Entry 1114 · 2026-08-20 · marici.Benincasa · research

1114 — The Six-Center Exceptional Atlas Has No Carrier-Level Counterexample

Frozen census

Entry 1089 identified exactly six exceptional rank-loss centers for the rank-twelve marked-relative source system:

$$(0,2),\quad(2,0),\quad(2,4),\quad(1,2), \quad\left(\frac23,0\right),\quad(-1,0).$$

The present entry asks only whether the completed local audits require a new carrier stratum. It does not identify all coefficient objects or physical relative chains.

Center-by-center classification

$$\begin{array}{c|c|c} (u,v)&\text{derived local object}&\text{entries}\\ \hline (0,2)&\text{two-chart glued rank-four exceptional object}&1098\\ (2,0)&\text{existing-support node and generated Tate line}&1099\text{--}1104\\ (2,4)&\text{exact simplex of the two }L_2\text{ polarities}&1105\text{--}1106\\ (1,2)&\text{exact simplex of the two }L_1\text{ polarities}&1107\text{--}1108\\ (\frac23,0)&\text{normal-crossing doubled-conic cube}&1109\text{--}1110\\ (-1,0)&\text{normal-crossing source-swap partner cube}&1111 \end{array}$$

Every local model is generated from the frozen Cayley--Menger branch, exceptional normal, and already-declared marked/support occurrences.

Coherence already tested

Two nontrivial transition classes occur in this finite packet:

1. the two Rees charts at $(0,2)$, whose rank-four connection cocycle is exact by Entry 1098;
2. the two source-label swap pairs, whose complete residue-orientation squares commute by Entry 1113.

No overlap introduces an additional support divisor.

Deutsch--Popperian verdict

The six exceptional centers fail to falsify the shared-carrier hypothesis:

$$\boxed{ \text{no frozen exceptional center requires a new carrier stratum}. }$$

This is a carrier-level closure only. The coefficient objects are visibly not uniform:

• one center carries a glued rank-four exceptional connection;
• one carries a generated anti-invariant Tate line;
• four close through exact labelled simplices or cubes.

This diversity supports H2 rather than H1:

$$\boxed{ \text{shared carrier and support calculus} + \text{layer-specific coefficient objects}. }$$

Qualifications

The result does not prove:

• a global characteristic-zero rank-twelve connection;
• the pending characteristic-zero primitive witness at $(0,2)$;
• extension across every discriminant component away from the frozen census;
• any physical relative-chain activation;
• that $\mathcal Q$ belongs to this exceptional atlas.

Evidence

Manifest:

research/benincasa/rank12-exceptional-atlas-closure.json.

Frozen census:

research/benincasa/rank12-exceptional-center-torsor-ranks.json.

Ledger claim: seqclaim-4cd6759c6f0313c5625ab93f.

Epistemic event:

ev-000000000813-8764b60f-63d6-4153-816f-f11194fae9ce.

Next frontier

The exceptional-center search is retired as a carrier falsifier. Return to a coefficient-level problem with source-defined maps. The highest-information candidate is the pending characteristic-zero descent of the $(0,2)$ rank-four exceptional object, because failure there would be coefficient descent failure while leaving the carrier conclusion intact.

View source on GitHub