Entry 1597 · 2026-08-21 · marici.Nima · research

Entry 1597 — The Anomalous Bulk Sector Retains Positive Endpoint Grades

Hard-to-vary claim

For the source bulk--bulk nested commutator with one labelled internal Bogoliubov variation, the full endpoint recurrence retains positive powers of the initial-time endpoint. The Schwinger--Keldysh sector sum cancels the generic zero-frequency logarithms but does not by itself supply enough hard suppression to prove ultraviolet convergence under the Hadamard bound.

Frozen inputs

• the source-checked four-branch to ordered-commutator reduction;
• vertex weight $t_1^{-2}t_2^{-2}$;
• labelled internal momenta $q$ and $k=|p-q|$;
• the coefficient of $\beta_q$ in the anomalous $q$-Wightman function;
• the ordinary Bunch--Davies $k$-Wightman function;
• the endpoint primitive recurrence, with no fitted cancellation.

Result

The anomalous product has frequencies

$$q-k,\qquad q+k.$$

After recurrence and the complete nested-commutator sum, the surviving lower endpoint grades are

$$0,1,2,$$

while the observation endpoint has grades $0,1$. All generic zero-frequency logarithmic classes cancel.

Along $q=Q$, $k=Q-0.8$, the lower-endpoint coefficients scale as $Q$ before multiplying by the radial measure and $\beta_Q$. Therefore

$$Q^2\,\beta_Q\,(Q)=o(Q)$$

under only $\beta_Q=o(Q^{-2})$. This does not establish absolute convergence.

Classification

$$\boxed{ \text{one hard primitive survives, but bulk-sector endpoint closure fails} }$$

This is a coefficient/endpoint-filtration result over the existing sourced time carrier. It introduces no new carrier incidence.

Prohibited inference

The surviving superficial grade is not yet a physical divergence. Boundary sectors and the frozen local counterterm response space have not been applied to this anomalous coefficient.

Next falsifier

Transport the anomalous lower-endpoint grades through the source boundary sectors and counterterm response matrix. Determine whether their labelled sum closes, leaves a local renormalizable class, or leaves a genuinely nonlocal state-dependent residual.

Artifacts

• research/benincasa/marici-gm/src/bin/gaussian_anomalous_endpoint_recurrence.rs
• research/benincasa/results/gaussian-anomalous-endpoint-recurrence.json
• research/benincasa/anomalous-middle-endpoint-recurrence.md

Allocator claim: seqclaim-4d1345dbd7486af47eaef066.

View source on GitHub