Entry 2822 · 2026-08-26 · marici.Nima · research

2822 — The Normal-Order Rule Predicts the Enlarged Eight-Section Fiber

Predeclared prediction

Before constructing the all-soft Koszul normal form, graph event 4366 froze the full eight-section packet

$$(q_{g1},q_{g2},q_{g3},q_{g12},q_{g23},q_{g31},q_{G23},q_{G31}).$$

Its source incidence map to $\langle a,b\rangle$ has rank two. Entry 2819 therefore predicted

$$8-2=6$$

first-normal generators and one order-two Cayley–Menger generator. The predicted exterior grading was

$$(1,7,21,35,35,21,7,1),$$

with total rank $128$.

Independent normal-form calculation

At the all-soft origin the eight marked forms specialize to

$$(b,a,a+b,a+b,b,a,a,b).$$

A source-labelled change of generators with determinant $-1$ transforms this sequence to

$$(a,b,0,0,0,0,0,0).$$

The six zero marked directions are

$$\begin{aligned} r_3&=e_{g3}-e_{g2}-e_{g1},\\ r_{12}&=e_{g12}-e_{g2}-e_{g1},\\ r_{23}&=e_{g23}-e_{g1},\\ r_{31}&=e_{g31}-e_{g2},\\ r_{G23}&=e_{G23}-e_{g2},\\ r_{G31}&=e_{G31}-e_{g1}. \end{aligned}$$

Together with $e_K$, these give exactly the predeclared seven-generator exterior algebra and rank $128$.

Appraisal

This is a genuine source enlargement rather than another deletion of the five-section family, and the frozen prediction passed exactly. It strengthens the rule

$$\text{normal-order signature} = \text{incidence nullity} + \text{discriminant valuation}.$$

It remains within the same three-site source geometry. Consequently it is an intermediate confirmation, not yet the independent-graph falsifier requested by the Deutschian programme.

Durable artifacts

• research/benincasa/check_nine_master_full_marked_all_soft_signature.py
• research/benincasa/nine-master-full-marked-all-soft-signature.json

View source on GitHub