# 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).

**Verdict: VERIFIED.**

For each exact model and disjoint `(A,B,C)`, the audit asks whether evolutionary separation at generation `T`, conditional on every earlier selection indicator, implies the static separation conditional on `S`. It separately counts cases where the static graph says independent but the evolutionary graph remains connected.

| Quantity | Result |
| --- | ---: |
| exact relations, `T=1,2,3` | 1,433,520 |
| Lemma 1 implication violations | 0 |
| strict converse-failure witnesses | 17,712 |
| finite PC spurious adjacencies, evolution | 46 |
| finite PC spurious adjacencies, selection off | 8 |
| evolution spurious edges explained by `G^+` | 38/46 |

The finite comparison is paired: the evolutionary and no-selection samples share the same DAG, coefficients, selection weights, and noise variances. Only the reproduction rule changes.

## Destructive control

Deleting inheritance edges `epsilon_i^(t) -> epsilon_i^(t+1)` destroys the repeated-selection propagation path. The 17,712 strict witnesses fall to exactly zero.

## Evidence

Exact relations: `outputs/exact_graph_audit.json`. Native causal-learn PC: `outputs/finite_native_algorithms.json`. Controls: `outputs/destructive_controls.json`.

## Limitations

PC's residual eight no-selection false adjacencies are ordinary finite-sample CI errors. The verdict rests on the exact d-separation audit; the PC run demonstrates the practical consequence.