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Finite-time branch-record accumulation in one-dimensional baths: independent baselines, amplification, and nonredundant records

Samuele Garbati

Published Jun 12, 2026• 0 citations
Publisher

Abstract

This record contains the preprint, supplemental material, source files, figures, and numerical data archive for the manuscript “Finite-time branch-record accumulation in one-dimensional baths: independent baselines, amplification, and nonredundant records”. Quantum Darwinism diagnoses objectivity through a redundancy plateau: many small, disjoint environment fragments independently reveal the same branch information. This manuscript studies finite-time branch-record accumulation in one-dimensional baths and separates the magnitude of the environmental record from the normalized shape with which that record is accessed locally. For weak uniform deposition, matched field-only controls with J_X = 0 remain close to the analytic independent-site accumulation law, while the interacting bath increases the total environmental branch distinguishability. In a five-point matched scan at t = 3.6 and g_X = 0.8, 0.9, 1.0, 1.1, 1.2, the interacting denominator is larger than the corresponding field-only denominator by factors 2.56–3.00. At the critical point, D_E = 0.266513 instead of 0.090818, corresponding to a 2.93-fold increase in trace-distance amplitude and an 8.90-fold increase in the effective per-site signal. After matching the independent null to the interacting value of D_E, the normalized fragment profile remains close to independent accumulation: bulk windows lie slightly above the homogeneous null while edge-attached windows lie below it. A solvable free-fermion benchmark with a local branch perturbation shows a complementary geometry: the record is locally detectable near the perturbation but is not broadcast to distant small fragments. The result is not a universal failure of Darwinism and not strong data hiding. It is a finite-time classification of independent accumulation, interaction-driven magnitude amplification, small geometry-dependent shape deviations, and local nonredundant records.

