,787 relations. |
| 4 | Theorem 2 establishes that applying standard constraint-based algorithms such as PC or GES (Algorithm 1) to G^+ is sound and complete: oriented edges correspond to true causal relations, while unoriented edges may reflect the presence of selection (Section 3, Theorem 2, Algorithm 1). | VERIFIED | Across 8,688 exact models, 52,128/52,128 adjacency cells, 2,640/2,640 oriented edges, and 39,030/39,030 unoriented-edge completeness cases pass. |
| 5 | Theorem 4 shows that combining heterogeneous data from multiple environments/domains via the CDNOD-based procedure (Algorithm 2) improves identifiability of the evolutionary selection model compared to single-environment data (Section 4, Theorem 4, Algorithm 2). | VERIFIED | Multi-domain identification loses 0 single-domain orientations and is strictly better in 88,176/269,328 configurations; native CDNOD orients 4.65 correct edges versus 3.55 for single-domain PC. |
| 6 | The proposed identification procedure is validated on synthetic graphs of varying size and on seven real-world datasets spanning biology, agriculture, and social science (Section 5). | FALSIFIED AS LITERALLY REGISTERED | In 750 native synthetic runs, oriented-only PC beats the standard interpretation in only 3/15 grid-cell means and 0/5 d=20 cells; the PanTHERIA rerun gives 0.40 oriented versus 1.00 unoriented precision at the registered log/alpha-0.05 sensitivity cell. |

## Claim 1 — VERIFIED

> Definition 1 formalizes an evolutionary selection model as a DAG G^(T) over trait variables X^(0)...X^(T), heritable factors epsilon^(0)...epsilon^(T), and reproduction/selection indicators S^(0)...S^(T-1), distinguishing it from one-shot static selection models (Section 2, Definition 1).

- Decisive quantitative result: 26,064/26,064 exhaustive constructions and 60/60 larger constructions are acyclic and match the exact node count, edge count, and required edge families.
- Native scale: All 8,688 four-trait static models are unrolled at T=1,2,3 for 26,064 exact constructions, followed by 60 larger constructions through d=20 and T=5.
- Source locator: arXiv 2606.05689v1, Section 2, Definition 1 and its four-item edge inventory.
- Upstream pin:
  - sha256: `9b3075a937ce509d5883709a90fba12a35111d6b20f92e033d3e64636728c070`
  - source: `https://arxiv.org/html/2606.05689v1`
  - version: `2606.05689v1`
- Independent evidence:
  - `outputs/exact_graph_audit.json`
  - `outputs/results.json`
- Executed outputs:
  - `outputs/exact_graph_audit.json`
  - `outputs/results.json`
- Independent oracle paths:
  - `outputs/oracle_gates.json`
  - `SOURCE_EXCERPTS.md`
- Control paths:
  - `outputs/destructive_controls.json`
- Destructive or boundary control: One inheritance edge is deleted from an otherwise valid G^(3); the exact edge-count and edge-family checker rejects the mutant.
- Rate relation: no rate-evidence fields are present in the matrix.
- Limitation: The construction audit verifies the formal graph object, not biological adequacy of independent component-wise heritable factors.
- Scope boundary: Verification covers Definition 1's graph construction and its distinction from a one-shot model, not arbitrary alternative evolutionary models.

## Claim 2 — VERIFIED

> Lemma 1 shows that repeated evolutionary selection induces conditional dependencies among variables that are absent under static selection models, so applying static-selection graphical models to evolutionary data can yield false causal discoveries (Section 2, Lemma 1).

- Decisive quantitative result: Lemma 1 has 0 violations in 1,433,520 exact relations and 17,712 strict converse-failure witnesses; paired PC finds 46 spurious adjacencies with evolution versus 8 without selection.
- Native scale: All 1,433,520 disjoint-set relations from 8,688 source models at T=1,2,3 are enumerated, plus twenty paired 5,000-sample PC trials at d=8.
- Source locator: arXiv 2606.05689v1, Section 2, Lemma 1 and the paragraph immediately following it.
- Upstream pin:
  - sha256: `9b3075a937ce509d5883709a90fba12a35111d6b20f92e033d3e64636728c070`
  - source: `https://arxiv.org/html/2606.05689v1`
  - version: `2606.05689v1`
- Independent evidence:
  - `outputs/exact_graph_audit.json`
  - `outputs/finite_native_algorithms.json`
  - `outputs/results.json`
- Executed outputs:
  - `outputs/exact_graph_audit.json`
  - `outputs/finite_native_algorithms.json`
- Independent oracle paths:
  - `outputs/oracle_gates.json`
  - `SOURCE_EXCERPTS.md`
- Control paths:
  - `outputs/destructive_controls.json`
  - `outputs/finite_native_algorithms.json`
- Destructive or boundary control: Deleting all inheritance edges removes every one of the 17,712 converse-failure witnesses; switching selection off reduces native PC false adjacencies from 46 to 8.
- Rate relation: no rate-evidence fields are present in the matrix.
- Limitation: Finite PC counts include ordinary type-I and type-II CI errors; the exact graphical enumeration supplies the decisive lemma result.
- Scope boundary: Verification concerns conditional-dependence structure and its false-discovery mechanism, not the frequency of false discoveries in every empirical domain.

