We introduce a finite-dimensional coherent-sector (CS) framework in which ordinary quantum degrees of freedom are supplemented by affiliation and retained-record labels. The construction explores whether measurement-like branching can be modeled phenomenologically as dynamics on an enlarged state space, rather than imposed only through an external state-update rule. In the strict limiting version of the minimal model studied here, coherent exchange terms act within a common CS, while inter-CS couplings are represented by record-producing channels. We formulate the framework for a two-degree, two-level system. The one-CS model reproduces ordinary coherent exchange, whereas the two-CS model leads to affiliation-changing dynamics governed by finite-dimensional Markov channels. In the first-record approximation, probability is transferred from an initial no-record class into branch classes. In the ongoing-affiliation model, the coarse-grained affiliation probabilities obey a closed master equation. The strict limiting model also predicts a direct Stage-1 signature: an initially mixed-affiliation pair need not exhibit immediate coherent Rabi exchange, because coherent exchange begins only after affiliation-changing transitions produce same-CS branches. We then formulate a two-stage affiliation-memory diagnostic in which, after a Stage-1 inter-CS interaction, the ordinary pre-probe state is prepared, verified, or post-selected before a Stage-2 coherence probe. Standard quantum mechanics predicts the Stage-2 coherent response to depend only on this ordinary pre-probe state, whereas the CS model predicts an additional dependence through the pre-probe conditioned CS-affiliation distribution generated during Stage 1. The construction is developed as a minimal finite-dimensional framework for deriving experimentally testable, model-conditional consequences of CS-affiliation dynamics. This manuscript is a preprint and has not undergone peer review.
We introduce a finite-dimensional coherent-sector (CS) framework in which ordinary quantum degrees of freedom are supplemented by affiliation and retained-record labels. The construction explores whether measurement-like branching can be modeled phenomenologically as dynamics on an enlarged state space, rather than imposed only through an external state-update rule. In the strict limiting version of the minimal model studied here, coherent exchange terms act within a common CS, while inter-CS couplings are represented by record-producing channels. We formulate the framework for a two-degree, two-level system. The one-CS model reproduces ordinary coherent exchange, whereas the two-CS model leads to affiliation-changing dynamics governed by finite-dimensional Markov channels. In the first-record approximation, probability is transferred from an initial no-record class into branch classes. In the ongoing-affiliation model, the coarse-grained affiliation probabilities obey a closed master equation. The strict limiting model also predicts a direct Stage-1 signature: an initially mixed-affiliation pair need not exhibit immediate coherent Rabi exchange, because coherent exchange begins only after affiliation-changing transitions produce same-CS branches. We then formulate a two-stage affiliation-memory diagnostic in which, after a Stage-1 inter-CS interaction, the ordinary pre-probe state is prepared, verified, or post-selected before a Stage-2 coherence probe. Standard quantum mechanics predicts the Stage-2 coherent response to depend only on this ordinary pre-probe state, whereas the CS model predicts an additional dependence through the pre-probe conditioned CS-affiliation distribution generated during Stage 1. The construction is developed as a minimal finite-dimensional framework for deriving experimentally testable, model-conditional consequences of CS-affiliation dynamics. This manuscript is a preprint and has not undergone peer review.
This work investigates which outcome-like behaviors can arise in closed, momentum-accounted quantum models before any additional irreversible state-selection mechanism is introduced. A hierarchy of conservative controls is developed using a finite-mass beam splitter, explicit record degrees of freedom, conditioned and unconditioned branch histories, nonlinear two-mode many-body dynamics, many-mode record sectors, and recoil-dependent visibility and distinguishability. The analysis shows that several behaviors commonly associated with measurement-like dynamics can be reproduced within the closed models considered here. A finite-mass splitter supports explicit entanglement between recoil and field apparatus while preserving the total momentum ledger. Record formation suppresses reduced-state coherence and produces strongly branch-polarized conditioned histories, while the unconditioned state retains both alternatives. A separate many-body status analysis shows that collective nonlinear dynamics can generate genuine self-trapping and long-lived population imbalance, while the interaction studied becomes branch-independent in the single-excitation sector through Jz2 = I/4. Increasing record complexity can also strongly suppress finite-window recoherence through effective spectral participation and phase structure without introducing nonunitary dynamics. Finally, the finite apparatus degree of freedom that carries recoil is connected directly to branch-state overlap, interference visibility, and optimal path distinguishability, providing a common quantitative description of momentum exchange and which-path information. The results do not constitute a solution to the quantum measurement problem, a derivation of a unique measurement outcome or the Born rule, or a no-go theorem for modified quantum dynamics. Rather, they establish a reproducible control hierarchy: outcome-like behavior should first be tested against closed standard models capable of reproducing the same observable signature before it is interpreted as evidence for an additional irreversible state-selection mechanism. Data and reproducibility: Numerical data, source code, diagnostic outputs, and publication figures supporting the computational controls are available in the associated Zenodo reproducibility archive.