DOI
10.5281/zenodo.20662375

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This record contains the preprint, supplemental material, source files, figures, and numerical data archive for the manuscript “Finite-time branch-record accumulation in one-dimensional baths: independent baselines, amplification, and nonredundant records”. Quantum Darwinism diagnoses objectivity through a redundancy plateau: many small, disjoint environment fragments independently reveal the same branch information. This manuscript studies finite-time branch-record accumulation in one-dimensional baths and separates the magnitude of the environmental record from the normalized shape with which that record is accessed locally. For weak uniform deposition, matched field-only controls with J_X = 0 remain close to the analytic independent-site accumulation law, while the interacting bath increases the total environmental branch distinguishability. In a five-point matched scan at t = 3.6 and g_X = 0.8, 0.9, 1.0, 1.1, 1.2, the interacting denominator is larger than the corresponding field-only denominator by factors 2.56–3.00. At the critical point, D_E = 0.266513 instead of 0.090818, corresponding to a 2.93-fold increase in trace-distance amplitude and an 8.90-fold increase in the effective per-site signal. After matching the independent null to the interacting value of D_E, the normalized fragment profile remains close to independent accumulation: bulk windows lie slightly above the homogeneous null while edge-attached windows lie below it. A solvable free-fermion benchmark with a local branch perturbation shows a complementary geometry: the record is locally detectable near the perturbation but is not broadcast to distant small fragments. The result is not a universal failure of Darwinism and not strong data hiding. It is a finite-time classification of independent accumulation, interaction-driven magnitude amplification, small geometry-dependent shape deviations, and local nonredundant records.
Quantum Darwinism explains objective information through redundant environmental records. Earlier work established that imperfect records can be amplified and that environment self-evolution can enhance or suppress their formation. We investigate how preparation, interaction angle, and field disorder combine in an imperfect-CNOT model with random Gaussian couplings and pure, noninteracting environment qubits. We find that, without fields, a single alignment parameter ΛΛΛ determines the preparation and interaction-angle dependence of conditional-state distinguishability. Increasing interaction imperfection or local field strength can improve or suppress recording. We explain this nonmonotonic response through the geometry of conditional branch separation. For the pure initial environments considered here, the ZZZ basis remains optimal for Holevo information, so field-assisted recording requires no change of the recorded system observable. Comparing uniform local field strengths with Gaussian-distributed strengths at equal root-mean-square strength shows how disorder broadens both beneficial and detrimental field effects. Exact expressions for fragment information and numerical simulations with up to 24 environment qubits quantify the distinction between high mean information and reliable records across fragments and throughout a finite observation window. These results connect the geometry of local information acquisition to the fragment sizes needed for robust recording. The branch-distinguishability analysis itself requires only the conditional evolution of each environment qubit and extends to other interactions that preserve a system pointer basis.
What does a rising redundancy curve actually prove? This deposit accompanies “Raw-Fragment Benchmarking for Redundancy Tests in Quantum Darwinism and Spectrum Broadcast Structure,” a paper built around a practical but often hidden problem in tests of quantum objectivity. Aggregate mutual-information curves can show that information grows with fragment size, but they do not reveal whether independent fragments really carry accessible, mutually consistent records of the same pointer variable. The missing evidence lives one level lower: in the raw, shot-indexed fragment records. The paper turns that gap into a reproducible benchmark. Starting from a fixed synthetic binary pointer-copy model with 100,000 shots and eight heterogeneous fragments, it asks what a raw-fragment evidence package should expose before redundancy, consensus, or Spectrum Broadcast Structure-style objectivity is inferred. The analysis enumerates all fragment subsets, separates mean-over-subsets and all-subsets threshold crossings, measures fragment disagreement, reproduces analytic binary-channel threshold maps, applies coupling-breaking negative controls, and stress-tests the result against hidden common-mode correlated errors. The resulting picture is sharper than an aggregate curve. In the baseline model, the 0.9 information-fraction threshold is crossed at subset size m=3 under the mean criterion, but only at m=4 under the stricter all-subsets criterion. Negative controls remain below threshold, while a hidden common-mode flip exposes the main fragility axis: many agreeing fragments can still fail as evidence for independent records if they share the same unobserved error source. The attached PDF gives the manuscript-level argument and results. The arXiv source package supports manuscript reproduction, and the ancillary benchmark archive contains the synthetic raw-shot data, subset diagnostics, disagreement tables, threshold maps, negative-control outputs, common-mode sensitivity maps, figures, scripts, manifests, and checksums. The scope is deliberately bounded. This is a synthetic/model-level benchmark and reproducibility package, not an experimental claim that Quantum Darwinism or Spectrum Broadcast Structure objectivity has been observed. Its purpose is to make explicit what future experimental raw-fragment evidence should provide before a plotted redundancy signature is treated as a claim of objective, independently accessible records.
Quantum Darwinism identifies objectivity with redundant environmental records of system information. A complementary question arises when more than one finite-strength diagnostic record is available to an observer with a declared access rule: which record is selected at a given fragment size? We formulate this question as a context-indexed public-record selector and derive a microscopic asymptotic mechanism for access-scale inversion. The model contains a central qubit coupled simultaneously to a local spin-meter bath that records a σz diagnostic and to a critical transverse-field Ising bath that records a σx diagnostic through the Ising order parameter. For contiguous fragments of length ℓ, the local meter gives trace-distance evidence Fz(ℓ,t)=Cz(t)ℓ+o(ℓ), whereas the critical bath gives Fx(ℓ,t)=Cx(t)ℓ^{7/4}+o(ℓ^{7/4}) in the Ising scaling regime. With public amplitude A_i^pub(ℓ)=[R(ℓ)F_i(ℓ)]^{1/2} and block redundancy R(ℓ)=N/ℓ, the local record is selected at small access scales but the critical record is selected for ℓ>ℓc, with ℓc=[Cz(t)/Cx(t)]^{4/3} up to sector-size and scaling corrections. The crossover is not simultaneous perfect broadcasting of incompatible observables; it is a context-indexed finite-record selection rule. An exact free-fermion/Toeplitz scaling check of the critical bath gives a block-susceptibility exponent consistent with 7/4, while exact diagonalization of a small noncommuting Hamiltonian and parameter scans are included as finite-size pilots of the selector mechanism. This record is a public preprint/manuscript version and has not been peer-reviewed as a journal publication.