## Claim 3 — VERIFIED

> Theorem 1 proves that the clique-augmented DAG G^+ (Definition 2) fully captures all d-separation/conditional-independence constraints implied by the evolutionary selection model, without needing to explicitly model the selection variables (Section 3, Definition 2, Theorem 1).

- Decisive quantitative result: G^(T) and G^+ agree on all 1,433,520 exact d-separation relations with 0 violations; the naive S-deleted control mismatches 98,787 relations.
- Native scale: The complete d=4 model space yields 1,433,520 exact biconditional cells over T=1,2,3, with a further 143,811 random cells through d=10 and T=5.
- Source locator: arXiv 2606.05689v1, Section 3.1, Definition 2 and Theorem 1.
- Upstream pin:
  - sha256: `9b3075a937ce509d5883709a90fba12a35111d6b20f92e033d3e64636728c070`
  - source: `https://arxiv.org/html/2606.05689v1`
  - version: `2606.05689v1`
- Independent evidence:
  - `outputs/exact_graph_audit.json`
  - `outputs/oracle_gates.json`
  - `outputs/results.json`
- Executed outputs:
  - `outputs/exact_graph_audit.json`
- Independent oracle paths:
  - `outputs/oracle_gates.json`
  - `SOURCE_EXCERPTS.md`
- Control paths:
  - `outputs/destructive_controls.json`
- Destructive or boundary control: Replacing G^+ with the selection-blind S-deleted DAG creates 98,787 exact mismatches, so agreement cannot come from an inert augmentation.
- Rate relation: no rate-evidence fields are present in the matrix.
- Limitation: Finite enumeration is exhaustive at four traits and randomized above that size; the theorem, not this audit, establishes unbounded-size validity.
- Scope boundary: Verification covers the paper's causally sufficient evolutionary DAG class and does not extend to dependent heritable-factor models.

## Claim 4 — VERIFIED

> Theorem 2 establishes that applying standard constraint-based algorithms such as PC or GES (Algorithm 1) to G^+ is sound and complete: oriented edges correspond to true causal relations, while unoriented edges may reflect the presence of selection (Section 3, Theorem 2, Algorithm 1).

- Decisive quantitative result: Across 8,688 exact models, 52,128/52,128 adjacency cells, 2,640/2,640 oriented edges, and 39,030/39,030 unoriented-edge completeness cases pass.
- Native scale: All 8,688 four-trait source models cover 52,128 adjacency cells, 2,640 compelled orientations, and 39,030 unoriented-edge alternatives; PC/GES also run in 750 paper-scale trials.
- Source locator: arXiv 2606.05689v1, Section 3.2, Algorithm 1 and Theorem 2.
- Upstream pin:
  - sha256: `9b3075a937ce509d5883709a90fba12a35111d6b20f92e033d3e64636728c070`
  - source: `https://arxiv.org/html/2606.05689v1`
  - version: `2606.05689v1`
- Independent evidence:
  - `outputs/exact_graph_audit.json`
  - `outputs/oracle_gates.json`
  - `outputs/synthetic_native_pipeline.json`
  - `outputs/results.json`
- Executed outputs:
  - `outputs/exact_graph_audit.json`
  - `outputs/synthetic_native_pipeline.json`
- Independent oracle paths:
  - `outputs/oracle_gates.json`
  - `SOURCE_EXCERPTS.md`
- Control paths:
  - `outputs/destructive_controls.json`
- Destructive or boundary control: A compelled CPDAG orientation is reversed in 328 eligible source models, and the Theorem 2 soundness checker rejects all 328 mutants.
- Rate relation: no rate-evidence fields are present in the matrix.
- Limitation: The exact verdict assumes the theorem's large-sample faithfulness premise; finite-sample PC and GES can and do violate oracle-level orientation soundness.
- Scope boundary: Verification is for Algorithm 1 under Theorem 2's premises, not a guarantee that finite-sample CI testing always returns the population CPDAG.

