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.
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.
We develop a claim-graded theory of quantum records and history measures from completely positive instruments. Class operators and Hilbert-valued event measures generate strongly positive decoherence functionals and a canonical history Hilbert space. In the declared linear-instrument class, event probabilities are affine in the state and additive in effects, hence have Born trace form; an independent physical exponent coordinate is incompatible with this structure. Outcome probabilities factor through effects, whereas conditional post-record states factor through complete CP operations. A single Stinespring dilation yields both the unconditional channel and the conditional states, so no second collapse map is required. In a gap-protected record parent, the fixed algebra retains outcome and CP-operation data while erasing implementation gauge, and its center supplies objective event propositions; nevertheless, deterministic unconditional CPTP evolution cannot select one pure central branch from a mixed central state while fixing all pure branches. Explicit jump–diffusion record dilations realize the same reduced dephasing semigroup with inequivalent path laws, proving that the reduced channel does not select a unique physical unravelling. Competing admissible information and work utilities likewise select inequivalent readouts. Bounded marked-Poisson parents, compensated interaction-picture measures, modularly damped Wick classes, and Boolean–Möbius/Borel-resummed local nets provide projective strongly positive histories in named finite and quasi-local classes. By contrast, global extensive event counts, positive-Poisson continuum uniformization, raw all-Fock absolute semivariation, and fixed final energy damping obey class-level No-Go theorems. The paper establishes no physical -flow, no unique unravelling, no universal utility, no deterministic collapse theorem, and no completed interacting relativistic QFT history measure.
This preprint studies operational equivalence and recovery in a twenty-dimensional residual system with a fixed four-sector representation of dimensions 8, 8, 2 and 2. It distinguishes what a declared observation algebra can detect, what a channel preserves, and what a retained classical record makes recoverable. Record-resolved criteria separate useful reversible-error records from unrelated labels and measured-sector records, even when the discarded channel is the same. For a specified coarse-record model, the work identifies exactly recoverable observable algebras and proves an optimal entanglement-fidelity expression on a fixed four-state orbit code. Preparation-aware recovery is then classified over all one-use isometric subspaces in the stated family. An explicit ten-dimensional marker code attains exact recovery under a specified stochastic record where the whole-sector support restriction permits only eight dimensions. Its encoding, nonbaseline marker measurement, and conditional inverse operations remain supplied resources. Scoped Lean evidence verifies the explicit arbitrary-complex-matrix recovery construction and related finite identities; it does not formalize the general complete-positivity/reference framework or optimal-dimension theorem. The recorded-error model is not derived from the companion exchange-timing model, and no protection of its long pulse sequence is claimed.
We derive a causal law of observer-indexed entropy retrieval: retrieved reference information grows toward the supply available to a finite observer. A recorded admission-and-readout instrument produces orthogonal operational sectors from arbitrary coherent radiation; exact diary fidelity and decoupling give the flagged family, while branch errors bound its approximate realization. An exact quantum transfer channel yields the remaining-gap law and its continuous Lindblad evolution. The channel has an explicit unitary collision realization: admitted reference information moves from radiation to memory, while the capture record remains diary-blind. Its memory marginal is the Choi state of an erasure channel, giving an intrinsic positive-coherent-information boundary at retrieved fraction r = 1/2. A strip-holomorphic modular speed limit bounds how rapidly the channel can activate, with the hyperbolic tangent selected uniquely at extremality. The integrated retrieval dose is invariant under a change of clock, making the Kerr lapse cancellation one geometric instance of a general result. At fixed supply and kinetic rate under an affine clock, the transfer and activation laws compose into a closed proper-time retrieval trajectory on the equality branch, identify that trajectory as the sharp fastest-retrieval envelope, and fix the earliest admissible retrieval horizon. In the continuum formulation, Araki relative entropy defines retrieval on restricted observable algebras, and a split Type-I factor provides the regulated density-operator representation. The experimental program follows the same causal sequence through retrospective analysis and staged intervention. Tier 0A determines whether archived analog-horizon data retain the shot-level, timing, protocol, and processing information needed to ask the retrieval question. Tier 0B then tests whether qualifying data contain observer-, protocol-, readout-, or analysis-operator-indexed correlation structure that standard pooling or filtering suppresses. A positive Tier 0B result identifies retrieval-relevant structure and motivates Tier 1; it does not by itself confirm the complete law. The prospective Tier 1 BEC program targets the held-out g²(t₁,t₂) surface, bandwidth scaling, and protocol dependence. Independent activation readout tests the modular bound and tanh rigidity. Reference-tagged supply and memory test cumulative dose, composite-hazard recovery, degraded-channel ordering, and two-memory allocation. The v2 verification artifact provides synthetic benchmarks and numerical consistency checks at bond dimensions D = 4 and D = 8 for the transfer law, inverse recovery, finite-resolution robustness, and matched adversarial alternatives. Standard RT/HRT geometry and a separate accessibility functional place the retrieval dynamics within holographic language. The retrieval law closes the observer-local path between global encoding and retained access. Information conservation, radiation encoding, causal collection, finite-observer retrieval, formal reconstruction, and comprehension are distinct physical operations. The black-hole information problem contains a proper-time access dynamics that global entropy accounting alone does not determine. Physical complexity enters through encoding, supply, clock, activation, transfer, retention, and observation. Those layers locate each source of retrieval failure instead of idealizing it away. The theory orders the encoding, supply, and retrieval clocks; distinguishes late supply from early supply through their overlap with future transfer dose; and gives an exact finite-lifetime retrieval criterion. Here rᵢ(τ) is the normalized reference information retained by observer i, eᵢ(τ) is the causally available supply, kᵢ(τ) is the composite access hazard, and τ_char is the characteristic activation scale.
