Combinatorics / CONCEPT
A bad Anderson potential without nontrivial shared symmetry
A potential on the eight-cycle has an eigenvector with a zero coordinate at every real coupling, while every matrix commuting with its Laplacian and potential is scalar. Thus no orthogonal shared symmetry other than I and -I exists.
Closed
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES1
PROOF DEPTH0
DOCUMENT LINKS1
The eight-cycle refutation
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
None recorded in this release.
Certified topology / DOWNSTREAM
Consequences
RELATED KNOWLEDGE
Structural connections
- Adjacent units from the actual defect geometrystructural-affinity · Closed
- Catalan Root and Lagrange Coefficient Transformstructural-affinity · Closed
- Cyclic tridiagonal determinants and transfer tracesstructural-affinity · Closed
- Diagonal units propagate around a cyclestructural-affinity · Closed
- PathCHSNormClosedFormstructural-affinity · Closed
- Power Traces from Trace and Determinant in Size Twostructural-affinity · Closed
- The actual defect family on a cyclestructural-affinity · Closed
- The binomial coefficient with an integer lower indexstructural-affinity · Closed
Documents & exposition
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
Loading release versions...
Browse the archiveCertified provenance