## Claim 5 — VERIFIED

> Theorem 4 shows that combining heterogeneous data from multiple environments/domains via the CDNOD-based procedure (Algorithm 2) improves identifiability of the evolutionary selection model compared to single-environment data (Section 4, Theorem 4, Algorithm 2).

- Decisive quantitative result: Multi-domain identification loses 0 single-domain orientations and is strictly better in 88,176/269,328 configurations; native CDNOD orients 4.65 correct edges versus 3.55 for single-domain PC.
- Native scale: All 8,688 four-trait source models are crossed with 31 nonempty change sets for 269,328 exact configurations, plus twenty four-domain CDNOD runs with 5,000 samples per domain.
- Source locator: arXiv 2606.05689v1, Section 4, Theorem 3, Algorithm 2, and Theorem 4.
- Upstream pin:
  - sha256: `9b3075a937ce509d5883709a90fba12a35111d6b20f92e033d3e64636728c070`
  - source: `https://arxiv.org/html/2606.05689v1`
  - version: `2606.05689v1`
- Independent evidence:
  - `outputs/exact_graph_audit.json`
  - `outputs/finite_native_algorithms.json`
  - `outputs/results.json`
- Executed outputs:
  - `outputs/exact_graph_audit.json`
  - `outputs/finite_native_algorithms.json`
- Independent oracle paths:
  - `outputs/oracle_gates.json`
  - `SOURCE_EXCERPTS.md`
- Control paths:
  - `outputs/destructive_controls.json`
- Destructive or boundary control: Omitting Theorem 3's changed-selection ancestor expansion creates 583,356 orientation-soundness violations across the same 269,328 configurations.
- Rate relation: no rate-evidence fields are present in the matrix.
- Limitation: Strict improvement is model-dependent at 32.74%, while Theorem 4's universal statement is monotonic non-loss rather than strict gain in every configuration.
- Scope boundary: Verification assumes fixed causal and selection structures across domains with mechanism parameters changing as specified by the paper.

## Claim 6 — FALSIFIED AS LITERALLY REGISTERED

> The proposed identification procedure is validated on synthetic graphs of varying size and on seven real-world datasets spanning biology, agriculture, and social science (Section 5).

- Decisive quantitative result: In 750 native synthetic runs, oriented-only PC beats the standard interpretation in only 3/15 grid-cell means and 0/5 d=20 cells; the PanTHERIA rerun gives 0.40 oriented versus 1.00 unoriented precision at the registered log/alpha-0.05 sensitivity cell.
- Native scale: The synthetic grid has d=10,15,20, T=1,2,3,5,10, N=5,000, and 50 seeds per cell; all seven real-data tables are audited and PanTHERIA is independently rerun.
- Source locator: arXiv 2606.05689v1, Sections 5.1-5.2, Figure 6, Appendix D.1, and Figures 13-19.
- Upstream pin:
  - sha256: `9b3075a937ce509d5883709a90fba12a35111d6b20f92e033d3e64636728c070`
  - source: `https://arxiv.org/html/2606.05689v1`
  - version: `2606.05689v1`
- Independent evidence:
  - `outputs/synthetic_native_pipeline.json`
  - `outputs/realdata_native_and_source_audit.json`
  - `outputs/results.json`
- Executed outputs:
  - `outputs/synthetic_native_pipeline.json`
  - `outputs/realdata_native_and_source_audit.json`
- Independent oracle paths:
  - `outputs/realdata_native_and_source_audit.json`
  - `inputs/PanTHERIA_1-0_WR05_Aug2008.txt`
  - `SOURCE_EXCERPTS.md`
- Control paths:
  - `outputs/destructive_controls.json`
- Destructive or boundary control: Changing one printed DGRP numerator makes the arithmetic audit fail, and flipping one PanTHERIA input byte is independently detected by the pinned SHA-256.
- Rate relation: no rate-evidence fields are present in the matrix.
- Limitation: Only PanTHERIA is rerun from raw real data; the other six real datasets are audited from the paper's printed outputs, whose pseudo ground truth the paper itself calls an unreliable surrogate.
- Scope boundary: Falsification targets the compound empirical-validation claim and does not dispute that the authors ran analyses on seven named datasets or the exact oracle theorems in Claims 1-5.