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 This record is a public preprint/manuscript version and has not been peer-reviewed as a journal publication.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 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 and related objectivity frameworks study how information about a quantum system is redundantly recorded in its environment. This preprint studies a downstream selection problem: when several candidate records coexist, which one is public under a specified access channel? The problem is formulated as access-limited quantum hypothesis testing. The global Chernoff distinguishability of a candidate record is compared with the public Chernoff distinguishability after a declared sequence of completely positive trace-preserving access maps. The main result is a sufficient access-algebra separation mechanism: if a broadcast record has extensive distinguishability inside the public access algebra, while a globally stronger encoded record is hidden from that algebra at subextensive rate, then global information density and public distinguishability density have opposite thermodynamic orderings. This is not a definition of objectivity in the sense of Spectrum Broadcast Structure or Strong Quantum Darwinism; it is an operational separation theorem for a declared public decision problem. The preprint gives a random-linear access-algebra construction and controlled realizations based on code distance, local circuits, operator spreading, and protected Hamiltonian access algebras.
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.
We prove a finite-depth access-threshold separation theorem for public quantum records. In a single four-branch many-body environment, one label is encoded in a positive-rate, positive-distance quantum code while a second label is redundantly broadcast in local environmental degrees of freedom. Although unrestricted global decoding selects the encoded record, every public fragment below a distance/light-cone threshold has exactly zero distinguishability for that record, while the broadcast label remains publicly distinguishable with positive density. Conversely, above a complementary high-access threshold, erasure recovery reconstructs the encoded record. The result formalizes a separation between globally decodable environmental information and public objectivity under a declared fragment-access structure.
Quantum Darwinism explains classical objectivity through the redundant proliferation of records in an environment. This note studies that mechanism inside a gauge theory, where Gauss's law constrains which records can exist and where they can be stored. Using exact lattice Schwinger model calculations with both open and periodic boundaries, including the Wilson-line rotor, this work shows that record redundancy is determined by the relation between information and gauge constraints. Three fundamental record classes are identified. First, unscreenable charges produce perfectly redundant records: every accessible downstream region can read the same information because the constraint itself distributes the record without requiring copying dynamics. Second, screened charges produce bilocal records, with information divided between the screening cloud and the boundary-delivered image while intermediate regions remain blind. Third, symmetry-breaking order produces graded redundant records, while topological flux records represent the opposite extreme: globally distinguishable but invisible to local matter fragments. The study also reveals a constraint-induced discordant split. In the flux sector, mutual information can remain large while readable evidence is almost absent, showing that a gauge theory can contain correlations that no local fragment can convert into classical information. The central conclusion is that classical objectivity in gauge theories is not determined only by environmental interaction. It is controlled by the structure of the constraints: Gauss's law decides which records can be broadcast, localized, or hidden. All results are obtained through exact diagonalization with independent verification checks and documented numerical convergence tests.
Abstract Decoherence suppresses interference, but an observer’s ability to reconstruct a classical pointer value depends on additional resources: distinguishable conditional environmental states, an allowed measurement, sufficient accessible fragments, and sufficiently independent records. We provide an explicit minimal quantum-to-operational bridge that places these requirements in one chain. A system qubit is correlated with conditional environmental qubit states, permitting exact expressions for residual coherence, quantum mutual information, pointer Holevo information, accessible information, and Helstrom discrimination error. Full density-matrix calculations validate the formulas across 280 endpoint and interior cases. An accessible-sector/hidden-bath construction shows that coherence can fall below 2.3 × 10⁻⁵ while the observer’s record information and error remain fixed at 0.0803 bits and 0.4009. Measurement policies shift recovery thresholds: for record overlap 0.8 and error tolerance 0.05, collective or optimized adaptive-local discrimination requires four fragments, a fixed canonical-basis measurement requires six, and repeated one-fragment Helstrom measurements followed by classical decoding require seven. More importantly, records matched at the one-fragment level can have radically different collective behavior. For a binary pointer, the common-mode classical channel has an exact accessible-information ceiling of 1 − h₂(0.1) = 0.5310 bits, while the noncommuting hidden-memory ensemble approaches the same Holevo-information ceiling; matched independent records approach one bit and zero error. Disjoint observer counts and unanimous agreement likewise depend on shared error structure. Finally, declared local measurements induce classical record channels that are subjected to held-out model selection, predictive checks, abstention, and simultaneous finite-sample threshold certification. The resulting framework supplies the validated quantum-to-operational record model used in the companion analysis of operational capacity bounds for distinguishable decoherent histories.
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)≥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.