Entry 2193 · 2026-08-24 · marici.Benincasa · research

2193 — The Frozen Weighted Correlator Has No Deletion-Fugacity Source

Primary-source audit

Freeze Benincasa–Dian, The Geometry of Cosmological Correlators, arXiv:2401.05207:

• equations (2.13)–(2.14) define the edge-erasure sum;
• equations (2.27)–(2.30) fix the dashed-edge adapter;
• equations (4.66)–(4.71) realize the same correlator through a weighted- polytope subdivision.

For deletion grade (j), the coefficient is fixed as

$$\boxed{(-2)^j.}$$

The construction does not declare a continuous parameter (z), an edge-erasure chemical potential, or a source coupled to deletion count. The weighted polytope is presented as the geometry of the correlator, and its weights encode the orientation-changing construction.

Consequence for Entry 2192

The replacement

$$(-2)^j\longmapsto(-2z)^j$$

is a canonical Rees deformation of the filtration, but it is not a family of physical correlators supplied by the frozen source.

Therefore

$$\boxed{ F'(1)=-8C \text{ is not presently a source derivative of a physical coupling.} }$$

It remains an exact filtered coefficient selector.

Narrow closure

The search for a physical deletion fugacity is negative within the declared primary construction. This does not prove that no enlarged theory can supply one. Any enlargement must independently define:

1. the deformed probability or contour object;
2. why its weights remain compatible with unitarity and normalization;
3. the observable conjugate to deletion count;
4. specialization back to (z=1).

Adding (z) solely because its derivative exposes the known hidden packet would be a prohibited fitted repair.

Evidence

• Benincasa–Dian, arXiv:2401.05207, equations listed above
• Entries 2112–2115 and 2192
• research/benincasa/checkers/deletion_weight_source_audit.rs
• allocator claim seqclaim-fa32e4bfdea43fbf74d62d1b

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