We formulate the proposed connection between quantum magic and matter-responsive geometry at a finite, already-prepared quantum carrier interface. The complete output is an isometry V from C to R tensor B, and residual response means that its complete complementary channel is not constant on the logical code. Exact recovery from R is equivalent to the absence of that response.The proposed unconditional implication from non-Clifford resources to residual response is false. We prove explicit counterexamples: a Clifford copying circuit has a nonconstant complement, whereas non-Clifford logical evolution—and even a fixed syndrome containing bipartite non-local magic—can coexist with a constant complement and exact logical recovery. We therefore separate magic, residual response, and physical geometric backreaction.For a specified controlled-rotation family, we construct a non-Clifford responding program and obtain the exact formulas: delta leak of theta equals sine theta divided by two, and epsilon rec R of theta equals one minus cosine theta, divided by two, for theta between zero and pi over two, inclusive. A general first-order residual-observable witness gives a quantitative sufficient condition for response under a declared deformation. A Pauli-compression criterion separately characterizes constant complements for Clifford encoders.Destructive Born–Lüders readout consumes measured quantum names and returns a classical interface. Readout-and-drop of an unobserved residual is exactly partial trace and does not further change the radiation channel. The four-Majorana recovery obstruction, finite-channel certificates, access-preserving endpoint continuity, and finite-proxy recurrence are retained with their proper scope. No metric, field-to-memory receiver, admitted analytic quantum coefficient, or gravitational backreaction theorem is constructed.
We formulate the proposed connection between quantum magic and matter-responsive geometry at a finite, already-prepared quantum carrier interface. The complete output is an isometry V from C to R tensor B, and residual response means that its complete complementary channel is not constant on the logical code. Exact recovery from R is equivalent to the absence of that response.The proposed unconditional implication from non-Clifford resources to residual response is false. We prove explicit counterexamples: a Clifford copying circuit has a nonconstant complement, whereas non-Clifford logical evolution—and even a fixed syndrome containing bipartite non-local magic—can coexist with a constant complement and exact logical recovery. We therefore separate magic, residual response, and physical geometric backreaction.For a specified controlled-rotation family, we construct a non-Clifford responding program and obtain the exact formulas: delta leak of theta equals sine theta divided by two, and epsilon rec R of theta equals one minus cosine theta, divided by two, for theta between zero and pi over two, inclusive. A general first-order residual-observable witness gives a quantitative sufficient condition for response under a declared deformation. A Pauli-compression criterion separately characterizes constant complements for Clifford encoders.Destructive Born–Lüders readout consumes measured quantum names and returns a classical interface. Readout-and-drop of an unobserved residual is exactly partial trace and does not further change the radiation channel. The four-Majorana recovery obstruction, finite-channel certificates, access-preserving endpoint continuity, and finite-proxy recurrence are retained with their proper scope. No metric, field-to-memory receiver, admitted analytic quantum coefficient, or gravitational backreaction theorem 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.
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 develop the “shredder” analogy as a precise distinction between destructive classical readout and coherent quantum return. The underlying Enter interface consumes measured quantum names, retains every declared residual and failure, and returns finite classical words or stochastic symbols. Its principal quantitative consequence is uniform in the length and precision of any finite classical transcript: if the complete accessible output of an unknown d-dimensional code is classical, every deterministic decoder has reference-preserving half-diamond error at least 1 − 1/d. The constant is sharp, and a complete implementation allowance δ weakens it by at most δ. The distinct Haar-average state-estimation infidelity bound is (d − 1)/(d + 1). On a prescribed conical product, an explicitly declared scalar Friedrichs kernel supplies image arrivals and an apex-diffracted echo functional. Image-isolated windows distinguish prescribed deficits, and sufficiently short nonzero windows are injective on compact non-shadow sectors. These informative classical laws do not constitute quantum-return decoders. For neutral smooth cores, strong-resolvent convergence gives finite-precision indistinguishability of fixed smeared reports, not non-injectivity of finitely many exact real functionals. The horizon and quantum-computer comparisons are developed as analogies that make the recovery obstruction, echo functional, and conditional thermal balance quantitative. Append-only transcript entropy is monotone, whereas quantum radiation entropy is a different object. A finite thermal-reservoir identity replaces an unconditional positive-heat claim; readout alone determines neither heating nor an explosion. Explicit terminal continuations establish endpoint underdetermination. The contribution is an integrated, error-controlled account of how records can reveal geometry without restoring an arbitrary unknown quantum code. Established entanglement-breaking and thermodynamic principles are attributed rather than claimed as new. The analogy does not identify the cone apex with a horizon or Hawking radiation with a classical register. No Page curve, evaporation dynamics, physical spin-2 Hessian, Einstein source law, or spacetime emergence is constructed.
