Continuum physical theories model states as real- or complex-valued fields and dynamics as linear operators on infinite dimensional spaces. Under explanatory realism, an ontic interpretation incurs two semantic commitments: (i) real-valued physical magnitudes must denote relative to the theory’s admissible state interface, and (ii) the theory must be semantically closed under its own evolution and readout rules. Denotation is interface-relative: it requires the existence of a total continuous witness on names. Equivalently, it requires bounded input dependence at each fixed finite precision. Failure of bounded input dependence is captured by forced extensional totalization (FET), in which even coarse output precision cannot be stabilized by any finite prefix of a state name. We give a physics-facing construction of FET for the three-dimensional wave equation with Kirchhoff point readout. We construct a countable family of smooth, compactly supported, finite-energy initial states localized on pairwise disjoint shrinking latitude belts on the Huygens sphere, and restrict the admissible domain to states containing at most one localized contingency. Each nonzero belt perturbation is normalized to contribute the same order-one amount to the readout, while the zero state contributes none. Under any non oracular state interface satisfying a minimal locality-of-access condition, no finite prefix can rule out activation of some sufficiently deep belt. The induced point readout therefore behaves like the existential predicate "some belt is active'', exhibits FET at the zero state, and fails to denote. Semantic closure fails: the evolution-readout pipeline yields a localized point magnitude that is non-denoting relative to the fixed state interface. The result isolates a semantic obstruction to ontic readings of continuum dynamics. It is independent of computability, predictability, or measurement feasibility, and it holds despite smooth compact support, finite energy, and classical well-posedness.
Continuum physical theories model states as real- or complex-valued fields and dynamics as linear operators on infinite dimensional spaces. Under explanatory realism, an ontic interpretation incurs two semantic commitments: (i) real-valued physical magnitudes must denote relative to the theory’s admissible state interface, and (ii) the theory must be semantically closed under its own evolution and readout rules. Denotation is interface-relative: it requires the existence of a total continuous witness on names. Equivalently, it requires bounded input dependence at each fixed finite precision. Failure of bounded input dependence is captured by forced extensional totalization (FET), in which even coarse output precision cannot be stabilized by any finite prefix of a state name. We give a physics-facing construction of FET for the three-dimensional wave equation with Kirchhoff point readout. We construct a countable family of smooth, compactly supported, finite-energy initial states localized on pairwise disjoint shrinking latitude belts on the Huygens sphere, and restrict the admissible domain to states containing at most one localized contingency. Each nonzero belt perturbation is normalized to contribute the same order-one amount to the readout, while the zero state contributes none. Under any non oracular state interface satisfying a minimal locality-of-access condition, no finite prefix can rule out activation of some sufficiently deep belt. The induced point readout therefore behaves like the existential predicate "some belt is active'', exhibits FET at the zero state, and fails to denote. Semantic closure fails: the evolution-readout pipeline yields a localized point magnitude that is non-denoting relative to the fixed state interface. The result isolates a semantic obstruction to ontic readings of continuum dynamics. It is independent of computability, predictability, or measurement feasibility, and it holds despite smooth compact support, finite energy, and classical well-posedness.
Continuum physics represents states as real- or complex-valued fields and dynamics as operators on infinite-dimensional function spaces. Under an ontic interpretation, however, fundamental evolution must be semantically total: it must take every admissible state specification to a successor state specification in which all admitted magnitudes remain denoting. We make this requirement explicit using standard admissible representations, in which denotation is characterized by bounded finite-precision input dependence on state descriptions. We show that standard continuum dynamics can violate this semantic closure requirement even when the underlying PDE is linear, well posed, and uniquely solvable. The obstruction is forced extensional totalization: a regional readout can require joint control over countably many individually well-behaved contributions in a way that destroys bounded input dependence and hence denotation. Because locality commits a field ontology to treating spatial restrictions on compact regions as single physical magnitudes, this failure mode cannot be avoided by appealing to pointwise readouts or sequential access. Reanalyzed in these terms, the Pour-El and Richards Theorem 2 construction for the three-dimensional wave equation provides a concrete witness: admissible finite-energy initial data evolve to states whose regional field restrictions do not admit admissible names in the required function-space topology. The obstruction is semantic rather than epistemic: it does not concern what can be computed or observed, but the failure of continuum evolution to preserve denotation under realist locality commitments. The conclusion is eliminative: unrestricted continuum field ontology cannot serve as the basis of a semantically closed fundamental dynamics.
Computable Wavefunction Realism (CWFR) is an ontological framework for quantum theory derived from the semantic commitments of explanatory realism. Explanatory realism requires that physical magnitudes denote under admissible representations and that lawful evolution be closed on the intended ontic domain. Read literally, continuum ontology challenges these requirements through three distinct forms of semantic instability: domain instability arising from unbounded aggregation of fine-scale structure, range instability arising from non-open predicate structure, and closure failure under lawful evolution. CWFR does not begin by postulating computability or finite information; both arise as consequences of the semantic conditions required for physically meaningful ontology. The resulting answer is given by four postulates: Lorentz-invariant spectral band-limitation, identification of the ontic domain with states admitting Type-2 computable names under the chosen representation, admissible successor dynamics given by total Type-2 computable maps on the admissible domain, and restriction of physically meaningful predicates to those whose truth sets are open in the representation topology. The paper develops the structural consequences of these constraints and establishes non-vacuity through explicit admissible successor constructions. CWFR is not proposed as a replacement for continuum quantum mechanics at the level of mathematical formalism, but as a restriction on ontological interpretation imposed by semantic stability conditions. Macroscopic structure arises from refinement geometry induced by admissible stability predicates, classical worlds emerge as maximal refinement threads, and probability assignments operate on locally finite refinement partitions. Extension to realistic interacting quantum field theories is identified as a programmatic direction rather than a completed result.
