Quantum / CONCEPT
Strong cospectrality does not satisfy the general multiplicity bound
The connected graph K_{2,3} has two pairwise strongly cospectral vertices and an adjacency eigenspace of dimension at least three, contradicting the proposed multiplicity bound.
Closed
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES0
PROOF DEPTH1
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A counterexample on five vertices
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
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RELATED KNOWLEDGE
Structural connections
- Connected nonnegative conductances on the original finite vertex setstructural-affinity · Closed
- Fixed resistance does not force an invariant Fiedler maximizerstructural-affinity · Closed
- Original tripartite conductances, trace compression and boundary rigiditystructural-affinity · Closed
- The complete graph maximizes the trace of the average mixing matrixstructural-affinity · Closed
- The discriminant clears average mixing denominatorsstructural-affinity · Closed
- The fixed-resistance optimizer on the full labelled K2m familystructural-affinity · Closed
- The sharp product and its two positive spectral raysstructural-affinity · Closed
- The star bound for the least-energy uniform overlap failsstructural-affinity · Closed
Documents & exposition
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