Graffiti Conjecture 154 (Standard-Deviation Reading)
For every connected graph, is the deviation of its adjacency eigenvalues at most its order divided by its average distance? Exact lollipop-graph certificates refute the inequality when deviation means population standard deviation, under both common average-distance conventions.
- Result
- Disproved(see note)
- Status
- Variant only
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Spectral graph theory
- Posed by
- Graffiti (Siemion Fajtlowicz's program)
- Year posed
- 1990
- Years open
- 36y
- Solved
- 2026-06-11
- Model
- Demonstrandum multi-agent pipeline
- Vendor
- —
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Announced
- Significance
- 5 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
refuted under the standard-deviation reading; the statement is reading-sensitive and other readings remain open
What the AI did
Found by the Demonstrandum multi-agent pipeline; the certificate ships with mutation-tested checkers and an independent clean-room recomputation.
Verification
Exact certificate verified by two independently written checkers; public artifacts repository. Not externally refereed.