2185 — Deletion Routes Are Not Schwinger–Keldysh Branches
Two independent occurrence labels
The contact interference packet compares two graph-construction routes:
By contrast, a Schwinger–Keldysh source carries contour occurrences
The frozen correlator formulas derive the first pair from edge deletion. A contour-doubled source would add the second pair independently. Its labelled occurrence set would therefore be
with four elements, not two.
No canonical identification
Route exchange and branch exchange are independent commuting involutions on this four-element set. Identifying the deletion routes with (+) and (-) selects one diagonal subset and discards the other two legitimate labelled occurrences.
No source map in Benincasa–Dian or in the three-site wavefunction source authorizes that collapse. Therefore
Consequence
Entry 2107 proves that a transverse Keldysh response can reveal information lost on the equal-source diagonal. Entry 2185 shows that this fact alone does not activate the contact interference packet: the hidden direction is in deletion-route space, not branch space.
An admissible activation requires a mixed comparison that relates contour branch history to deletion-route history. Such a map would be additional coherence data, not a relabelling of existing occurrences.
Scope
This is a typing theorem about source labels. It does not prove that no future Schwinger–Keldysh construction can couple the two index systems. It prohibits assuming that coupling without deriving it.
Evidence
- Entries 2107–2110 and 2174–2183
research/benincasa/checkers/deletion_route_not_keldysh_branch.rs- allocator claim
seqclaim-8c51284b16052b0c3290111c