Split out of #153's measurement round (design memo of 2026-08-02; closing record on #153 has the summary).
The measured fact
For candidates where the skeletal-merge test fires WITHOUT interior improvement — (∃i: c[i]==1.0 ∧ r[i]==1.0) ∧ ¬(∃i≠j: c[i]·r[j] > closed[i][j]) — the join provably contributes zero diversity: Mag(S ∪ {x}) = Mag(S) exactly, as a real number. Measured across the #153 sweep: 268/268 such candidates return a value bitwise-equal to base_value() on both the incremental and fresh routes.
Yet value_with currently routes every merge candidate through value_with_slow: an O(m²) re-border + re-skeletalize + O(k³) re-inversion — all to compute a number we can prove equals the cached base_mag before doing any of it. Since #153 (PR #207) the predicate is already computed and named in value_with_core (it feeds ZeroDiversityProof::SkeletalMerge).
Why this is its own issue, not part of #153
Short-circuiting merge-only → return base_mag changes error behaviour: the slow path can currently Err (singular re-inversion), and error-parity with fresh evaluation is a documented #31 contract point (the module's seeded_grid_fresh_vs_incremental asserts it). The #153 measurements suggest a merge-only bordered ζ′ is singular iff ζ_S is (det ζ′ = det ζ_S · s with the merged structure), i.e. the short-circuit may be error-parity-safe — but that claim was NOT part of the #153 evidence base and needs its own argument + sweep before shipping.
Scope sketch
Split out of #153's measurement round (design memo of 2026-08-02; closing record on #153 has the summary).
The measured fact
For candidates where the skeletal-merge test fires WITHOUT interior improvement —
(∃i: c[i]==1.0 ∧ r[i]==1.0) ∧ ¬(∃i≠j: c[i]·r[j] > closed[i][j])— the join provably contributes zero diversity:Mag(S ∪ {x}) = Mag(S)exactly, as a real number. Measured across the #153 sweep: 268/268 such candidates return a value bitwise-equal tobase_value()on both the incremental and fresh routes.Yet
value_withcurrently routes every merge candidate throughvalue_with_slow: an O(m²) re-border + re-skeletalize + O(k³) re-inversion — all to compute a number we can prove equals the cachedbase_magbefore doing any of it. Since #153 (PR #207) the predicate is already computed and named invalue_with_core(it feedsZeroDiversityProof::SkeletalMerge).Why this is its own issue, not part of #153
Short-circuiting
merge-only → return base_magchanges error behaviour: the slow path can currentlyErr(singular re-inversion), and error-parity with fresh evaluation is a documented #31 contract point (the module'sseeded_grid_fresh_vs_incrementalasserts it). The #153 measurements suggest a merge-only bordered ζ′ is singular iff ζ_S is (det ζ′ = det ζ_S · s with the merged structure), i.e. the short-circuit may be error-parity-safe — but that claim was NOT part of the #153 evidence base and needs its own argument + sweep before shipping.Scope sketch
value_with_core(both REPORT arms), keepingEvalPathreporting honest (a new variant or documented reuse ofSlow).base_mag, which the slow path was measured to reproduce bitwise 268/268) — but the sweep must re-verify against the incremental coalition magnitude: paired/cached evaluation for the decision hot path #31 contract tests.