This work extends the continuum theory of quantum records from 1+1 dimensions to 2+1 and 3+1 dimensions, where long-range fields, asymptotic charges, and gravitational information become physically relevant. Using Gaussian free fields in finite Dirichlet boxes, the study computes the exact fidelity-based record retained by spatial regions for localized charge and dipole histories. Five principal results are obtained. First, the exponential lock law survives dimensional extension: record evidence at distance L decays approximately as exp(−2mL) in both 2+1 and 3+1 dimensions. Second, the long-range charge record behaves qualitatively differently with dimension. As the mass is reduced toward the Coulomb regime, the 3+1-dimensional charge record approaches a finite value, while the corresponding 1+1-dimensional record diverges. The 2+1-dimensional behavior lies between these cases. Third, the study finds that finite Dirichlet boundaries are not passive. They behave as grounded walls carrying image charge and therefore retain part of the physical record. Boundary ownership is present in every tested dimension but is weakest in 3+1 dimensions. When the correlation length becomes short enough that the walls are Yukawa-screened, the boundary dependence nearly disappears. Fourth, charge records increasingly dominate dipole or rearrangement records with distance. Finite boundaries and finite mass both reduce this multipole distinguishability, providing two distinct mechanisms for record erasure. Fifth, lattice refinement shows clean convergence toward the continuum result. The results provide a controlled higher-dimensional realization of the record framework and show that finite long-range charge memory naturally emerges in 3+1 dimensions. They also reveal a concrete mechanism by which information not retained locally in the bulk can be carried by the boundary. The present model uses free fields, coherent histories, and grounded Dirichlet boundaries. It does not compute dynamical gravity; insulating boundaries, interacting theories, asymptotic limits, and gravity remain open problems.
This work extends the continuum theory of quantum records from 1+1 dimensions to 2+1 and 3+1 dimensions, where long-range fields, asymptotic charges, and gravitational information become physically relevant. Using Gaussian free fields in finite Dirichlet boxes, the study computes the exact fidelity-based record retained by spatial regions for localized charge and dipole histories. Five principal results are obtained. First, the exponential lock law survives dimensional extension: record evidence at distance L decays approximately as exp(−2mL) in both 2+1 and 3+1 dimensions. Second, the long-range charge record behaves qualitatively differently with dimension. As the mass is reduced toward the Coulomb regime, the 3+1-dimensional charge record approaches a finite value, while the corresponding 1+1-dimensional record diverges. The 2+1-dimensional behavior lies between these cases. Third, the study finds that finite Dirichlet boundaries are not passive. They behave as grounded walls carrying image charge and therefore retain part of the physical record. Boundary ownership is present in every tested dimension but is weakest in 3+1 dimensions. When the correlation length becomes short enough that the walls are Yukawa-screened, the boundary dependence nearly disappears. Fourth, charge records increasingly dominate dipole or rearrangement records with distance. Finite boundaries and finite mass both reduce this multipole distinguishability, providing two distinct mechanisms for record erasure. Fifth, lattice refinement shows clean convergence toward the continuum result. The results provide a controlled higher-dimensional realization of the record framework and show that finite long-range charge memory naturally emerges in 3+1 dimensions. They also reveal a concrete mechanism by which information not retained locally in the bulk can be carried by the boundary. The present model uses free fields, coherent histories, and grounded Dirichlet boundaries. It does not compute dynamical gravity; insulating boundaries, interacting theories, asymptotic limits, and gravity remain open problems.
