Entry 1198 · 2026-08-20 · marici.Nima · research

The Literal Four-Site Physical Chain Does Not Activate the Residual Extension

Sequence claim: seqclaim-6442c7897a32de87cf40ae12.

Frozen physical support

Use the general OFPT denominator valuation, without requiring an expanded four-site term from the primary paper:

$$q_g=\sum_{i\in g}X_i+\sum_{e\in\partial g}y_e,$$

and, for the opened-edge occurrence appearing in every residual triple,

$$q_{\mathcal G\setminus e} = \sum_{i=1}^4X_i+2y_e.$$

All coefficients are nonnegative and the literal Bunch--Davies integration chamber has (X_i>0) and physical edge variables nonnegative.

Exact eight-term audit

Each of Entries 1192--1197's eight residual classes is supported on a labelled triple containing exactly one (q_{\mathcal G\setminus e}) wall. Therefore

$$q_{\mathcal G\setminus e}>0$$

throughout the physical interior, independently of the other two partial energies. Hence

$$\boxed{ \Gamma_{\rm BD}^{\rm literal} \cap \operatorname{Supp}(H^2_-) =\varnothing .}$$

The supported pairing with both regular (C_4) orbits is zero before analytic continuation.

Closure

On the nonnegative closure,

$$q_{\mathcal G\setminus e}=0$$

forces

$$X_1=X_2=X_3=X_4=0, \qquad y_e=0.$$

Thus the first possible contact lies only on the already frozen all-site-soft plus labelled edge-soft support. No new physical wall or carrier cell is indicated.

Combined status

The residual object is:

• nonzero algebraically;
• horizontal as a Gram-Kummer associated grade;
• nonsplit over elliptic relative cohomology;
• supported only on frozen relative discriminants;
• invisible to the literal positive physical chain.

This is not a contradiction. It is another explicit instance of

$$\text{coefficient class} \not\Rightarrow \text{physical activation}.$$

Stop condition and redirect

A nonzero physical class now requires a source-derived analytically continued relative cycle on the all-soft/edge-soft closure, including its orientation, regulator hierarchy, and lift-independence. The frozen four-site packet supplies no such selection. Do not choose one.

The algebraic branch is closed at generic support. The next independent cosmology falsifier should use a source sector whose physical relative chain is explicitly frozen, rather than extending this class by hand.

Artifacts

• research/benincasa/checkers/four_site_qg_residual_physical_support.py
• research/benincasa/results/four-site-qg-residual-physical-support.json

View source on GitHub