Quantum Darwinism explains effective classical objectivity through the selective proliferation of information about preferred quantum states into multiple environmental fragments. Its mature formulations operate within quantum theory, using a system-environment decomposition, decoherence or einselection, and information-theoretic or broadcast-structure criteria for redundant accessibility.This paper asks an upstream question from Registration Theory (RT): what makes a physical distinction a record before that record is described as information available to an observer? Canonical RT answers that retained registration is persistent organization constraining later evolution, that a distinction becomes a physical record only when it remains consequential, and that persistent physical organization is prior to information extracted from it.The paper assembles a theorem-backed finite-model chain now available in the RT corpus. Canonical ACRF dynamics supplies write-retain-read consequential history. The exact finite-amplitude ACRF-4 quotient identifies a nine-dimensional host-host-boundary state. The certified consequence-minimality theorem (DOI 10.6084/m9.figshare.34063464) shows that the retained relational boundary contributes irreducible future-consequence directions. The spectrum-preserving ACRF-8 redundant-record theorem (DOI 10.6084/m9.figshare.34063500) then proves an explicit local witness in which one quotient-valid source distinction is written into two disjoint retained fragments that are locally recoverable, counterfactually separable, and independently readable, giving RRT(q)≥2R_{RT}(q)\ge 2RRT​(q)≥2 under the stated criteria.The resulting distinction from Quantum Darwinism is precise but bounded. RT recordhood is consequence-based, while Darwinian objectivity is an accessibility-and-redundancy criterion formulated within quantum theory. The ACRF witness demonstrates redundant retained record formation without assuming Hilbert space, density operators, mutual information, decoherence, einselection, Born probabilities, or an observer-defined environment. Therefore, multiple persistent records of one distinction are not definitionally identical to Quantum-Darwinian redundancy.The paper does not claim that Quantum Darwinism is false or that RT has derived quantum mechanics, decoherence, Born probabilities, a mutual-information redundancy plateau, or macroscopic objectivity. Instead, it proposes a disciplined hierarchy: consequential distinction → retention → persistent record → branching → redundant retained records → redundant accessibility → environmental objectivity. The final two steps remain open in RT. A future bridge must dynamically select and scale multi-host redundancy and map consequence-bearing RT records into quantum environmental fragments that satisfy decoherence and strong objectivity conditions.
A quantum record can have locally accessible populations while its distinguishing phase remains correlated with a distant source. We study this access boundary in a specified finite recording apparatus with a returning, vacuum/one-excitation source. Source-position weights give finite-time cutoff bounds without removing any physical hopping or return coupling. For an initially far-tagged record and its incoherent mixture, every reader in a declared position-preserving local-control class obeys a phase-visibility envelope and a necessary access-time inequality. A separate finite local probe shows why that state-discrimination limit is not an unrestricted limit on distinguishing two dynamical laws: fresh local coherence can reveal a stipulated added dephaser without recovering the old record phase. We construct a bounded, degree-three reader accessing only source positions 1–32. With the initial tag fixed at position 65, exact finite-source arrival certificates and an analytical tail comparison yield recovery uniformly over every finite total source length at least 65. Accessible control faults are charged against the arrived signed-phase norm, while source-moving drift is charged against the full norm. At the fixed deadline 25.02/J, the matched phase-dependent difference between coherent and archive-gated dynamics exceeds 0.005, including the stated simultaneous control faults and four additional absolute response allowances of 0.008 each. Complementary results cover a vacuum-ready source and a stronger endpoint-prepared finite example. The conclusions are conditional on the supplied model, preparations, common realized controls and calibration bounds. They are not a switchable-fundamental-law experiment, a nuisance-independent classifier, an optimal-speed theorem or an end-to-end formal verification. The supporting Lean companion contains 59 declarations in eight modules with accepted returned Mac compilation, type and axiom evidence; physical analytical interfaces remain explicit hypotheses or outside that subset. The deposit files include the main manuscript, technical supplement and full research/reproduction package.
Quantum Darwinism explains classical objectivity through the redundant spread of information across fragments of the environment. This note studies the opposite regime: an environment whose record is distributed through entangled correlations rather than independent fragments. The model considers a mediator carrying a which-branch displacement record while being purified by an unobserved environment. The central question is: how much of the original quantum information can an observer recover when only part of the environment is accessible? The paper proves that any fragment excluding the record-bearing mode contains exactly zero which-branch information. No individual fragment carries a readable record, and redundancy disappears completely. A closed-form partial-information curve is derived. The amount of accessible evidence depends only on the captured fraction of the environment purification and is governed by a single rational function. The curve connects two limits: the minimal information available to an external observer and the full information recovered when the complete environment is captured. A precise threshold is obtained: strong environmental entanglement requires capturing almost the entire environment before objectivity emerges. The results show that decoherence and objectivity are not equivalent. The same loss of coherence can either create a public, redundantly observable fact or leave information hidden entirely in nonlocal correlations. The structure of the environment determines whether quantum information becomes an objective classical fact or remains inaccessible. All results are derived in exactly solvable Gaussian models, verified analytically and numerically, and accompanied by a reproducibility package.