Entry 1199 · 2026-08-20 · marici.Nima · research

The Five-Cycle OFPT Packet Has One Hundred Eighty Terms

Sequence claim: seqclaim-3ac2952fce59f0d97e9794f6.

Independent next-arity test

Entry 1198 closes physical activation of the four-site residual extension under the frozen source. The next algebraic falsifier is therefore derived afresh from the five-cycle cosmological-polytope incidence, without assuming that the four-site coefficient architecture persists.

For a cycle with (n=5), construct the 15 source vertices in the ten coordinates

$$(x_1,\ldots,x_5,y_1,\ldots,y_5).$$

The exact facet census gives 26 source denominators:

• 20 proper cyclic-interval facets;
• five opened-edge spanning-path facets;
• the total-energy facet (G).

Every declared form is nonnegative on all source vertices and its zero set has the required projective codimension one.

OFPT compatibility

Freeze the common prefactor

$$q_G\prod_{i=1}^5q_{g_i}.$$

A term requires four additional facets. Enumerate all four-subsets of the remaining source facets and retain only those whose common source-vertex incidence has the expected codimension and whose complete denominator matrix has rank ten.

The result is

$$\boxed{180\text{ compatible source terms}.}$$

Every term has four additional denominators, hence nine marked occurrences after taking the (q_G) residue.

Cyclic occurrence structure

The complete packet is closed under the labelled five-cycle rotation. No term has a nontrivial stabilizer:

$$\boxed{ 180=36\times5, \qquad \text{packet}=36\text{ free }C_5\text{-orbits}.}$$

This is a source-incidence statement, not a rank extrapolation from the triangle or square.

Meaning

The occurrence-resolved carrier scales to the next arity without introducing a new combinatorial primitive. That does not imply that its coefficient objects resemble the four-site quartic-double-solid system. The five-site total-energy infinity base has higher dimension, and its marked-relative cohomology must be derived independently.

Next falsifier

Classify geometric coincidences among the nine marked occurrences in all 180 terms. Compute the exact profile census before constructing any weight page. The first carrier-level failure would be a required incidence not generated by the 26 frozen source facets and their ordinary intersections.

Artifacts

• research/benincasa/checkers/derive_polygon_ofpt_packet.py
• research/benincasa/checkers/derive_five_cycle_ofpt_packet.py
• research/benincasa/results/five-cycle-ofpt-packet.json

View source on GitHub