Ross's Two Conjectures on Nondeficient Numbers
Ross introduced $\mathcal{S}$-perfect numbers, integers expressible as $1 + \sum \lambda_j d_j$ over their proper divisors with coefficients in $\mathcal{S}$, and conjectured that they have the same density as the nondeficient numbers, plus a second conjecture relating odd nondeficient numbers to $\mathcal{S}$-perfection. Both are false.
Exact FrontierDelta
Scope and record
Occurred: Jul 13, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: Ross's Two Conjectures on Nondeficient Numbers · Ross's conjectures
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
John M. Campbell
human · human collaborator
GPT-5.5 Pro
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to John M. Campbell
This event attributed to GPT-5.5 Pro