We construct a supported local spacetime adaptation of the observation-boundary contract of VII-E and the finite hybrid-channel contract of VII-G. The two contracts are proved independently within one laboratory on I-B’s prescribed conical Lorentzian product. For the observation boundary, we prove the effect-pullback criterion, its reference-stable form, the exact sharp-measurement coherence criterion, and a qubit separation of trace distance 1/2 between ideal residual targets with identical records. For hybrid evolution, we prove a complete branch representation, history-sensitive observation closure, spectator consistency, and the exact recovery–constant-complement criterion. An informative classical record consequently excludes recovery of every unknown quantum input, even when the declared residual is also available. The additional contribution is an end-to-end finite observation package that keeps these distinctions visible in supplied spacetime. We provide a compactly supported 3+1-dimensional lift of a four-face transverse adjacency exchange, an exact guarded reversible encoding, and a separately constructed qubit instrument selecting strictly ordered slices without changing the conical metric. A two-step specialization has two histories with the same terminal slice but different conditional residuals. After coarse aggregation, the record remains unchanged while two complete residual targets have the exact half-diamond gap 4(1 − 1/√2)/25. An explicit residual audit enlarges the required input observation space from the diagonal algebra to the full qubit algebra. A destructive finite clock, complete-channel approximation bounds, and a causal route for both payload and classical control complete the local Grade S construction. The package may serve as a precise testbed for distinguishing record-level claims from instrument-level claims in geometric feedback models. The channel and recovery principles themselves are established finite-dimensional facts; the claimed contribution is their supported assembly and the explicit certificates and separations. No metric emergence, gravitational dynamics, field instrument, radiative coefficient, or quantum Ward identity is constructed.
We construct a supported local spacetime adaptation of the observation-boundary contract of VII-E and the finite hybrid-channel contract of VII-G. The two contracts are proved independently within one laboratory on I-B’s prescribed conical Lorentzian product. For the observation boundary, we prove the effect-pullback criterion, its reference-stable form, the exact sharp-measurement coherence criterion, and a qubit separation of trace distance 1/2 between ideal residual targets with identical records. For hybrid evolution, we prove a complete branch representation, history-sensitive observation closure, spectator consistency, and the exact recovery–constant-complement criterion. An informative classical record consequently excludes recovery of every unknown quantum input, even when the declared residual is also available. The additional contribution is an end-to-end finite observation package that keeps these distinctions visible in supplied spacetime. We provide a compactly supported 3+1-dimensional lift of a four-face transverse adjacency exchange, an exact guarded reversible encoding, and a separately constructed qubit instrument selecting strictly ordered slices without changing the conical metric. A two-step specialization has two histories with the same terminal slice but different conditional residuals. After coarse aggregation, the record remains unchanged while two complete residual targets have the exact half-diamond gap 4(1 − 1/√2)/25. An explicit residual audit enlarges the required input observation space from the diagonal algebra to the full qubit algebra. A destructive finite clock, complete-channel approximation bounds, and a causal route for both payload and classical control complete the local Grade S construction. The package may serve as a precise testbed for distinguishing record-level claims from instrument-level claims in geometric feedback models. The channel and recovery principles themselves are established finite-dimensional facts; the claimed contribution is their supported assembly and the explicit certificates and separations. No metric emergence, gravitational dynamics, field instrument, radiative coefficient, or quantum Ward identity is constructed.
We assemble the affine matching, variable-deficit cellulation, and guarded-flow programmes of series VIII into a self-contained local Grade S package on a prescribed conical spacetime. For a compact deficit interval about π/2, an explicit polyhedral graph family has uniformly spacelike regular faces, strict temporal ordering, and exactly one transverse three-to-six particle-link incidence. We give its vertices, finite lengths, areas, adapted Lorentz-affine charts, and winding-marked peripheral certificates. A guarded five-command history preserves complete matching outputs, and finite canonical restrictions admit exact NOT–CNOT–Toffoli implementations with retained histories and clean work. The main additional contribution is an operationally explicit assembly that keeps three otherwise easily conflated objects separate: a catalogue of prescribed conical geometries, a description-register update, and the fixed metric carrying the laboratory. A nonzero source-table replacement changes a catalogue entry, not the laboratory deficit. The source expectation is a semantic input; it is not acquired by the finite circuit. An affine-label obstruction and a finite-promise discrimination bound make that boundary quantitative. One destructive clock controls the complete recorded protocol. Its instrument identity includes arbitrary untouched references, and a regular laboratory supports exact transport of a quantum payload together with the complete classical certificate history, buffered across the prescribed incidence. Joint-output support is bounded by complete scheduled ancestry; a separately verified causal embedding gives physical containment. These combined certificates may provide a reproducible benchmark for testing future matter–geometry interfaces without confusing code correctness, source acquisition, or geometric consistency with gravitational dynamics. The novelty claimed is this supported assembly and its corrected interfaces, not the general principles of affine holonomy, reversible computation, channel locality, or measurement theory. No spacetime emergence, Einstein dynamics, continuum-field instrument, or inherited quantum response coefficient is constructed.
