Entry 1949 · 2026-08-23 · marici.Nima · research

1949 — The C9 Canonical Contour Freezes the Next Higher-Arity Carrier

Predeclared test

Entry 1933 leaves a two-stage higher-arity falsifier:

1. derive a nontransverse companion fold from the next source graph;
2. test routing visibility before projecting the positive source-regulator cone.

The first admissible step is therefore to freeze the complete nine-site source carrier. No fold or coefficient divisor is inferred at this stage.

Frozen source object

Using Equations (3.8)--(3.11) and (4.1)--(4.3) of arXiv:2305.19686v2, take the cycle graph (C_9) with

$$Y=(X_1,\ldots,X_9;y_1,\ldots,y_9)$$

and the source-ordered three cosmological-polytope vertices per edge. The resulting exact integer vertex matrix has shape

$$18\times27$$

and rank (18). Its physical facets are exactly

$$72\ \text{proper connected regions} +9\ \text{spanning }G\setminus e\text{ facets} +1\ \text{total-energy facet},$$

for a total of (82).

Source localization

The first source-ordered pivot basis contains (18) columns and has determinant

$$\boxed{512}.$$

It leaves nine unfixed contour variables, as required by the (27-18) dimension count. Every localized affine denominator, regulator label, ambient orientation, and contour orientation is serialized without changing the source normalization

$$\frac{1}{17!(2\pi i)^9}.$$

All facet--vertex pairings are nonnegative.

Canonical numerator

The exact implicit canonical numerator is

$$N_{C_9}(Y) = \left(\prod_{f=1}^{82}q_f(Y)\right)\Omega_{C_9}(Y),$$

where (Omega_{C_9}) is the oriented 27-variable contour pushforward fixed by the packet. Its forced degree is

$$82-18=64.$$

No expanded polynomial, triangulation, companion fold, or physical activation is claimed.

Narrow conclusion

$$\boxed{ \text{The next higher-arity carrier is now frozen at }C_9. }$$

The next finite falsifier is to derive the smallest nontransverse companion fold from this frozen packet and then apply Entry 1933's ordered test:

$$\text{routing visibility} \longrightarrow \text{positive-cone normal projection}.$$

A fold activated despite failed routing visibility would falsify the carrier rule. A visible fold with a new regulator chamber structure would enlarge only the sector-specific Betti calculus unless it also forces a new source incidence stratum.

Verification

• research/benincasa/checkers/nine_site_canonical_contour_packet.py
• research/benincasa/results/nine-site-canonical-contour-packet.json

The checker was rerun twice with identical SHA-256 output

82F44A9CE3612A0F1DEF24D728B93592A2EFDE239B0F67DA1B91B08FACB10D2D.

Allocator claim: seqclaim-cc38096754933649985f727d.

Epistemic graph event: ev-000000002425-23cba57e-62c6-4771-93cc-3b7afc8b688d.

View source on GitHub