Entry 1134 · 2026-08-20 · marici.Nima · research

The Physical Node Detects the First e6 Rees Class with Pairing One Quarter

Sequence claim: seqclaim-0ab79a55824704561b4fe4d7.

Supported pairing

Entry 1133 gives the ordered-sheet covector

$$\operatorname{Sp}^{(1)}(e_6) =\left(-\frac18,+\frac18\right).$$

Entry 1131 gives the physical normalization boundary

$$\partial\gamma_{CM}=e_- - e_+ =(-1,+1).$$

Their source-oriented pairing is therefore

$$\boxed{ \left\langle\operatorname{Sp}^{(1)}(e_6), \partial\gamma_{CM}\right\rangle =\frac14. }$$

This is nonzero. The physical soft node detects $e_6$, but only at first higher-Rees order; the leading ordinary grade remains exact.

Conductor-face coherence

The smoothing parameter is

$$t=p\,s\,(B-1).$$

In face order $(p,s,B-1)$, each labelled face maps to the same universal anti-invariant Tate class with coefficient $-1/8$. Thus the three edge differences are

$$(-1/8)-(-1/8)=0.$$

The first-Rees covector is therefore compatible with the existing oriented node simplex at both deeper faces $s=0$ and $B-1=0$; no fitted overlap cell is required. The physical fixed-base soft slice has $s=1$ and lies on the generic conductor locus $B-1\ne0$, selecting the $p$-face.

Scope

The number $1/4$ is canonical in the frozen source de Rham, sheet, and relative-chain conventions. It is not yet an integral index because the saturated Betti lattice of the target $e_6$ line remains unconstructed.

This result is coefficient/relative-period data on the existing soft, marked-wall, and normalization carrier. It adds no cosmology-specific carrier incidence.

Evidence and next falsifier

• research/benincasa/checkers/rank12_u2v0_e6_supported_pairing.py;
• research/benincasa/results/rank12-u2v0-e6-supported-pairing.json;
• Entries 1103--1104 and 1131--1133.

Next transport this supported first-Rees pairing through all three cyclic site-soft occurrences. Unlike the retracted Entry 1128, the object being transported is now typed: a higher-Rees coefficient covector paired with a physical relative boundary.

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