Relational quantum causal processes formulate finite operational contexts as normal positive functionals on local completely positive maps. Response differences generate an influence algebra, and its central projections define jointly readable Boolean events. We develop this starting point through a sequence of exact and controlled models. Fresh-environment unitary collision circuits produce dephasing-exchange kinetics with an exact charge-center fixed algebra, a uniform finite-step limit at fixed response order, and graph-controlled metastable Markov dynamics. An absorbing-state model exhibits a sharp transition between non-Abelian quantum memory and Boolean records. A reversal-covariant defect dynamics generates a locally finite partial order on a restricted graph family without assuming a Lyapunov time. Conditional on a certified order, a positive additive record measure, compactness, and identifiability, we prove subsequential convergence to a Lorentzian metric-measure space, finite reconstruction bounds, and uniqueness of admissible smooth limits. Complementary finite regulators provide controlled tests of modular-to-boost response, null tomography, same-update variational identities, induced quadratic gravity, and compatible common-refinement limits. These results are exact or controlled within their stated models, but they do not yet constitute a single background-independent microscopic law that jointly generates adjacency, time, volume normalization, dimension, signature, nonlinear Einstein constraints, and quantum matter. We therefore present RQCP-QG as a theorem-indexed framework that separates established mechanisms, conditional compositions, and open assumptions.
This manuscript reframes a series of IBM superconducting-qubit experiments as a targeted validation study for the Directed Acyclic Graph Interpretation (DAGI), with emphasis on the operational distinction between \emph{record creation} and \emph{record erasure}, and on how that distinction manifests in different classes of observables. DAGI models quantum processes as a directed acyclic graph of informational events: branching is permitted only when an interaction produces a durable record at the relevant coarse-graining scale, while coherent erasure can restore interference by removing the distinguishing record. We consolidate three falsifier-friendly hypotheses: (H1) remote record activity need not produce a universal ``clock slowdown'' for arbitrary local probes; (H2) remote influence is expected to appear preferentially in observables supported by a relational/entangled substrate; and (H3) the record/eraser distinction should be directly visible in distributed witnesses under strictly pulse-matched controls. Using the C1 ``informational time dilation'' series as the local benchmark, and the T4 remote-closure suite as the nonlocal stress test, we report a split outcome: clock-side remote slowdown remains bounded and proxy-dominated in tested geometries, yet a GHZ-class distributed coherence witness exhibits a large, replicated record-creation (REC) versus reversible sham (SHAM) separation on both ibm_fez and ibm_marrakesh, and is strongly restored by coherent erasure (ERASE). We position this pattern as evidence for observable-selective remote sensitivity that is consistent with DAGI's record/eraser mechanism while remaining conservative about hardware backaction channels.
The Directed Acyclic Graph Interpretation (DAGI) represents physical processes as a single locally finite directed acyclic graph of informational states, records, and admissible updates. This note refines the meaning of ``branch'' inside that ontology. A branch is not an ontologically duplicated universe, an arbitrary subset of nodes, or a complete microscopic path. It is an \emph{observer-local causal accessibility sector}: the strict quotient of a record-conditioned causal cone by exact indistinguishability over the accessible record algebra of a specified observer or observable class. The local temporal asymmetry of a node is expressed without adding a stochastic primitive to the ontology: the resolved past is the set of persistent accessible records, while the unresolved future is the set of admissible record-candidates that may become persistent records along directed continuations. Interference is described as amplitude-level evaluation over histories that share the same persistent-record trace, where concurrent accessible records are retained as a partial order rather than forced into a linear word. A distinguishing record refines a coherent macro-node into subnodes; erasure coarsens the accessible record trace and can restore conditional interference classes. In strict graph language, nodes are coarse-grained informational states or events, edges are admissible update relations that change downstream reachability or distinguishability, and records are topologically persistent updates whose distinguishing descendants remain accessible beyond the local decorrelation scale. Charge, field, observer, branch, and connection are not additional ontological entities above the graph, but coarse-grained descriptions of stable subgraph structure and reusable edge-update rules. Causal-cone posets provide a natural computational representation of such accessibility sectors, while powerset decompositions remain useful but physically less structured baselines. The resulting branch ontology is concise: the global DAG contains the admissible informational structure; a local observer occupies a record-conditioned accessibility sector; persistent records refine that sector; admissible record-candidates define possible future refinements; erasure coarsens it; macro-nodes quotient inaccessible micro-variation; and physically meaningful posets are those that track causal accessibility rather than arbitrary set membership. Keywords: DAGI, causal cones, observer-local branching, causal accessibility, posets, quantum erasure, higher-order information, emergent spacetime, relational quantum mechanics, macro-nodes, charge-conditioned edge composition