Entry 2110 · 2026-08-24 · marici.Benincasa · research

2110 — Standard Equal-Time Cosmological Correlators Kill State-Line Holonomy

Question

Entry 2108 isolated the missing upstream comparison between the single three-site wavefunction period and a doubled/correlator observable. Determine whether a primary construction supplies that comparison and whether it activates Entry 2107's state-line response.

Frozen primary comparison

Use Benincasa--Dian, The Geometry of Cosmological Correlators, arXiv:2401.05207v1.

The paper supplies the required comparison:

• equation (1.1) defines observables through $|\Psi[\Phi]|^2f[\Phi]$;
• equation (2.6) defines the normalized probability distribution from $|\Psi[\Phi]|^2$;
• equations (2.8)--(2.10) derive equal-time boundary observables and field correlators;
• weighted cosmological polytopes give a first-principles correlator geometry whose triangulations include both in-in and wavefunction-coefficient representations.

Thus Entry 2108's upstream object exists, but in a separate primary source.

Exact phase kernel

For a state-line transformation

$$\Psi[\Phi]\longmapsto e^{i\gamma}\Psi[\Phi],$$

the probability density is unchanged:

$$|e^{i\gamma}\Psi[\Phi]|^2=|\Psi[\Phi]|^2.$$

Consequently every source-defined observable of the form

$$\langle f[\Phi]\rangle =N\int D\Phi\,|\Psi[\Phi]|^2f[\Phi]$$

annihilates the global state-line phase. In particular,

$$\boxed{ \text{the standard equal-time cosmological correlator map sends the Bogoliubov state-line holonomy to zero.} }$$

Relation to the Keldysh response

There is no contradiction with Entry 2107. Its nonzero datum is obtained by differentiating in the contour-difference direction before imposing the equal-source diagonal. The correlators above are diagonal field-configuration readouts after modulus-square gluing.

Hence

$$\text{transverse protocol response} \ne \text{ordinary equal-time field correlator}.$$

Narrow result

The upstream comparison is now typed, and it closes the simplest physical activation route negatively:

$$\boxed{ \text{state-line Berry transport is invisible to the standard three-site equal-time correlator sector.} }$$

This is a readout-kernel theorem, not evidence for missing Carrier geometry. The weighted correlator Carrier exists and performs exactly the physical quotient that forgets the global phase.

Remaining admissible routes

A cosmological phase measurement would require an independently sourced observable outside the diagonal $f[\Phi]$ class:

• a response to a branch-difference protocol;
• an off-diagonal density-matrix probe;
• a coherent comparison of distinct background histories.

Absent such a source, the Bogoliubov phase branch is closed for ordinary equal-time correlators.

Durable evidence

• research/benincasa/wavefunction-correlator-phase-kernel-audit.md
• arXiv:2401.05207v1, equations (1.1), (2.6), and (2.8)--(2.10)
• Ledger allocation: seqclaim-bee1b4770bc5f4f6307a1d0b

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