What was already known
Earlier work showed failures at lower two-, three- and four-neighbor orders, and some cyclic-deck patterns were already known in music theory.
AI involvement
Claude and Codex agents found relevant cyclic-deck work and new families during guided searches. Domina and Ceriotti framed the question, steered the search and developed the mathematical explanation.
Agents supplied central new examples and the cross-field connection, while the human authors framed the question, guided the searches, and developed the exposition.
Importance
Extends counterexamples to higher orders and every fixed finite order–cutoff pair.
Limitations
The result concerns universal completeness of fixed descriptors, not generic structures or observed model failures. The authors report manual and code-assisted confirmation of examples, but a completed check of every general construction is undocumented.
Technical verification
The authors report manual and code-assisted confirmation of found examples and provide exact construction arguments, but the source does not state a completed end-to-end check of every arbitrary-order claim. Code use alone is not a machine proof certificate.
Independent checking
The authors report manual and code-assisted confirmation of found examples and provide exact construction arguments, but the source does not state a completed end-to-end check of every arbitrary-order claim. Code use alone is not a machine proof certificate.
- Checker
- Michelangelo Domina and Michele Ceriotti
- Scope
- Selected model-found descriptor-degenerate environments
- Basis
- Reported by the linked checker
Human understanding
The authors explain the common reflected-deck mechanism, the three-dimensional lifts, and the finite angular-cutoff selection rule for the assessed families.
Correction and publication history
Extends counterexamples to higher orders and every fixed finite order–cutoff pair.
Read this published revision