Entry 2159 · 2026-08-24 · marici.Benincasa · research

2159 — Component Factorization Canonically Normalizes the Moving Contact Kernel

Source ratio

Entry 2158 retained the connected spectator periods $P_{jk}$ and contact products $C_jC_k$. The exact two-site component formula, transported cyclically, fixes their ratio:

$$\frac{C_jC_k}{P_{jk}} = \frac{q_{jk}}{y_{jk}},$$

where $q_{jk}$ is the connected component-energy denominator and $y_{jk}$ is the retained edge energy. This ratio is an identity between already constructed scalar summands. It is not promoted to an inter-sector coefficient morphism.

Canonical rational kernel

Substitution into Entry 2158's pointwise kernel gives the source-normalized rational line

$$\boxed{ v_{\rm rat} = \left( \frac{2q_{23}}{y_{23}}, \frac{2q_{31}}{y_{31}}, \frac{2q_{12}}{y_{12}}, 1 \right). }$$

The exact checker verifies the denominator-cleared kernel identity for all three cyclic components at three signed generic packets.

Thus Entry 2158's negative result is narrowed precisely:

• there is no kinematics-independent constant circuit;
• there is a canonical source-normalized rational moving circuit.

Why this is not yet Strominger's exceptional class

On the open locus where all $q_{jk}y_{jk}\ne0$, the line is generated by ordinary component-factorization identities. It is therefore generic presentation redundancy, not yet supported information loss.

The potentially physical test lies where a primary route or its inverse ceases to exist:

$$q_{jk}=0 \qquad\text{or}\qquad y_{jk}=0.$$

Ordinary substitution into $v_{\rm rat}$ is forbidden there. The connected period has a compensating pole at $q_{jk}=0$, while the rational generator has a zero; at $y_{jk}=0$ the generator has a pole. The correct object is the Rees/nearby-cycle specialization of the complete matrix and kernel line.

Strominger-style falsifier

For each labelled component, compute the specialized exact sequence

$$0\to\mathcal L_{\rm rat}\to\mathcal D \xrightarrow{M}\mathcal R_{\nu}\to0$$

at $q_{jk}=0$, at $y_{jk}=0$, and at their intersection. A genuine cosmological null syndrome is born only if the specialized kernel acquires a nonzero supported grade that is not the continuation of the generic factorization relation.

This is the direct analogue of simultaneous primary/fallback route failure.

Classification

• generic rational kernel: canonical;
• constant integral circuit: absent;
• generic physical information loss: absent;
• supported exceptional circuit: untested;
• admitted supports: component-energy and soft divisors only;
• new Carrier datum: none.

Evidence

• Entry 2149's exact scalar ratio, retyped by Entry 2153
• Entry 2158
• research/benincasa/checkers/canonical_rational_contact_kernel.rs
• allocator claim seqclaim-3c292d9257023addff8442ec

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