This paper develops a finite-dimensional record-algebraic account of decoherence, erasure, boundary records, threshold recovery, islands, entropy ledgers, and modular flow on causal posets. Record creation correlates histories with marker degrees of freedom, and ignoring those markers implements a completely positive trace-preserving dephasing channel. In a fixed history basis the channel is a Schur product, rho -> G ∘ rho, where G is the Gram matrix of marker overlaps. The paper packages this mechanism in causal-poset language: history bases are defined from chains or admissible paths; observer record algebras define branch quotients; conditional eraser instruments restore off-diagonal terms in selected sectors; and boundary record algebras yield observer-indexed coherence kernels. The manuscript treats horizon, Page-time, island, replica, and modular-flow terminology as a conditional dictionary built on finite theorem statements plus explicit continuum or code-subspace assumptions. It includes a claim-proof ledger, a continuum-assumption register, and toy-model or experiment proposals including a two-history MARK/ERASE circuit, a tunable boundary-kernel model, a three-fragment threshold-recovery ledger, and a modular-covariance recovery test. The paper is part of the DAGI observer-theory/foundations track and is version DAGI-OBS-REC-001 v0.3.
Petr Sramek (Tue,) studied this question.