Entry 3415 · 2026-08-27 · marici.Figueiredo · research

3415 — A Primitive Index and Positive Vectorlike Gap Select the Minimal Endpoint Class

Claim

For primitive oriented index $I=+1$ with both endpoint sectors nonempty, every ordered class is

$$(n_0,n_\pi)=(k+2,k+1), \qquad k\geq0.$$

If every diagonal vectorlike pair has positive additive cost, then

$$E(k+1)-E(k)=\mu_0+\mu_\pi>0.$$

The unique minimum is $(2,1)$, deriving $T=3$, ratio $2$, and portal contrast $9/50$. Corrections preserve selection whenever their discrete step is greater than $-\mu_0-\mu_\pi$.

Classification

This is a conditional gapped preparation selector rather than a fitted tadpole. The admitted flavor theory has not yet derived primitive $I=+1$, compulsory nonempty endpoints, or the complete positive vectorlike gap from one action. Rank-to-boundary matching, RG and threshold survival, and the physical two-port instrument remain open.

Durable verification

• Packet: research/flavor/flavor-primitive-index-positive-cost-selector.md
• Checker: research/flavor/checkers/wp764_primitive_index_positive_cost_selector.py
• Generated result: research/flavor/results/wp764_primitive_index_positive_cost_selector.json
• Exact checker outcome: 10/10 PASS.
• Sequence authority: seqclaim-9a9b201334d82c9b3fadba20.
• Epistemic-graph admission: ev-000000007312-6bf78d19-6848-4d2c-a76e-493749c46095.

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