Integrated Geometric and Quantum-Informational Portal Channels in the TEBAC 9D/9D+ Framework: Spectral Stability, Energy-Condition Audit, and Claim-Safe Quantum Transfer

This is a revised, expanded, and mathematically strengthened Zenodo version of the preprint on integrated geometric and quantum-informational portal channels in the TEBAC 9D/9D+ framework. The manuscript develops a claim-safe mathematical model of high-dimensional portal-channel geometry, spectral stability, and quantum-information transfer. It combines a generalized Morris--Thorne-type portal metric, shape-function analysis, weak/ null/ averaged energy-condition diagnostics, topological Chern-pairing structure, Dirac-type spectral stability, Fredholm and Birman--Schwinger determinant criteria, and finite-dimensional quantum-channel diagnostics. Compared with the original July 2025 version, this revised version substantially improves the mathematical organization, claim-safety, proof structure, figure provenance, and referee readability. The paper separates analytic theorems, numerical diagnostics, toy-channel simulations, conceptual schematics, and physical open problems. It does not claim an experimentally realized traversable wormhole or superluminal communication protocol. A central geometric object is the generalized portal metric\[ds²=-exp\!(2Φ(r))\,dt²+{dr²}{1-{b(r)}{r\,n-2}}+r²\,dΩₙ₋₁²,\]with power-law shape profile\[bα(r)=r₀\,n-2({r₀}{r})α.\] The revised version proves and records the precise distinction between geometric throat admissibility and energy-condition obstruction for this profile family. It also upgrades the quantum-information discussion from pure-state toy vectors to a claim-safe completely positive trace-preserving (CPTP) channel framework, with fidelity diagnostics interpreted as finite-dimensional model tests rather than physical evidence for an implemented portal. The manuscript also includes a methodological spectral-determinant bridge to the broader TEBAC 9D/9D+ programme, including the RH and BSD modules. This connection is structural and non-deductive: RH/BSD determinant methods are used only as part of the common TEBAC spectral-operator philosophy, not as physical inputs for portal construction or experimental claims. The work is intended as a public-release, referee-readable mathematical physics module within the broader TEBAC 9D/9D+ research programme.