When initially disjoint observers later consult physical records, under what specified conditions should their readouts agree? This paper gives a sufficient, access-relative certification within standard quantum mechanics. This certification requires stable, repeatably readable labels, low accessible sensitivity to coherence between the corresponding outcome sectors, and, for distributed consultation, carriers encoding a common label. Sequential nondemolition readouts of a single carrier with orthonormal record labels produce memory registers whose product record-basis outcomes match with Born probability one, independently of coherence in the carrier. For disjoint carriers, if their accessible joint state is close in trace distance to the corresponding marginal of an ideal spectrum broadcast structure, disagreement is bounded by that distance and by the two local discrimination errors. In a two-outcome model, the relevant coherence belongs to the branch-bearing system-record state rather than the record-only marginal; defining dephasing and off-diagonal observables on that same space yields an interference bound. These results concern record statistics, not interpretation-neutral identity of first-person experiences or observer-independent reality. Applied to Extended Wigner’s Friend scenarios, they support ideal ask-the-friend agreement. That fixed-setting equality supplies neither the setting-indexed joint model required by Absoluteness of Observed Events in Local Friendliness nor Brukner’s common Boolean representation, and it does not entail Frauchiger and Renner’s distinct quantum certainty, inter-agent-consistency, and single-valuedness assumptions. The no-go results remain valid conditional consequences of those premises.
Abstract This study formulates a deterministic finite memory extension of classical Newtonian mechanics in which every interaction is evaluated strictly from realized past history over explicit memory horizons. Within this past only causal structure, we show that two familiar phenomenological organizations can emerge from one unified law on internally certified coherent segments, quantum type behavior in push pull interaction channels and relativistic type bookkeeping in attraction only specializations. In the quantum type regime, a structured comparison of past anchored interaction imprints across a nonzero coherence horizon together with an inertial memory horizon produces a reproducible two scale phase organization under repeated deterministic preparations. From these preparation ensembles we construct a complex spatial wavefield and a minimal rotation invariant quadratic intensity as derived diagnostics, while enforcing a strict audit boundary that prevents any ensemble based construction from entering force evaluation. Numerical experiments exhibit robust interference like hit density fringes in a double slit geometry and tunneling like under barrier transmission trends with systematic dependence on barrier shape. In the relativistic type regime, attraction only inward transport consumption on coherent increments yields operational time dilation and an emergent quadratic invariant remainder, and Lorentz type symmetry appears as a derived consequence of this invariance rather than an imposed spacetime axiom. Coherence and closure conditions serve as regime selection and remainder control devices, enabling controlled extraction of Kepler range reductions and secular drift while predicting failure modes when coherence breaks. Overall, the framework supplies explicit causal content for both quantum like and relativistic like phenomena within one strictly past only finite memory mechanics.
A classical record can survive a quantum event, be read without demolition, and change later quantum dynamics. This work gives, under the displayed premises for each stage, a self-contained finite proof of the constructive chain from the first informative bit through one-, two-, and three-dimensional formation to an accessible 24-address classical fact, durable quantum-nondemolition record, operational clocks, and record-controlled quantum dynamics. The conjunction of finite formation, readable memory, native and noncommuting control, and a closed conditional regional solution is established here. The bridge maps are mathematically distinct, but their physical composition is conditional on those stage premises—including the adopted formation allocation and regional composition inputs—and on the parent event firing; the regional continuation uses the preserved completion statistic rather than the full fine address/facet record. An exact seven-branch Kraus intertwiner covers coherent inputs across 16,807 five-event histories, six physical lineages, and the complete no-event complement. The retained fine record controls a native repeat/comparison channel with hit probability eleven twenty-fifths, nonzero mutual information, and exact source-address independence, plus a noncommuting three-qubit response. A persistent occurrence projector autonomously enables a later instrument while preserving all admitted archive blocks. Worked continuations include an eight-write resource cycle, a record-preserving 16-cell consumer, and exact predictive compression. The conditional Fast-Time/Timescape continuation supplies an exact clock map, a closed scalar Buchert solution, an infinite connected shell-free Darmois collar family, and a positive-energy LRS completion family. Its approximately 88.2718196824 percent Hubble mismatch is a dependency-separated conditional kinematic diagnostic using an explicitly adopted measured matter fraction and derived radiation fiducial, with no dataset split or fitted parameter. It is not, by itself, an independent observational validation. No historical first claim or exhaustive classification is asserted; within the regional continuation, unique physical-member and optical-law selection remains open. Within those boundaries, the constructions establish a full-history bridge from the first distinction to durable fact, operational time, later quantum control, and an explicit closed conditional regional continuation.
