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| Format: | Recurso digital |
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Zenodo
2026
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| Online Access: | https://doi.org/10.5281/zenodo.19508605 |
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Table of Contents:
- <div>Quantum graphs provide one of the clearest settings in which geometry, operator structure,</div> <div>boundary coupling, spectral response, and inverse reconstruction are inseparably linked. In</div> <div>this paper, we propose that recent developments in inverse stability, M-function methods,</div> <div>isospectral/isoscattering constructions, and Dirac-type graph operators can be reorganized</div> <div>into a PAC–µ 8 framework of stable inverse certificates. Our central claim is that a quantum</div> <div>graph is not determined by its bulk operator alone, but by the triple</div> <div>(KΓ, BΓ, Πedge),</div> <div>where KΓ is the graph operator, BΓ the vertex protocol layer, and Πedge the boundary-access</div> <div>projector specifying which sectors are interrogated. The relevant PAC–µ 8 chain is</div> <div>Γ → (KΓ, BΓ, Πedge) → DΓ → CΓ,</div> <div>where DΓ denotes a boundary-visible data package assembled from spectral, Weyl/M</div> <div>function, and scattering witnesses, and CΓ is the resulting inverse certificate. We argue</div> <div>that stable inverse recovery results support a rigorous certificate language, while isospectral</div> <div>and isoscattering constructions show that no single witness channel is universally complete.</div> <div>This leads naturally to a PAC–µ 8 doctrine of concordance: strong reconstruction requires</div> <div>agreement among heterogeneous boundary-visible witness families. We further propose</div> <div>that recent Dirac-type quantum graph results indicate a natural lifting from second-order</div> <div>boundary-certified spectral networks to first-order interface-certified graph systems. The</div> <div>paper is conceptual and programmatic rather than theorem-proving. Its goal is to provide a</div> <div>theorem-level research template for inverse certification on quantum graphs within PAC–µ 8 .</div>