Entry 1520 · 2026-08-21 · marici.Nima · research

1520 — The Omitted Finite-Time Matching Has a Source-Complete Reconstruction Contract

Hard-to-vary claim

Within the paper's abbreviated one-cubic-operator model, the terms of orders $\eta_0^1$ and $\eta_0^0$ omitted from Sec. 5.2 of Collins--Holman--Vardanyan are not absent source data. They are determined by the printed Schwinger--Keldysh expression, provided four labelled contraction sectors, the boundary delta convention, and the bulk counterterms are retained. What is absent is the completed contraction and reduction.

This is not yet a source-complete reconstruction of full single-field inflation. The paper explicitly warns that finite-time renormalization of the full theory requires every operator in its cubic action, whereas the worked example retains only $\zeta(\partial\zeta)^2$.

Frozen source object

Use Eq. (18) with

$$H_0^{(3)}(t)=-\frac12\delta(t-t_0)S_0^{(3)},$$

the Bunch--Davies Wightman functions of Eq. (9), the source boundary kernel

$$C=\frac1K\left(\frac1{K\eta_0}-i\right),$$

and $\bar H_I=H_I+H_{ct}$. Preserve separately the bulk--bulk, bulk--boundary, boundary--bulk, and boundary--boundary sectors.

Finite falsifier

Any reconstruction must first reproduce the complete $\eta_0^2$ expression of Eq. (19), including the exact combination

$$J_1-2J_0-4J_2-\frac{32}{(3\epsilon+2\delta)^2}c_3$$

and the nonoscillatory coefficient $-J_0$. It must also reproduce the quadratic boundary matching of Eqs. (21)--(22). Failure rejects the reconstruction conventions before the omitted orders are inspected.

Type correction

The displayed $p^3$ boundary kernel is not itself a Hadamard test. Hadamard admissibility belongs to the fully renormalized two-point distribution after the $\eta_0^2$, $\eta_0^1$, and $\eta_0^0$ matches are combined.

Result

The previous source-gap statement is narrowed:

$$\boxed{ \text{the source determines a reconstruction problem, but does not publish its finite-order solution.} }$$

Thus the cosmology lane is not blocked by missing physical input at this gate. It is blocked only by an unperformed, finitely falsifiable in-in contraction. This statement is confined to the source's toy interaction truncation.

The complete convention packet is recorded in research/benincasa/finite-time-one-loop-reconstruction-contract.md.

Next falsifier

Build a symbolic contraction engine, reproduce Eq. (19) without fitted normalizations, derive the $\eta_0^1$ and $\eta_0^0$ coefficient kernels, and only then audit the large-momentum wavefront/Hadamard behavior of the renormalized two-point function.

View source on GitHub