This work tests whether the theory of quantum records survives the transition from finite lattice models to continuum quantum field theory. Using a free scalar field in 1+1 dimensions with two histories differing by a localized classical source, the record accessible to a spatial region is expressed exactly through the fidelity of equal-covariance Gaussian states. Four principal results are established. First, the continuum record functional is verified against direct truncated-Fock-space Uhlmann fidelity calculations with agreement at approximately 10^−10. Second, the lattice record converges monotonically toward the exact continuum mode-sum result under refinement from 256 to 2048 lattice sites, demonstrating that the framework is not a lattice artifact. Third, a continuum lock law is found: record evidence measured a distance L from a localized source decays as exp(−2mL), with the fitted decay rate agreeing with 2m to high precision. This identifies the finite-volume suppression observed in earlier discrete models as the lattice manifestation of a continuum correlation-length law. Fourth, the distinction between constraint records and arrangement records survives the continuum limit. As the screening length diverges, the ratio between net-charge and zero-charge rearrangement records grows approximately as 1/m², causing the constraint-class record to dominate without bound. An exploratory study of disjoint regions also finds uniformly subadditive record evidence, consistent with redundant access to a common source through continuum vacuum correlations. The results establish the first continuum realization of the record framework in an exactly controlled quantum field theory. The present analysis is restricted to a free scalar field in 1+1 dimensions and coherent mean-shift histories; interacting fields, gauge theories, massless limits, higher dimensions, and gravity remain open.
This work extends the theory of quantum records from free continuum field theory to an interacting gauge theory using the exactly solvable massless Schwinger model. The study asks whether the continuum record law survives when the relevant correlation length is not imposed by a bare mass but generated dynamically through the chiral anomaly. Using the open-boundary staggered lattice Schwinger model at fixed physical volume, external charge configurations are introduced through Gauss-law strings and records are quantified by the fidelity distinguishability of reduced edge states relative to the vacuum. Four main results are obtained. First, the gauge-theory record shows systematic convergence under lattice refinement. Although the available lattice sizes do not yet establish a high-precision continuum value, successive differences decrease and independent discretization schemes approach one another. Second, the record obeys an exponential lock law. Its distance dependence is extremely close to E ∼ exp(−2MD), where M = g/√π is the anomaly-generated Schwinger boson mass. Independent lattice sizes and source separations reproduce the predicted decay rate to within a few percent. Third, the record functional detects bosonization. The same physical record is calculated in the bosonized description as a Gaussian record of a free massive scalar field. The fermionic-to-bosonic record ratio decreases monotonically toward an order-one value under refinement, providing a direct information-theoretic bridge between the two descriptions. Fourth, a net-charge configuration produces a stable constraint record under refinement when its Gauss-law flux necessarily crosses the observer's region. The results show that the continuum record framework survives its first interacting gauge-theory test and that the exponential information-locking scale is controlled by a dynamically generated physical mass. The present study is restricted to the 1+1-dimensional massless Schwinger model, finite lattice sizes, integer external charges, and open boundaries. Higher-dimensional gauge theories and the full continuum extrapolation remain open.
This note extends the record-classification framework into a two-dimensional lattice gauge theory by studying pure Z2 gauge theory on finite tori. Using exact diagonalization in winding sectors, the work tests how quantum information is stored, distributed, and destroyed across different gauge phases. The classification survives and becomes sharper. The constraint record becomes a topological redundancy: any enclosing loop can recover the enclosed charge parity exactly at every coupling and in every phase, as a direct consequence of Gauss's law. String records appear only where confinement localizes flux into physical strings. The toric-code sector qubit forms a matter-blind record class, preserved in the topological phase but destroyed by confinement. Across the phase diagram, different records migrate or disappear, but the constraint record remains invariant. The study also identifies an important boundary case: antipodally placed charges do not produce a missing record, but an undefined local record because degenerate winding routes prevent a unique assignment. The results show that quantum records in gauge theories are determined by the underlying constraint structure and topology. Some information becomes redundantly accessible through global constraints, some becomes localized through confinement, and some survives only as nonlocal topological information. All results are obtained through exact finite-lattice calculations with documented verification checks and reproducibility data.
