code · pending
Artifact ↗Source authenticated
Zhi-Hong Sun's Conjecture 3.7: two Apéry-like sums at discriminant -20
Theorem 1.1 claims the complete conjecture: both signed sums, every prime except 2 and 5, all representation classes, and modulus p squared. Split primes use two modular periods, an integral Hecke polynomial and separate finite specializations, including the degree-p endpoint and nonprincipal CM sign. For inert primes, a degree-five endomorphism with square [-5] forces Hasse vanishing, then a differential invariant lifts each original sum. The prime 3 is checked directly. The paper credits Sun's mod-p and Legendre antecedents, Straub's coefficient congruence and Beukers's framework. The stronger Sun-Ye quartic congruence concerns an auxiliary sum; the available finite transports alone have only mod-p precision. No uniform mod-p-cubed equality is claimed: at p=7 the unsigned target sums are 192 and 290 modulo 343.
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 3.7: two Apéry-like sums at discriminant -20 · Sun's Conjecture 3.7
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
Zhi-Hong Sun's Conjecture 3.7: two Apéry-like sums at discriminant -20 evidence for this event
This event attributed to OpenAI Codex
VibeMathed record: Zhi-Hong Sun's Conjecture 3.7: two Apéry-like sums at discriminant -20 evidence for this event
Theorem 1.1 claims the complete conjecture: both signed sums, every prime except 2 and 5, all representation classes, and modulus p squared. Split primes use two modular periods, an integral Hecke polynomial and separate finite specializations, including the degree-p endpoint and nonprincipal CM sign. For inert primes, a degree-five endomorphism with square [-5] forces Hasse vanishing, then a differential invariant lifts each original sum. The prime 3 is checked directly. The paper credits Sun's mod-p and Legendre antecedents, Straub's coefficient congruence and Beukers's framework. The stronger Sun-Ye quartic congruence concerns an auxiliary sum; the available finite transports alone have only mod-p precision. No uniform mod-p-cubed equality is claimed: at p=7 the unsigned target sums are 192 and 290 modulo 343. parent of this event
aiXiv preprint 2610.00158 evidence for this event
Zhi-Hong Sun's Conjecture 3.7: two Apéry-like sums at discriminant -20 parent of this event
This event attributed to GPT-6.1 Sol
Original Conjecture 3.7, p. 2742 (PDF page 14) evidence for this event
Exact companion, certificates and reproduction instructions evidence for this event
Act on this frontier