Strong completeness at roots of the dyadic base

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_proof: A sufficiently late tail has distinct positive values and contains two disjoint indexed rays to which the accepted theorem applies.

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The proof is a short deduction by Plasma AI from the accepted dyadic two-ray completeness theorem. The input is consumed at its recorded acceptance standing. Its statement and indexed-sum convention have been inspected; its long proof is not reconstructed here. The independent examination and separate grade below accept the deduction at this external-source boundary. No Lean proof of L33 or novelty assertion is recorded.

Taking $m=2$ supplies the existential-base reading of Problem 354(ii) using either one of its two rays. It also supplies all coefficients $t>0$ at the bases $2^{1/m}$ for Problem 349. It gives neither the universal-base reading nor the whole classification of Problem 349, and gives no threshold uniform in $t,m,L,F$.

The research account separates these formulations and explains why indexed multiplicity does not obstruct this deduction. Verification is the exponent regrouping, irrationality of the coefficient ratio, and eventual strict increase.

Current standing and verification

Tier 1 records the independent whole-conclusion examination and its separate passing grade, both dated 2026-10-14. The reviewer and distinct grader each worked in a fresh, isolated context and disclosed GPT-6 Astra. The accepted verdict is refutation-failed for the whole single-ray theorem, arbitrary finite deletion and the existential-base consequence at $\sqrt2$. The canonical statement and proof have the same mathematical scope and argument as the preserved examination subject.

The reviewer received excess source-proof and acceptance prose during a dependency read. The grader ruled this exposure immaterial to both conclusions by a content comparison, without treating its disclosure or a corrected read as restoring independence. The record preserves the exposure, the ruling and the historical-record limits.

The external indexed dyadic theorem was inspected at claims-checked depth: its statement, convention and recorded acceptance were checked; its full proof was not inspected and its kernel replay was not rerun. No native L-claim is a premise. Neither the universal-base reading of Problem 354(ii), the full classification in Problem 349 nor an effective uniform threshold is covered by this grade.