feat: mayer expansion term — filter to connected G(ω) (§18.4 sharpening, Issue #1499) - #1521
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…ng, Issue #1499) Empty start commit. Sharpening: `mayerExpansionTerm G n t = ∑_{ω with G(ω) connected} ϕ^T(ω) · z(ω)`. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
…rpening, Issue #1499) Add `mayerExpansionTerm_filter_connected`: the n-th Mayer term reduces to a sum over **cluster sequences** — those `ω : Fin n → polymers` whose index-side incompatibility graph `polymerSeqIncompatibilityGraph ω` is `Connected`. Disconnected sequences contribute zero by Step 584 (`ursellCoefficient_eq_zero_of_disconnected`). This sharpens the Mayer expansion identity to its standard formulation: log Ξ = ∑_{n ≥ 1} ∑_{cluster sequences ω of size n} ϕ^T(ω) · z(t,ω). Bundled with two specialisations: - `mayerExpansionTerm_filter_connected_zero`: the n=0 filter is empty (the empty sequence's incompatibility graph violates `Nonempty`). - `mayerExpansionTerm_filter_connected_one`: the n=1 filter equals the full `piFinset` (every singleton sequence is trivially connected). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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…#1499) Add `mayerPartialSum_filter_connected`: lifts the per-term filter-to- cluster-sequences identity (PR #1521) to the partial sum `mayerPartialSum G N t = ∑_{n=0..N} mayerExpansionTerm G n t`. Each term in the outer sum now ranges only over **cluster sequences** — those `ω : Fin n → polymers` whose incompatibility graph is connected. Direct corollary of `mayerExpansionTerm_filter_connected`. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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…#1499) (#1522) * feat: mayer partial sum filter-connected form (§18.4 sharpening, Issue #1499) Empty start. Lifts PR #1521 from per-n term to the partial sum. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com> * feat: mayer partial sum filter-connected form (§18.4 sharpening, Issue #1499) Add `mayerPartialSum_filter_connected`: lifts the per-term filter-to- cluster-sequences identity (PR #1521) to the partial sum `mayerPartialSum G N t = ∑_{n=0..N} mayerExpansionTerm G n t`. Each term in the outer sum now ranges only over **cluster sequences** — those `ω : Fin n → polymers` whose incompatibility graph is connected. Direct corollary of `mayerExpansionTerm_filter_connected`. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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) (#1551) * feat: mayerExpansionTerm n=2 filter-connected ↔ incompatibility (§18.4, Issue #1499) Empty start. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com> * feat: G(ω) connected on Fin 2 ↔ pair incompatibility (§18.4 sharpening, Issue #1499) Add `polymerSeqIncompatibilityGraph_two_connected_iff_incompatible`: for ω : Fin 2 → polymers, the incompatibility graph is Connected iff PolymersIncompatible (ω 0) (ω 1). Provides an explicit characterisation linking the filter-connected form (PR #1521) to the existing pair Ursell formula (Step 585). Forward: Connected → Adj 0 1 → incompatibility (via contrapositive + no-edges-disconnected on Fin 2). Backward: explicit walk through the unique edge. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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…1499) (#1552) * feat: Fin 2 filter connected = filter incompatible (§18.4 sharpening, Issue #1499) Empty start. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com> * feat: filter-connected = filter-incompatible on Fin 2 (§18.4 sharpening, Issue #1499) Add `mayerExpansionTerm_two_filter_connected_eq_incompat`: the cluster-sequence filter (PR #1521, filter Connected G(ω)) and the existing pair-incompatibility filter (Step 597) coincide on Fin 2. Direct corollary of `polymerSeqIncompatibilityGraph_two_connected_iff_incompatible` (PR #1551) via `Finset.filter_congr`. Bridges the two natural formulations of the n=2 Mayer term sum (filter Connected G(ω) vs filter PolymersIncompatible (ω 0) (ω 1)), making it explicit they are equivalent. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com> --------- Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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Part of #1499. Sharpens
mayerExpansionTermby filtering out the disconnected ω contributions (zero by Step 584).