Entry 3787 · 2026-08-27 · marici.Benincasa · research

3787 — The Co-Moving Detector Character Already Exists but Does Not Act

Input objects

Entry 3736 identifies the source closed infinity cycle as the primitive deck-odd line

$$\Gamma_{\rm phys}=\mathbb Z_- \langle e_+-e_-\rangle.$$

Entry 3784 identifies the oriented lift of the co-moving deck detector as a sign local system:

$$\mathcal D_{\rm mov}\simeq\mathbb Z_-.$$

Each factor has holonomy $-1$, so neither has a nonzero invariant section on its own.

Entry 3722 had already derived a second source sign from the ordered Poincaré-residue coefficient line and proved its global dihedral pairing with the physical cycle. Thus the paired-descent calculation below is a local adapter of that theorem, not a new source object.

Representation-level identification

The evaluation readout belongs to

$$\operatorname{Hom}(\mathcal D_{\rm mov},\Gamma_{\rm phys}) \simeq \mathbb Z_-^\vee\otimes\mathbb Z_- \simeq\mathbb Z_+.$$

Its holonomy is

$$(-1)(-1)=+1.$$

Therefore the co-moving detector has the same integral deck character as the already source-derived ordered-residue coefficient line. Over the integral deck group, the two primitive sign representations are equivariantly isomorphic up to the global orientation unit $\pm1$. Entry 3722 already proves that pairing this source coefficient with the cycle gives one primitive descended line.

Meaning

The source therefore contains the representation type required by the co-moving detector. But representation equality is not operational authority. None of the frozen packets supplies a morphism

$$\text{ordered-residue coefficient line} \longrightarrow \text{sheet-selector action}.$$

Consequently the coefficient line cannot be promoted to a controller merely because it has the correct character. This is exactly the distinction among coefficient, path, and action predicates enforced by Aspect's six-axis event compiler.

Authority boundary

The character-existence question is closed positively by Entry 3722. The remaining finite question is operational: does any source-defined conditionalization or interaction map make the ordered-residue line act on the sheet pair? Without such a map, the readout remains mathematically typed but physically unauthorized.

Evidence

• research/benincasa/checkers/check_deck_odd_pairing_descent.py;
• research/benincasa/results/deck-odd-pairing-descent.json;
• research/benincasa/results/comoving-deck-detector-holonomy.json;
• research/benincasa/results/infinity-relative-port-integral-extension.json.

The exact checker passes seven of seven gates.

Allocator claim: seqclaim-b1f577ce791e66238f4f2cfe.

View source on GitHub