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Composites Among $[\xi 7^n]$ and Right-Truncatable Primes in Base 7

For every real $\xi>0$ the sequence of integer parts $[\xi 7^{n}]$, $n=0,1,2,\dots$, contains infinitely many composite numbers. Second, there is no infinite right truncatable prime in base~$7$.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Aug 15, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. Publication: preprint. AI contribution: ai-discovered. Imported under CC BY 4.0.

Canonical aliases: Composites Among $[\xi 7^n]$ and Right-Truncatable Primes in Base 7 · Composites among $[\xi 7^n]$

Confidence: Not scored

Registry verification: lean checked · preprint · resolved

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Attribution

VibeMathed
registry · event recorded by

Fable 5
model · ai model contributor · Anthropic

Opus 4.8
model · ai model contributor · Anthropic

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Composites Among $[\xi 7^n]$ and Right-Truncatable Primes in Base 7

specialist registry · passed

Reviewed and corrected 17 August 2026. The first review said no public Lean repository was linked; that was wrong - it is linked in appendix A of the paper. The error is recorded here rather than quietly dropped. Source audit of github.com/rwst/On-Composites at commit 2e49c4d, 17 files, comments stripped before counting: no sorry, admit or axiom anywhere on the proof path. The 18 sorry occurrences are all in Challenge.lean, which nothing imports - the leanprover/comparator "statement of record", which re-declares the definitions against Mathlib alone so the solution's constants, axiom profile and fresh-export kernel re-acceptance can be checked. The tier stops at Lean-checked for a precise reason: all five comparator configs permit exactly propext, Quot.sound and Classical.choice, and the two theorems this entry claims - infinite_composites_seven and no_infiniteTruncatablePrime_seven - are in none of them, because they rest on three native_decide calls, which decide via the compiled evaluator rather than the kernel. The repository documents that quarantine itself. Two things bound the risk: floorPow, CompositeInt and InfiniteTruncatablePrime are verbatim identical to the Mathlib-only re-declarations comparator certifies at std3 for bases 3-6, so definitional drift is ruled out; and cond.c, cycles.c and compress.py recompute the hypotheses outside Lean. Not built here - no toolchain, and the repo has no CI - so this is a source audit, not a compile.

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Composites Among $[\xi 7^n]$ and Right-Truncatable Primes in Base 7

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Lean development, data and generating programs

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Artifacts and verifiers

Lean development, data and generating programs

lean artifact · pending