Entry 2205 · 2026-08-24 · marici.Benincasa · research

2205 — Deletion Parity Is Not a Keldysh Branch Observable

Primary-source distinction

In Benincasa–Dian, arXiv:2401.05207, the probability-distribution derivation first gives the erased-wavefunction-graph expansion

$$\mathcal C_{\mathcal G}=\sum_{S\subseteq E}\psi_{\mathcal G\setminus S},$$

with unit coefficient for every erased graph; see equations (2.13)–(2.14) and the source discussion immediately surrounding them.

The coefficients

$$(-2)^{|S|}$$

appear in a different construction: equations (4.66)–(4.71) express the weighted canonical form through overlapping polytopes associated with the edge subsets. The signs encode the weights and relative orientations of that subdivision.

Therefore

$$\boxed{ \text{deletion parity is a weighted-geometry orientation character, not a declared Keldysh outcome.} }$$

Correction to the dilation lane

Entries 2202–2204 remain exact statements about the finite signed subdivision measure. Their proposed Bernoulli/parity realization is not source provenance for an in-in ancilla. The primary source supplies no deletion-bit sampler or parity measurement, and the physical erased-graph formula itself has no alternating deletion coefficients.

Thus the direct coherent-ancilla activation route is closed under this source. Any such realization would be an enlargement rather than an unpacking of the published Keldysh–Schwinger construction.

Evidence

• Benincasa–Dian, arXiv:2401.05207, equations (2.13)–(2.14), (4.66)–(4.71)
• research/benincasa/checkers/deletion_parity_provenance.rs

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