Finite Causal-Screen Holography: Boundary Capacity, Bulk Recovery, and Gluing Obstruction

Finite Causal-Screen Holography: Boundary Capacity, Bulk Recovery, and Gluing Obstruction introduces finite causal-screen holography as the first holographic bridge paper of the Finite Distinction Systems (FDS) program. The central claim is that holography should be understood first as a finite boundary recovery problem: a bulk distinction is physically accessible relative to a finite screen only when it can be encoded, maintained, and recovered through a boundary ledger with finite capacity, redundancy structure, recovery maps, and gluing consistency. The paper reframes standard holographic structures in finite-recovery terms. Holographic entropy is interpreted as a screen-capacity ledger; entanglement-wedge reconstruction is interpreted as finite boundary distinction recovery; and reconstruction failure is interpreted as capacity deficit, leakage, or gluing obstruction. Standard AdS/CFT and related asymptotic holographic structures are treated as sharp high-capacity model classes in which finite recovery deficits and gluing obstructions are idealized away or controlled. H1 defines the basic finite-screen objects needed for the H-series: finite screen ledgers, screen-relative bulk distinctions, task-relative recovery demand, finite recovery nets, exact and tolerant gluing criteria, recovery holonomy, and recovery-obstruction diagnostics. It proves finite recovery-net consistency results in both exact and tolerant forms, including a Lipschitz-controlled bound for error accumulation along recovery paths. It also gives a minimal matched-entropy / split-recovery proposition showing that local boundary entropy alone does not determine recoverability. The paper is deliberately scoped. It does not derive AdS/CFT, de Sitter holography, black-hole microstates, microscopic quantum gravity, the G1 residual branch, the M3/4 cosmological channel, the 3/4 Weyl projection, or rank-one horizon memory. Instead, it supplies the finite-screen recovery vocabulary and mathematical structure needed for later H-series work. H2 will test whether recovery obstruction projects to screen-response curl, while H3 will test whether restricted optical-screen recovery can constrain the M3/4 branch. In compressed form, the thesis is: holography is finite boundary distinction recovery under screen-capacity constraints.