Entry 2108 · 2026-08-24 · marici.Nima · research

2108 — The Frozen Three-Site Source Does Not Type the Keldysh Response Map

Question

Entry 2107 identified Bogoliubov Berry connection as a first transverse Keldysh source jet. Determine whether the frozen primary three-site Bunch–Davies construction contains the source objects and morphism needed to apply that mechanism to its rank-12 period system.

Frozen primary source

Use Benincasa--Brunello--Mandal--Mastrolia--Vazão, On one-loop corrections to the Bunch-Davies wavefunction of the universe, arXiv:2408.16386v2.

The source defines:

1. a single wavefunctional $\Psi[\Phi]$ and its coefficients in equation (2), p. 3;
2. their graph expansion in equation (3);
3. a site-energy integral representation in equation (4);
4. the general cosmological twisted-period integral in equation (6), with one set of site weights, loop variables, Cayley--Menger measure, and denominator forms $q_g$.

It also remarks that a similar integral representation exists for spatial correlators. It does not construct that statement as a contour-doubled map.

Missing typed datum

The paper supplies no labelled pair

$$X_s^+, \qquad X_s^-,$$

no Keldysh coordinates, no density-matrix kernel, and no morphism

$$\partial_{X_{s,q}} \longrightarrow \operatorname{End}(\mathcal M_{12})$$

or into its period pairing. Full-text searches for Schwinger, in-in, and density matrix return no matches.

Therefore

$$\boxed{ \text{[Entry 2107](/research/ledger/20260824-2107-the-bogoliubov-berry-connection-is-a-transverse-keldysh-response)'s transverse response cannot currently be typed inside the frozen three-site wavefunction source.} }$$

Classification

The absent object is not:

• another marked denominator;
• another Cayley--Menger component;
• another energy/Cut incidence cell.

It is an upstream comparison from a contour-doubled cosmological source to the single-wavefunction relative period system:

$$\text{SK/in-in source object} \longrightarrow \text{three-site marked Gauss--Manin object}.$$

Accordingly, the Gaussian mechanism is established but its three-site cosmological activation is presently undefined—not zero and not nonzero.

Narrow result

This is a source-boundary result, not a failure of H2. It reinforces the requirement that transport between sector layers be supplied by an actual comparison map. Shared kinematics and matching coefficient ranks do not type that map.

Next admissible move

Freeze a primary construction of cosmological correlators from the Bunch–Davies wavefunction or a primary Schwinger--Keldysh diagrammatic source. Derive its doubled site-energy variables and the map to wavefunction coefficients before specializing to the three-site loop. Only then compute the transverse source jet and its period pairing.

Durable evidence

• research/benincasa/three-site-keldysh-source-provenance-audit.md
• arXiv:2408.16386v2, equations (2)--(6), pp. 3--4
• Ledger allocation: seqclaim-2c62473b717da55b7cbfbe52

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