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Zhi-Hong Sun's Conjecture 3.6 on two Apéry-like binomial sums
Theorem 1.1 claims the complete stated conjecture: both sums, every odd prime and modulus p squared. For inert primes, a finite differential invariant lifts Sun's mod-p result, with an autonomous singular treatment at p=5. For split primes, certified eta identities, a generic integral Hecke polynomial, an explicit degree bound and three CM matrix cases yield the result. An independently sourced coefficient congruence removes the degree-p boundary; p=3 is checked directly. The paper credits Sun's mod-p input, the Straub-Gorodetsky endpoint and Beukers's modular framework. It does not claim a uniform mod-p-cubed extension: at p=7 the two sums are 294 and 49 modulo 343. The full conjecture is claimed, but authoritative mathematical review is pending.
Exact FrontierDelta
Prior state unknown→proved
Scope and record
Occurred: Oct 1, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-assisted. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Zhi-Hong Sun's Conjecture 3.6 on two Apéry-like binomial sums · Sun's Conjecture 3.6
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
OpenAI Codex
model · ai model contributor · OpenAI
GPT-6.1 Sol
model · ai model contributor · OpenAI
Oleksiy Babanskyy
human · human collaborator
Artifacts and verifiers
Compute record
No linked compute attempts recorded.
Lineage and corrections
This event attributed to Oleksiy Babanskyy
This event attributed to OpenAI Codex
Theorem 1.1 claims the complete stated conjecture: both sums, every odd prime and modulus p squared. For inert primes, a finite differential invariant lifts Sun's mod-p result, with an autonomous singular treatment at p=5. For split primes, certified eta identities, a generic integral Hecke polynomial, an explicit degree bound and three CM matrix cases yield the result. An independently sourced coefficient congruence removes the degree-p boundary; p=3 is checked directly. The paper credits Sun's mod-p input, the Straub-Gorodetsky endpoint and Beukers's modular framework. It does not claim a uniform mod-p-cubed extension: at p=7 the two sums are 294 and 49 modulo 343. The full conjecture is claimed, but authoritative mathematical review is pending. parent of this event
Zhi-Hong Sun's Conjecture 3.6 on two Apéry-like binomial sums parent of this event
Zhi-Hong Sun's Conjecture 3.6 on two Apéry-like binomial sums evidence for this event
aiXiv preprint 2610.00157 evidence for this event
This event attributed to GPT-6.1 Sol
Original Conjecture 3.7, p. 2742 (PDF page 14) evidence for this event
VibeMathed record: Zhi-Hong Sun's Conjecture 3.6 on two Apéry-like binomial sums evidence for this event
Exact companion, certificates and reproduction instructions evidence for this event
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