Recoverable-Support Geometry and Response Visibility: Descent, Holonomy Intertwiners, and the Premetric G1 Handoff

Finite causal-screen holography treats a bulk distinction as physically accessible relative to a finite screen only when boundary data support its recovery at a declared capacity, tolerance, and verification window. FDS–H1 introduced finite screen ledgers, regional recovery maps, overlap intertwiners, tolerant gluing, and recovery holonomy. H2 asks when that finite recovery structure can support a separately registered response obstruction. The paper distinguishes raw regional descent, quotient descent and liftability, mixed gluing– transport compatibility, and local connection curvature. Its principal geometric realization is a relative Kato connection on a smooth constant-rank recoverable-support bundle inside a registered ambient Hermitian bundle. This construction is deliberately support-limited: equal support projectors imply equal Kato connections and curvatures even when channel spectra, probabilities, fidelities, or actions differ. The response side is split into two independent bridge branches. In the operational-covector branch, a directly registered G1 response one-form ωth is related to physical recovery curvature by a pre-registered parallel functional, dωth = ℓ(Fphys), and is tested by Stokes-type loop–surface comparisons. A global covector bridge additionally requires the de Rham class [ℓ(Fphys)]dR to vanish. In the response-bundle branch, an independently registered response connection is related to recovery geometry by a parallel bundle morphism; existence is equivalent to holonomy intertwining at a base point. These branches have different data, global obstructions, approximation errors, and validation protocols. Character-based one-dimensional responses see only the Lie-algebra Abelianization of the identity component, whereas general parallel covector readouts obey a weaker holonomy-relative visibility bound. Discrete characters may additionally detect global flat monodromy. A three-qutrit calculation is retained only as a code-seeded candidate-support audit: the correctability-preserving control is flat, while the tested nonzero-support-curvature deformation fails the Knill–Laflamme criterion and is ineligible for physical-quotient analysis. H2 therefore establishes a formal recoverable-support bridge architecture, branch-specific existence criteria, visibility limits, and validation protocols. It does not yet provide a completed nontrivial physical bridge, a full recovery-channel geometry, a curved QEC realization, general relativity, the G1 residual tensor, or the M3/4 branch.