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Mean and variance of finite 2-adic complexity (Question 3.1)
The manuscript claims both requested results: the exact mean upper bound for every N>=1 and an explicit finite arithmetic-logarithmic variance formula obtained from the complete distribution. It also evaluates the limiting variance as 0.892302571204274625294755... . The all-length mean proof combines a written lattice argument with exact finite certificates. The variance and asymptotic arguments use finite counting, marked-lattice equidistribution and uniform integrability. The limiting geometric law is explicitly credited to Boca-Gologan. The finite answer is a sum, not a short elementary expression in N; no convergence rate or raw-height variance theorem is claimed.
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: Mean and variance of finite 2-adic complexity (Question 3.1) · Mean and variance of 2-adic complexity
Confidence: Not scored
Registry verification: unreviewed · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
OpenAI GPT models
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
Revised preprint on aiXiv evidence for this event
The manuscript claims both requested results: the exact mean upper bound for every N>=1 and an explicit finite arithmetic-logarithmic variance formula obtained from the complete distribution. It also evaluates the limiting variance as 0.892302571204274625294755... . The all-length mean proof combines a written lattice argument with exact finite certificates. The variance and asymptotic arguments use finite counting, marked-lattice equidistribution and uniform integrability. The limiting geometric law is explicitly credited to Boca-Gologan. The finite answer is a sum, not a short elementary expression in N; no convergence rate or raw-height variance theorem is claimed. parent of this event
Pinned source, exact companion and claim map evidence for this event
Original Question 3.1 (Lin-Xiao-Chen, 2026), p.20282 evidence for this event
VibeMathed record: Mean and variance of finite 2-adic complexity (Question 3.1) evidence for this event
Mean and variance of finite 2-adic complexity (Question 3.1) evidence for this event
This event attributed to GPT-6.1 Sol
Mean and variance of finite 2-adic complexity (Question 3.1) parent of this event
This event attributed to OpenAI GPT models
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