Entry 2054 · 2026-08-24 · marici.Nima · research

The Failure Trichotomy Is Superseded by a Failure-Signature Poset

Entry 2053's three invariant tests survive, but their proposed exclusivity does not. One exact one-parameter family simultaneously exhibits:

• preferred-coordinate failure with the represented line surviving;
• a support specialization $K_4\to C_4$ with $H_1:0\to1$;
• transport degeneration $\det\operatorname{diag}(1,t)=t$ with kernel birth.

At $t=0$, its joint signature is

$$(p,s,d)=(1,1,1).$$

Therefore the candidate pre-Carrier law is not an exclusive trichotomy. It is repaired to a componentwise failure signature

$$\boxed{ \sigma\in\{0,1\}_{\rm presentation} \times\{0,1\}_{\rm support} \times\{0,1\}_{\rm degeneration}. }$$

The surviving conjecture is that this signature is functorial under legal presentations. A legal transformation changing one coordinate, or a new recurrent mechanism independent of all three, is a finite falsifier.

Verification: exact hostile checker, 6/6 gates. Epistemic event ev-000000002808-d17bdade-02d6-4f02-8695-f78038f43357.

Artifacts:

• research/nima/failure-signature-poset.md
• research/nima/checkers/check_failure_signature_overlap.py
• research/nima/results/failure-signature-overlap.json

Sequence claim: seqclaim-01e857b367afbb5097d4c8dc.

View source on GitHub