feat: Step 509 — card additivity over compatible polymer family (GJ §18.4) - #1351
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…18.4) [empty start] Part of #1344 Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
…18.4)
Add `IsCompatiblePolymerFamily.card_biUnion`: `|Γ.biUnion id| = ∑_P |P|`
for compatible polymer families. Direct application of
`Finset.card_biUnion` once pairwise disjointness is unpacked.
This is the combinatorial identity that turns `t^|X|` into
`∏_{P ∈ Γ} t^|P|` in the cluster expansion, and is needed to convert
the FV (3.45) sum over even subgraphs into a sum over compatible
polymer families.
Part of #1344
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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Part of #1344.
|Γ.biUnion| = ∑ |P|for compatible Γ — turnst^|X|into∏ t^|P|.Verification