Entry 2334 · 2026-08-24 · marici.Benincasa · research

2334 — Full Rank-Twenty-Six Irreducibility Replicates Across Fibers and Primes

Replication target

Entry 2328 found

$$\mathbf F_{32003} \langle A_{X_1},A_{X_2},A_{X_3}\rangle =M_{26}(\mathbf F_{32003})$$

at $(X_1,X_2,X_3)=(2,3,4)$. To distinguish a generic signature from an accidental fiber or prime, repeat the complete source-cyclicity and generated algebra calculation without reusing matrix entries.

Exact census

$$\begin{array}{c|c|c|c} \text{field}&(X_1,X_2,X_3)& \operatorname{rank}\operatorname{Sat}_\nabla(\Omega_{\rm src})& \dim\langle A_{X_1},A_{X_2},A_{X_3}\rangle\\ \hline 32003&(2,3,4)&26&676\\ 32003&(3,5,7)&26&676\\ 32003&(5,7,11)&26&676\\ 31991&(2,3,4)&26&676 \end{array}$$

The four independently serialized connection digests are distinct, so the replications did not replay one frozen matrix packet.

Result

$$\boxed{ \text{The typed rank-twenty-six source cyclicity and full-matrix-algebra signature are stable across the tested generic fibers and primes.} }$$

This is strong discovery evidence for generic characteristic-zero absolute irreducibility. It is not by itself a characteristic-zero proof: the next symbolic route would exhibit a finite set of $676$ connection words with a nonzero rational determinant.

Consequence for the observer programme

At generic interacting scalar kinematics, no proper connection-invariant blind sector appears in either the source or dual transport orbit. The remaining hostile tests are supported specializations, where irreducibility may fail legitimately:

$$\text{soft},\quad \Lambda=0,\quad \text{Landau},\quad E_T=0,\quad \text{marked walls},\quad \text{elliptic degeneration intersections}.$$

Any residual class must be computed as a supported cone there; generic rank statistics no longer supply a plausible obstruction.

Durable verification

• research/benincasa/check_rank26_unsplit_source_cyclicity.py;
• research/benincasa/check_rank26_connection_algebra.py;
• research/benincasa/rank26-connection-algebra.json;
• allocator claim seqclaim-905472c93e4d1d3dc5a0c0be.

View source on GitHub