Can an autonomous quantum apparatus produce approximately Born-distributed outcomes and faithfully preserve its own earlier measurement label without assuming complete initial quantum equilibrium? This paper presents two finite autonomous Schrödinger–Bohmian constructions with explicit error bounds under restricted nonequilibrium initial laws. Each construction addresses three separate requirements: outcome calibration, copying the actual earlier configuration label, and retaining that label throughout a specified holding interval. The first model combines periodic focusing, a finite recoiling reference rotor, and a delayed compensated oscillator. Its record-distribution error is at most 0.004434840087, while failure to copy and retain its actual earlier label is at most 0.002327254798. The second model begins with a small radial Gaussian, includes autonomous preparation and activation, and incorporates the record writer from the original entrance. The joint law of its earlier label and complete symbolic holding record differs from an ideal constant Born-labelled record by less than 0.006086770113 in total variation. Its actual-label copy-and-hold failure probability is below 0.000552421956. The proofs combine bounded-variation calibration, exact recoil reduction, conditional-rank current estimates, finite-clock derivative bounds, and absolute probability-current estimates over the entire holding interval. The specialized derivations and coefficient calculations are included in the manuscript’s appendices. The two models retain distinct Hamiltonians and statistical assumptions. Neither establishes universal relaxation from arbitrary initial laws, supplies physical sources for every prescribed interaction, or demonstrates laboratory realization. External specialist verification remains open.
Can an autonomous quantum apparatus produce approximately Born-distributed outcomes and faithfully preserve its own earlier measurement label without assuming complete initial quantum equilibrium? This paper presents two finite autonomous Schrödinger–Bohmian constructions with explicit error bounds under restricted nonequilibrium initial laws. Each construction addresses three separate requirements: outcome calibration, copying the actual earlier configuration label, and retaining that label throughout a specified holding interval. The first model combines periodic focusing, a finite recoiling reference rotor, and a delayed compensated oscillator. Its record-distribution error is at most 0.004434840087, while failure to copy and retain its actual earlier label is at most 0.002327254798. The second model begins with a small radial Gaussian, includes autonomous preparation and activation, and incorporates the record writer from the original entrance. The joint law of its earlier label and complete symbolic holding record differs from an ideal constant Born-labelled record by less than 0.006086770113 in total variation. Its actual-label copy-and-hold failure probability is below 0.000552421956. The proofs combine bounded-variation calibration, exact recoil reduction, conditional-rank current estimates, finite-clock derivative bounds, and absolute probability-current estimates over the entire holding interval. The specialized derivations and coefficient calculations are included in the manuscript’s appendices. The two models retain distinct Hamiltonians and statistical assumptions. Neither establishes universal relaxation from arbitrary initial laws, supplies physical sources for every prescribed interaction, or demonstrates laboratory realization. External specialist verification remains open.
A measurement apparatus must do more than produce the correct final outcome frequencies: its records must faithfully preserve its own earlier declarations. This paper constructs autonomous quantum measurement chains that address both requirements within a specified nonrelativistic Schrödinger–Bohmian model. Assuming Bohmian guidance, complete initial quantum equilibrium, and a finite apparatus stock prepared independently of the unknown input, the manuscript gives a Hamiltonian bounded below that implements each fixed finite measurement programme to any prescribed positive tolerance. The complete model retains the source, pointers, internal clock, coherent resource products, copied archives, reset receivers, and an inaccessible quantum reference. Forced harmonic traps supply exact pointer motion. Retained orthogonal keys permit stationary record storage, while explicit copying and transfer preserve earlier records before working registers are reset. A finite-mass quantum clock replaces external time-dependent control. Weighted derivative estimates quantify its approximation error and bound the absolute probability current through archive decision surfaces. The resulting theorem separates final quantum-output accuracy from historical-record fidelity, including preservation throughout designated holding intervals. It retains coherent null outcomes and provides reproducible finite examples. Every positive tolerance uses finite resource choices for the fixed programme and observation horizon, although Gaussian packets retain unbounded tails. This is a conditional implementation and error-control result. It does not derive the initial Born law, uniquely determine Bohmian guidance, establish closeness of complete microscopic trajectories, or demonstrate laboratory realization of the admitted interactions.