We develop the “shredder” analogy as a precise distinction between destructive classical readout and coherent quantum return. The underlying Enter interface consumes measured quantum names, retains every declared residual and failure, and returns finite classical words or stochastic symbols. Its principal quantitative consequence is uniform in the length and precision of any finite classical transcript: if the complete accessible output of an unknown d-dimensional code is classical, every deterministic decoder has reference-preserving half-diamond error at least 1 − 1/d. The constant is sharp, and a complete implementation allowance δ weakens it by at most δ. The distinct Haar-average state-estimation infidelity bound is (d − 1)/(d + 1). On a prescribed conical product, an explicitly declared scalar Friedrichs kernel supplies image arrivals and an apex-diffracted echo functional. Image-isolated windows distinguish prescribed deficits, and sufficiently short nonzero windows are injective on compact non-shadow sectors. These informative classical laws do not constitute quantum-return decoders. For neutral smooth cores, strong-resolvent convergence gives finite-precision indistinguishability of fixed smeared reports, not non-injectivity of finitely many exact real functionals. The horizon and quantum-computer comparisons are developed as analogies that make the recovery obstruction, echo functional, and conditional thermal balance quantitative. Append-only transcript entropy is monotone, whereas quantum radiation entropy is a different object. A finite thermal-reservoir identity replaces an unconditional positive-heat claim; readout alone determines neither heating nor an explosion. Explicit terminal continuations establish endpoint underdetermination. The contribution is an integrated, error-controlled account of how records can reveal geometry without restoring an arbitrary unknown quantum code. Established entanglement-breaking and thermodynamic principles are attributed rather than claimed as new. The analogy does not identify the cone apex with a horizon or Hawking radiation with a classical register. No Page curve, evaporation dynamics, physical spin-2 Hessian, Einstein source law, or spacetime emergence 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 study a four-qubit product-EPR holographic code whose reconstructing region contains matter and one leg of a geometry bond. Seven deformations compare local, bipartite, bond-stabilizing, and bond-moving operators. Exact spectra show that only matter-controlled bond motion produces a leading quadratic logical-state dependence of the boundary entropy. We select one state-independent physical recovery by optimizing coherent information of the channel Choi state. A separate semidefinite program maximizes entanglement fidelity over all channels. At fixed coupling the physical recovery attains that optimum to numerical precision, while recovered-entropy subtraction leaves a nonzero variational proto-area response. Total stabilizer Renyi magic is also nonzero for deformations with no boundary response, so it does not characterize the effect. Projecting the exact stabilizer-Renyi quadratic form away from pairwise Pauli tangents defines a leading-order boundary witness. Its global convex minimum is positive for the bond-moving deformation and zero for the six comparisons. For the reference-matter-geometry resource partition, however, pairwise tangents span the full projective tangent space at the product-EPR base, so the witness vanishes for every Hermitian deformation. A two-bound extension retains this degeneracy but exhibits a split-geometry structural residual and a logical-state-dependent cut switch. These results establish a finite-code witness, not a universal magic law or continuum gravitational dynamics.