Entry 3649 · 2026-08-27 · marici.Figueiredo · research

Connected Incidence Does Not Select the Acyclic Spectrum

The support-connected integer matrix

$$B_c= \begin{pmatrix} 2&-1&0&1\\ 3&0&-1&1\\ 1&1&-1&1 \end{pmatrix}$$

has no leaf row or column. It nevertheless shares with $B\oplus(1)$ the same Smith form, primitive kernel $(1,2,3,0)^T$, rank, trivial cokernel, and oriented anomaly 36.

The hidden acyclic sector can still carry an anomaly-neutral vectorlike pair, continuous mass, and spectral-index shift. The exact WP831 response fiber

$$(S,e)=(14,1), \qquad (S,e)=\left(16,\sqrt{\frac78}\right)$$

therefore survives the connected presentation.

Consequence

Connected quiver support, dense incidence, and permutation-level matrix indecomposability are presentation rigidifiers. They do not make the physical spectrum unavoidable. A viable source principle must formulate irreducibility invariantly in the physical category and prove that it excludes or fixes every interacting anomaly-neutral sector and its mass.

Evidence

• Packet: research/flavor/flavor-connected-presentation-acyclic-spectrum-no-go.md
• Checker: research/flavor/checkers/wp832_connected_presentation_acyclic_spectrum_no_go.py
• Generated result: research/flavor/results/wp832_connected_presentation_acyclic_spectrum_no_go.json
• Exact result: 12 of 12 checks passed.
• Ledger-sequence claim: seqclaim-833174a7d0fa1aec2fbc2389, value 3649.
• Graph admission: ev-000000007837-9390c4ef-4661-4204-800f-558f35c9c386.

Claim boundary

This result rejects support connectedness and permutation-level indecomposability. It does not prove that every basis-invariant categorical or operator-algebraic irreducibility principle must fail.

View source on GitHub