Physical Sources, Finite Detectors, Persistent Records, and Actual Events This paper develops a unified account of quantum measurement under the Admissibility and Standing Constraint (AASC) framework, connecting constructed physical sources, quantum instruments, material amplification, finite record retention, event probabilities, and the actuality of measurement outcomes. The paper distinguishes three separate objects: a complete quantum instrument containing all outcome operations, including unresolved and failed outcomes; a material record carried by a physical system whose acquisition and retention can be analyzed; an actual history describing which occurrences belong to one original experimental run. A complete instrument and a persistent material record can be constructed without assuming that linear quantum dynamics alone selects one globally definite original-run history. Conversely, the admission of an actual event does not by itself determine its probability law or conditional quantum state. The physical construction contains two complementary measurement targets: a regulated interacting gauge–Higgs–fermion source with its full source Hamiltonian retained during finite receiver pulses; an explicitly parameterized six-mode cosine circuit with source and pump interfaces, losses, distinguishable outputs, a two-polarization intrinsic-spin receiver, and a finite energy-resolving thermal amplifier. The material-registration chain includes source-code loading, driven conversion, output registration, pump-displacement removal, transfer to an intrinsic material spin, finite Gibbs-collision amplification, endpoint reading, and quiet record retention. Electronic display labels, material flags, missed counts, dark displays, blanks, and unreadable outcomes remain distinct and are retained in the joint error ledger. The paper establishes: informative bounded receivers on an interacting quantum source; finite-pulse calibration with the complete source Hamiltonian retained; a complete monitored detector model; finite preparation and amplification bounds; coherent composition of instruments and records; adaptive record composition; local-instrument compatibility; calibrated affine probability uniqueness; sharp coherent calibration limits; sequential probability laws and compatible conditional states; explicit actual-history requirements. A finite Fourier residual certificate bounds the complete monitored detector instrument over its full 35.587ms interval by 0.063241 in restricted diamond norm. Exact interval arithmetic gives seeded amplifier endpoint fidelity greater than 0.9999235242 after 1,024 finite collisions, together with an explicit conditional survival bound for a subsequent 100ms quiet hold. The probability analysis shows that positivity, density-operator dependence, affinity under classical mixtures, and calibration fix the trace probability rule for the declared readout. Approximate sector calibration alone permits coherent deviations of order the square root of the calibration error; stronger linear bounds require additional structure. The paper’s central measurement-theoretic conclusion is deliberately separated from its successful detector construction. A complete instrument admits an exclusive-history completion, but linear quantum dynamics alone does not select one such history. Source-specific preparation, reader analysis, and a bounded counting-law completion supply the additional physical input required to select an actual history. The resulting framework substantially develops the material and probabilistic parts of quantum measurement while isolating apparatus errors, actual-history law, and event-selection assumptions as explicit obligations. The work does not claim to solve every interpretation of the measurement problem, derive a universal collapse law, establish unrestricted detector accuracy, or identify a finite calibration certificate with an experimental calibration. Principal contributions A unified source-to-detector account of quantum measurement. Constructed interacting quantum sources with finite receivers. Six-mode cosine-circuit detector realization. Material registration and finite amplification chain. Two-polarization intrinsic-spin receiver. Finite thermal collision and endpoint-reading model. Full-duration restricted diamond-norm detector bound. Interval-certified amplifier fidelity. Conditional quiet-hold survival bound. Retention of blanks, wrong, unreadable, and missed outcomes. Calibrated affine probability uniqueness. Sequential instruments and compatible conditional states. Explicit separation of complete instruments, material records, and actual histories. Source-specific conditions for actual-event selection. Complete physical error and assumption ledger.
This monograph develops the Shadow Theory quantum measurement programme through two distinct physical constitutions, connecting source dynamics to actual events, Born-rule measurement statistics, material records and subsequent measurements. The pilot-medium construction combines canonical current production, conservative packet export, independently prepared deterministic gas contacts, finite recombination and carrier-population tracking. Under its stated assumptions, the complete ordinary tagged path converges in total variation to the minimal Bell process in unchanged physical time. An autonomous finite-clock construction supplies faithful first-pass records, retained resources and noncommuting continuation. The separate massive-configuration construction adopts Bohmian guidance and complete initial quantum equilibrium. It supplies explicit material detectors, archives, reset operations and autonomous control, with separate bounds for retained outputs and historical record fidelity. The volume integrates proofs, counterexamples and the programme’s detector, preparation and protection results. It presents conditional internal completions within declared premises, rather than a derivation of those premises from source/readout incompleteness. The pilot result is a controlled effective limit; the massive result is a separate operational completion. This preprint is offered for independent scrutiny.