**Version v0.5 — Journal-Polish Update** This manuscript develops a conservative extension framework for Schrödinger dynamics in which an observed quantum system is embedded into an enlarged Hilbert space equipped with an auxiliary clock-information fiber. The fiber is not introduced as a macroscopic hidden spatial dimension, nor as a local hidden-variable register. Instead, it is treated as a quantum auxiliary sector carrying phase memory, clock/reference correlations, and correlation records that may appear as information loss or dephasing after partial tracing. The central contribution of this version is a residual-identifiability framework. Rather than claiming that unitary dilation itself is new, the paper asks whether a calibrated observed system can exhibit structured residuals after independent-bath subtraction and common-bath controls. The main diagnostic object is a log-residual statistic, Rχ(t;σref)=logCobs(t;σref)−logCind(t;σref), together with reference-covariance indices such as Iχ(t;σref)=∂σrefRχ(t;σref), and covariance/correlation-based diagnostics over controlled reference settings. The framework emphasizes that a nonzero residual alone is not sufficient evidence for an admissible clock-information fiber. A candidate residual must be non-factorizing, reproducible, reference-covariant, and not absorbed by independent local bath models, common classical noise, or generic common quantum bath controls. In particular, the admissible-fiber hypothesis is treated as a residual diagnostic condition, not as a proof of a new hidden variable, superluminal channel, or macroscopic extra dimension. The paper proves the elementary consistency statements for the enlarged dynamics: total unitarity under a self-adjoint total Hamiltonian, total energy conservation for time-independent generators, subsystem entropy growth under partial trace, and no-signalling compatibility under local trace-preserving operations. It also presents minimal toy models for phase-memory dephasing, shared-fiber cross-kernels, compact protected fiber sectors, and synthetic residual-fitting demonstrations. The synthetic fitting layer uses a representative model of the form $$C_{\rm obs}(t;\sigma_{\rm ref})=C_{\rm ind}(t)\exp[-a(\sigma_{\rm ref})t^2],\qquada(\sigma_{\rm ref})=a_0+a_1\sigma_{\rm ref}^2,$$ so that Rχ(t;σref)=−a(σref)t2. This example is intended as an identifiability demonstration: after calibrated independent-bath subtraction, a candidate clock-information fiber signature should appear as a reproducible residual with controlled reference covariance, rather than as an arbitrary fitting term. The experimental outlook focuses on Ramsey/spin-echo baselines, dynamical-decoupling response, superconducting qubit and Josephson platforms, tunneling phase-delay diagnostics, and reference-modulation protocols. The manuscript also formulates a common-bath control envelope, ∣Rχ(t;σref)−Rctrl(t;σref)∣≤δR(t;σref), to express the requirement that a proposed fiber residual should not be absorbed by generic common-bath control models within statistical uncertainty. ### Main updates in v0.5 - Shortened journal-style title and abstract.- Removal of version-history language from the abstract.- Strengthened common-bath control criterion.- Addition of a formal common-bath control envelope.- Improved diagnostic separation between independent local baths, common classical noise, generic common quantum baths, and admissible clock-information fibers.- Algorithm-style synthetic residual-identifiability test.- Synthetic residual-fitting demonstration using reference-covariant dephasing.- Improved table formatting and manuscript presentation for journal-style readability. ### Scope and non-claims This work should be read as a structured framework for residual diagnostics in extended Schrödinger dynamics. It is not a hidden-variable theory, not a superluminal-signalling model, not a derivation of measurement collapse, and not a completed microscopic theory of mass, charge, or quantum gravity.
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.