This note removes the open-boundary constraint from the lattice Schwinger model and studies the periodic theory with its physical Wilson-line zero mode. The goal is to determine which features of the previous lattice results belong to the gauge theory itself and which were caused by the boundary. Using exact diagonalization of the periodic lattice model with fermions and flux degrees of freedom, the study reveals four main results. The transition is restored: the mass-gap collapse and the critical response reappear, with the mass-direction evidence developing an interior peak near the transition region. The θ-lock is recovered at zero fermion mass, with the sector energy sensitivity strongly reduced compared with the open-boundary case, while the mass-induced unlock follows the expected perturbative behavior and becomes critically enhanced near the transition. The transition-amplifier law also returns: sector evidence grows monotonically with the mass deformation, showing that the open-boundary inversion was a boundary artifact caused by pinning both sectors to a single vacuum. The central result is a record-migration law. In the massless theory, the θ-record is stored mainly in matter correlations and can be accessed through charged endpoints of spatial cuts. In the massive broken phase, the record moves into the topological flux sector: the competing vacua differ by a Wilson-loop flux, making the information invisible to purely matter-based local observers. This establishes how the location of quantum information changes across phases of an interacting gauge theory: symmetry breaking does not only create records, it determines who can access them. The results are obtained within the finite periodic lattice framework, with bounded system sizes, rotor truncation checks, and no continuum extrapolation.
We establish a deterministic discrete-to-continuum theorem for free-information fields whose values are finite collections of quantum-register density operators. The local state space is the compact convex configuration space introduced in the companion finite theory, embedded in a finite-dimensional Hilbert space with the Hilbert–Schmidt metric. A mesh field carries two contributions: a finite-range quadratic register-mismatch energy and a local free-information density consisting of an energetic term, the relational-entropy hierarchy, and an optional log-determinant faithfulness barrier. Under explicit assumptions on cell quadrature, finite interaction range, directional second moments, discrete Poincaré compactness, and divergence consistency, the discrete Dirichlet forms Mosco-converge to an anisotropic continuum form. We then prove equicoercivity, the full Gamma-liminf inequality, a recovery theorem that respects the density-matrix constraints and the barrier, convergence of minima and almost minimizers, and mesh universality: any two admissible mesh sequences with the same limiting second-moment tensor have the same continuum functional. Natural Neumann and imposed Dirichlet boundary conditions are separated at the form level. In the convex regime the convergence strengthens to Mosco convergence of the complete functionals and therefore to convergence of resolvents and variational semigroups. We also give sharp failure statements: without a convergent directional tensor there need not be a unique full-sequence limit; the local continuum theorem does not solve the overlapping quantum marginal problem; and static Gamma-convergence alone does not derive a physical open-system dynamics. No random-substrate, Lorentzian, gravitational, gauge, particle-physics, cosmological, or empirical claim is made.
This note unifies two major parts of a long research program: the vacuum structure of quantum field theory and the theory of distributed quantum records. It identifies a θ-condensate as a distributed displacement record whose relative displacement lies exactly along the field’s zero mode. The question of “which vacuum?” becomes a question of which branch information is accessible. The paper proves that the infrared invisibility results of vacuum sectors and the zero-fragment theorem of distributed records are the same underlying structure. In mode space, any subset excluding the zero mode carries exactly zero information about the θ-sector, while any subset containing the zero mode carries the complete evidence. In spatial regions, the behavior is opposite: the condensate becomes a broadcast record. Every region contains more than its proportional share of information, complementary regions contain overlapping evidence, and in the massless limit every region can access the condensate at full strength, producing maximal spatial redundancy. The paper also proves an absolute charge lock: all charge-neutral, shift-invariant observables see identical sectors, meaning that no neutral observer can determine the θ-sector regardless of the amount of spatial information available. The central result is that broadcasting and hiding are not contradictory behaviors. Space broadcasts the condensate, while charge locks it. These are two complementary aspects of one information structure connecting vacuum sectors, quantum records, and the emergence of objectivity. All results are pre-registered and verified with reproducibility tools. The work is presented as a structural unification in solvable lattice models, while interacting-field and fully dynamical-gravity extensions remain open.