How can deterministic microscopic dynamics reproduce quantum jump histories, including their timing, while creating records faithful to actual earlier events? This paper constructs a conditional realization of the minimal Bell jump process using a deterministic hybrid model on a fixed finite configuration graph. The model combines a canonical complex field, conservative packet production, carrier–packet reactions, finite-rate recombination, and a finite spatial gas. Under explicit initial calibration and gas-independence assumptions, the ordinary-configuration path law converges in total variation to the Bell jump process without rescaling physical time. Quantitative estimates control the gas contact history, recombination error, and population tracking, including wavefunction nodes, current reversals, and zero-current intervals. An autonomous quantum clock carries a finite measurement circuit that retains fuel, loss channels, copied archives, reset receivers, feedback, and an inaccessible reference. At specified copying gates, the Bell path crosses the gate exactly once during the first pass. The archive therefore records its own actual earlier configuration and preserves that record under subsequent label-preserving operations. An explicit resource hierarchy provides an input-uniform polynomial convergence bound for a fixed engineered circuit. The theorem depends on the stated interaction catalogue and statistical preparation premises. It does not derive those premises, establish laboratory realization, or embed the complete hybrid dynamics in a single smooth material Hamiltonian. A supplementary smooth construction covers isolated contact modules.
This paper develops a semibounded material realization of a finite quantum measurement chain within a continuous-configuration theory. Its physical premises are spinor Schrödinger dynamics, Bohmian kinetic-momentum guidance and complete initial quantum equilibrium with a finite prepared resource stock. Smooth forced harmonic traps provide explicit pointer trajectories and crossing-time distributions. The construction retains pending excitation, loss products, fuel, reset receivers and inaccessible references. Physical archives, transported-trap reset and noncommuting continuation are incorporated into the same material inventory. A retained massive controller implements the programme autonomously. Weighted derivative estimates bound the complete retained-wave error, while absolute surface-current estimates separately control historical archive corruption. The closure theorem combines output, archive and pre-reset transfer errors. Explicit rival dynamics demonstrate that reliable records and Born-compatible endpoint statistics do not uniquely determine the underlying motion law. This is a separate constitutive completion, not a derivation of discrete Bell jumps. Guidance and initial equilibrium remain postulates, and the conclusions concern fixed finite programmes within the stated domain. This Version 2 preprint is a self-contained companion to the monograph and pilot-medium paper.
A durable quantum record, the location of its coherence, and a uniquely actual outcome are different physical questions. We study their separation in a supplied finite-dimensional quantum theory. An explicit, time-independent apparatus couples a system–detector encoding to a controller, a distinct archive, and a finite returning source. A conditional energy penalty suppresses release of the original record without deleting its return coupling. An invariant reduction and a one-sided spectral-gap estimate yield a certified interval with archive occupation above 0.98438, controller-latched occupation above 0.99161, and filled-but-unlatched weight below 2.402 × 10^-7 in one stated design. The same record statistics admit different source-label overlaps and hence different coherence on a specified retained boundary. A conserved product of complementary exchanges accesses that coherence when the finite source is included. Given a calibrated multiregister reader, its finite-duration response separates the coherent apparatus from an independently added archive-gated reduction law, with the added process left active during readout. A conservative example retains a response gap above 0.01717 after separately stipulated one-percent error allowances. The contribution is the finite construction and its quantitative retention, access, and readout interfaces. Quantum carriers, Hamiltonian couplings, trace readout, source preparation, and the reader are supplied; local reader synthesis, empirical calibration, absolute rate selection, and unique-event actualization are not established. Paper code: CFQR-P1 (Complementarity-First Quantum Records — Paper 1). The associated bundle contains the technical supplement, editable LaTeX, numerical checking programs and rational certificates, and selected Lean sources with returned build and axiom-audit evidence. The 39 supporting declarations are partially formalized; eleven recorded type excerpts contain printing elisions. This is not end-to-end formalization, external human peer review, an experimental detection of fundamental collapse, or a derivation of unique-event actualization. Author-owned manuscripts, documentation and mathematical data are CC BY 4.0; author-owned software is MIT, subject to the bundle’s licence map and third-party notices.