File size: 2,373 Bytes
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"release": "v1.0.0",
"external_sources": [
{
"id": "HKR2026",
"authors": "Harrell II, Kennedy, Ramos",
"title": "Bounds on eigenvalue ratios of quantum graph Laplacians",
"url": "https://arxiv.org/abs/2603.26172",
"role": [
"states the Dirichlet-tree Polya-type bound in the target setting",
"states the equality-characterization problem as open in the cited version",
"supplies/uses the generic perturbative nodal framework relied upon by the release"
],
"dependency_type": "external mathematical input"
},
{
"id": "BKKM2017",
"authors": "Berkolaiko, Kennedy, Kurasov, Mugnolo",
"title": "Edge connectivity and the spectral gap of combinatorial and quantum graphs",
"role": ["background spectral graph inequality machinery"],
"dependency_type": "literature background"
},
{
"id": "BKKS2019",
"authors": "Berkolaiko, Kennedy, Kurasov, Mugnolo",
"title": "Surgery principles for the spectral analysis of quantum graphs",
"role": ["metric-graph spectral surgery and comparison background"],
"dependency_type": "literature background"
},
{
"id": "BLS2019",
"authors": "Berkolaiko, Latushkin, Sukhtaiev",
"title": "Limits of quantum graph operators with shrinking edges",
"role": ["context for shrinking-edge operator limits; not required for the elementary branch-impedance proof"],
"dependency_type": "context only"
},
{
"id": "Friedlander2005",
"authors": "Friedlander",
"title": "Genericity of simple eigenvalues for a metric graph",
"role": ["generic spectral background"],
"dependency_type": "literature background"
},
{
"id": "Kurasov2024",
"authors": "Kurasov",
"title": "Spectral Geometry of Graphs",
"role": ["Dirichlet-tree and metric-graph spectral background, including diameter-type estimates"],
"dependency_type": "external mathematical input/background"
}
],
"methodological_provenance": {
"logical_dependency": false,
"note": "The author's transducer, defect-conservation, purity-rigidity, conductivity, and Hadamard research suggested proof architecture only; all required mathematics is proved independently in this release.",
"file": "METHODOLOGICAL_PROVENANCE.md"
}
}
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