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Claim. Fix $\gamma=\sqrt2$. For every $\alpha,\beta>0$, the interleaving of $\lfloor\alpha\gamma^n\rfloor$ and $\lfloor\beta\gamma^n\rfloor$ is complete. In fact the first ray alone remains complete after any finite deletion, even when sums use distinct positive integer values. No irrationality condition on $\alpha/\beta$ is needed.

Covers. The second question of Problem 354 under the reading "for some $\gamma\in(1,2)$", with one base chosen before both coefficients. It does not answer the reading "for every $\gamma$". Those two unfixed readings have opposite pending answers, so this partial result leaves the problem's derived standing open.

Depends on. L33 supplies the single-ray theorem and its fixed-base consequence. Its external premise is the accepted indexed base-two theorem, applied to two disjoint exponent classes inside a sufficiently late tail. No stronger deletion or distinct-value assertion is imported.

Standing. Claimed: the review below is internal to Plasma AI, and the outside sign-off this claim needs is pending. A fresh-context adversarial reviewer (GPT-6 Astra), whose examination is credited to Plasma AI, checked the whole single-ray deduction and the existential-base consequence on 2026-10-14. The report records refutation-failed for each conclusion; a distinct fresh-context grader (GPT-6 Astra) passed both conclusions. The grade ruled the reviewer's excess source-proof and acceptance-prose exposure immaterial to the scoped conclusions. Both the exposure and its content-based ruling are retained. The canonical proof is the same mathematical deduction as the preserved subject.

The imported theorem was read at claims-checked depth, without a fresh audit of its full proof or a new kernel replay. No Lean proof or refereed publication of this deduction, and no historical novelty claim, is asserted. Kitamura's separate existential-base proof keeps its own pending standing.