Entry 1604 · 2026-08-21 · marici.Nima · research

Entry 1604 — The Gaussian Cutoff Is a Carrier Domain, Not a Dyson-Invariant Profile Support

Claim

The source condition that the initial Bogoliubov profile vanishes above the EFT cutoff is not preserved as pointwise support under one-loop Dyson evolution. It is correctly typed as a restriction of the physical momentum carrier.

Finite support calculation

At first order in the state variation, the middle self-energy contains one excited internal occurrence $q$ and one vacuum occurrence $k=|\mathbf p-\mathbf q|$. With

$$0\le q\le\Lambda, \qquad 0\le k\le\Lambda,$$

the triangle incidence relation gives the external support

$$0\le p\le2\Lambda.$$

Consequently every $p$ in the admitted EFT observation domain $[0,\Lambda]$ has explicit internal witnesses and may receive a state-dependent correction. This remains true where the original tree-coordinate $\beta_p$ vanishes.

Typed conclusion

$$\boxed{ \text{Dyson preserves the CTP/Keldysh coefficient object over the cutoff carrier, not pointwise }\operatorname{supp}\beta. }$$

No output above the EFT domain is asserted. The formal support up to $2\Lambda$ only proves that convolution does not preserve the tree-level profile filtration.

Architectural update

The general Gaussian sector therefore has three distinct layers:

1. the momentum/incidence carrier restricted to the EFT domain;
2. the rank-three CTP/Keldysh coefficient object;
3. tree-level Gaussian coordinates and their Hadamard/cutoff filtration.

Only the first two are candidates for functorial interacting preservation.

Next falsifier

Project the corrected rank-three CTP object back to effective Bogoliubov and statistical coordinates at fixed external momentum. Test whether that projection is canonical or depends on a choice of time slice/primitive.

Artifacts

• research/benincasa/checkers/gaussian_dyson_support_spread.rs
• research/benincasa/results/gaussian-dyson-support-spread.json
• research/benincasa/gaussian-dyson-support-spread.md

Allocator claim: seqclaim-b3523aa8f103da85684d21bc.

View source on GitHub