We prove an exact interface adaptation of three separately represented binary measurements to a prescribed conical spacetime. A finite consumed clock context produces a classical time code and Ramsey outcome while retaining the complete conditional matter state, including arbitrary untouched references. The adaptation preserves the positive record contrasts and exact interpolation-off controls of the three represented models. Spectral-mask convergence at fixed particle-number cutoff is strengthened to convergence of the complete recorded channels in diamond norm; initial-edge removal in the unbounded model instead gives pointwise trace-norm convergence, without an unsupported uniform channel-norm claim. A separate target-adapted SWAP construction transports finite payloads exactly along prescribed local null segments, with an explicit register ledger. Two corrections are essential. Local flatness of a cone does not identify its global field representation or Newton inverse with the corresponding Minkowski objects. We therefore state the flat-completion prescription explicitly and prove its local pullback identities, rather than claiming an intrinsic quantum field theory on the entire cone. Likewise, assigning a time to a global controlled unitary does not establish a compact causal implementation. The causal theorem applies to the certified finite transport and control network, not to an unconstructed local realization of the global field apparatus. The contribution is thus an exact, reference-stable Grade-S interface construction with a precisely delimited geometric interpretation. Its potential usefulness is methodological: represented signals, conditional residuals, regulator errors, geometric calibration, and physical implementation can be compared without identifying their distinct mathematical objects. No priority claim is made for the underlying measurement identities. Records do not determine the metric, lapse, or deficit angle. No spacetime-emergence theorem, Einstein dynamics, gravity-generated-entanglement test, inherited gravitational quantum coefficient, or finite-qubit compilation is asserted.
We give a self-contained local Grade S adaptation of VII-J’s finite-network causality programme to I-B’s prescribed 3+1-dimensional conical product. The metric, deficit π/2, causal relation, slicing family, preparations, and communication permissions are inputs. Complete timed dependency graphs, including classical controllers, measurements, records, encoders, and decoders, bound the Heisenberg support of every jointly observed output. A causal embedding then bounds reference-assisted intervention influence by the prescribed spacetime causal relation. The operational addition is an explicit regular-part realization through the parameter of VII-F’s transverse three-to-six incidence. Unlike the source apex-register benchmark, no quantum register, gate, or communication path meets the singular worldsheet. A destructive two-qubit clock controls finite event metadata; a buffered gather–operate–distribute protocol implements a nontrivial two-qubit exchange, preserves arbitrary retained reference correlations, and has a unit signalling witness on an allowed route. The complete recorded channel, positive durations, blank registers, controller storage, copied records, and finite instruction reserves are specified. Directional certificates retain both cycle-velocity polytopes and finite-time offsets. A finite potential inequality exposes transient directional costs that an asymptotic velocity inclusion can miss. Approximate simulation is treated separately: signalling changes by at most twice the half-diamond error, while a finite-volume Hamiltonian tail is reference-stable but not an exact Lorentzian cutoff. These assembled certificates may provide a useful reproducible benchmark for distinguishing logical simulation accuracy, operational influence, and elementary causal realizability. The novelty claimed is the supported assembly and regular-part correction, not the general principles of channel locality, periodic-graph velocities, or destructive measurement. No continuum-field simulation, spacetime emergence, Einstein dynamics, or inherited quantum response coefficient is constructed.
We distinguish complete unitary preservation, subsystem quantum recovery, destructive observation, and operational discard in a reference-preserving channel formulation. A finite acyclic typed fragment represents allocation, specified unitary transformations, destructive computational readout, and classical forgetting. Quantum recovery returns a quantum register; terminal readout returns a classical record and is a different task. For a complete isometry V from C to R tensor B, we give an explicit global recovery channel and prove that exact recovery from R is equivalent to constancy of the complete complementary channel to B. A process retaining only classical outcomes cannot reconstruct an arbitrary d-dimensional quantum code with half-diamond error below 1 − 1/d. Unobserved readout of B, followed by discarding its outcomes, is exactly partial trace over B and leaves the radiation channel unchanged. Its coherent dilation retains the information omitted from the classical interface. Independently, a finite-band quartic source–scalar-reservoir Hamiltonian is constructed and approximated by finite-dimensional proxies with explicit complete-channel allowances. Separate qubit dictionaries preserve the accessible–inaccessible partition. For a commuting four-Majorana control, the exact radiation recovery error is (3 − √(1 − c_R(t)²))/4, the residual recovery error is (1 − c_R(t))/2, and the complete residual leakage is the maximum of 1/2 and (1 + 2c_R(t))/4. Thus, the complete output is reversible although neither output alone need recover the diary. Access-preserving endpoint continuity and fixed-proxy recurrence are proved separately from syntactic termination. The gravitational implication remains conditional on a same-model unitary dilation, outgoing access construction, and constant endpoint residual. No positive noncommuting recovery window, physical field-to-memory receiver, quantum-gravity unitarity theorem, or gravitational evaporation endpoint is established.
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 formulate a contract-relative operational test for whether future-predictive quantum information lies in the post-processing capability of any admissible present description. For a declared present-access family and typed recovery policy, the present-completion deficiency is the diamond-norm distance between the predictive target and a contract-defined present-capability set. The underlying quantum channel deficiency and sufficiency mathematics is established prior art; the contribution is its use inside a path-sensitive black-hole reconstruction framework that separates coarse endpoint from rich present state, claim descent from witness descent, information insufficiency from failure of joint realizability, and local recovery from path monodromy. We prove access- and target-monotonicity under explicit typed closure conditions, give a pairwise distinguishability-gap lower bound, state a finite-dimensional attainment criterion for finitely many compact channel-type components, and derive the single/joint/virtual access hierarchy. The exact [[5,1,3]] perfect-code benchmark covers all ten three-retained and all ten two-retained access channels: every three-retained channel is exactly reversible, every two-retained channel is completely depolarizing with optimal diamond-norm deficiency 3/2 to the logical identity, and a Bell-projector discrimination certificate attains that lower bound. Two distinct three-retained erasure histories have the same coarse endpoint but different rich-present channels while both remain exactly recoverable, providing a direct null calibration of the endpoint split. The Bousso-Kaya-Lin-Shahbazi-Moghaddam finite-region family is retained as a coarse-data insufficiency benchmark, not yet as a no-present-completion theorem. The next black-hole-specific target is a certified positive fiberwise completion lower bound surviving operational quotienting, joint-realizability controls, and declared contract variations.