What was already known
Sun’s original table stopped at p=23, before the first reported counterexample at p=29.
AI involvement
Claude agents found the p=29 counterexample in John Erlbacher’s directed Demonstrandum campaign. Erlbacher audited its verification gates.
Claude agents supplied the counterexample under Erlbacher’s direction; individual-result autonomy is not documented.
Importance
Settles the two sign clauses of a published number-theory conjecture.
Limitations
Part (i), the separate composite-number congruence, is not refuted. The exact calculations establish the listed values, not a replacement sign law.
Technical verification
Independent exact cyclotomic, subset-DP and CRT computations reportedly certify the p=29 values.
Independent checking
exact computation
- Checker
- Independent cyclotomic, subset-DP and CRT-uniqueness checkers in Demonstrandum release
- Scope
- Both sign failures at p=29 in Conjecture 4.6(ii)
- Basis
- Reported by the linked checker
Human understanding
No named person explains the individual calculation’s central mechanism; Few is the evidence default.
Correction and publication history
The p=29 values refute both sign clauses of part (ii).
Read this published revision