Abstract We present DLST Ver.11.0.0, a compact recurrence-classification framework for exact physical histories, relational time, and relativistic closure. Ver.11 explicitly corrects the earlier interpretation of DLST: finite signal speed, microscopic length, compactness, finite entropy, finite Hilbert dimension, or a discrete evolution label do not by themselves establish a fundamental discrete clock or exact recurrence. The central objects are instead the physical identity space, the stabilizer of an individual state, and the common global kernel of the evolution. This separates state-specific recurrence, universal recurrence, gauge stationarity, and observational indistinguishability. For autonomous discrete quantum evolution, we prove that a common exact projective return for all pure-state rays and density operators exists if and only if the one-step projective update [U] is a torsion element of PU(H), equivalently U^N = exp(i phi) I for some finite N. Membership in a finite projective unitary subgroup is therefore a sufficient special case. Finite-volume exact Clifford dynamics on finitely many prime-dimensional qudits provides an explicit conditional realization: the projective Clifford group is finite, so an exact Clifford quantum cellular automaton has a nonzero common recurrence period. This bridge does not require a finite quantum-state cardinality. Its scope is exact and finite-volume; infinite-lattice Clifford QCA or arbitrarily small irrational non-Clifford phases need not recur globally. Complementary positive criteria are given by finite same-law closure and spectral commensurability. For unitary evolution, exact recurrence of an occupied state requires its active eigenphase or energy differences to lie on a common arithmetic lattice. These results clarify why finite-dimensional Hilbert space alone is insufficient: exact recurrence is controlled by projective order and spectral arithmetic rather than vector-space dimension. The relativistic obstruction side is strengthened. In 1+d-dimensional Poincare-covariant quantum dynamics with d >= 2, if the scalar/projective translation kernel contains any nonzero translation—timelike, spacelike, or null—Lorentz covariance and additivity force the entire translation subgroup into the kernel. Hence a nontrivial translation representation cannot possess a nonzero universal spacetime period. A related connected simple-group obstruction excludes noncentral universal projective periods under the stated representation hypotheses. For relativistic scattering sectors, Haag-Ruelle wave-operator equivalence transfers the asymptotic energy spectral measure to the interacting sector. A nonzero non-atomic energy component is incompatible with the affine spectral lattice required for exact projective return, yielding an exact nonreturn criterion without assuming that every state belongs to the scattering sector. Independently, any strictly monotone extensional physical witness along the complete admitted history forbids exact recurrence. Ver.11 also proves a finite-window nonidentifiability result: for any finite observation horizon and tolerance, one can construct finite-dimensional Hamiltonians whose propagators remain arbitrarily close throughout the observed interval while belonging to different global recurrence classes. Finite measurement precision therefore cannot replace an exact structural bridge from observed dynamics to all-history recurrence. Related audits show that finite Hilbert dimension, Type II_1 finite-entropy language, gauge stationarity, and cosmological labels are not exact recurrence classifiers by themselves. Finite-dimensional completeness is also incompatible with a nontrivial exact continuous unitary representation of the standard connected de Sitter group under the stated assumptions. The resulting classification contains both positive and negative bridges. Positive exact routes include finite same-law closure, projective torsion, finite-volume exact Clifford QCA, and affine spectral lattices. Obstruction and nonreturn routes include Poincare symmetry, non-atomic scattering spectra, and strict extensional monotonicity. Gauge equivalence, compactness, finite observational windows, and coarse finiteness statements remain nonclassifying without additional physical input. The principal methodological change is therefore a shift from presumed temporal discreteness to fail-closed actuality promotion: a recurrence or nonrecurrence claim is promoted only after the physical identity relation, complete evolution law, and exact all-history bridge have been independently specified. DLST Ver.11.0.0 does not establish that the actual universe is periodic, aperiodic, fundamentally discrete in time, a finite Clifford automaton, or governed by a universal microscopic tick. C4 Ver.1.0.0 and OUROBOROS Ver.2.0.0 remain separate downstream research programs rather than premises of DLST. Deterministic reproducibility checks accompany the release for the finite-projective, Clifford-group, spectral, permutation, and finite-window constructions. These computational audits verify explicit finite examples and implementation details; the analytic theorems remain the scientific basis of the classification. DLST Ver.11.0.0 thus provides a compact framework connecting exact recurrence, dynamical stabilizers, projective unitary torsion, Clifford quantum cellular automata, Poincare symmetry, Haag-Ruelle scattering, operator-algebraic finiteness, de Sitter representation theory, and relational physical time under an explicit claim boundary.
Computable Wavefunction Realism (CWFR) is a finite-information ontology for quantum mechanics that preserves Everettian explanatory structure while rejecting continuum wavefunction realism as fundamental ontology. The motivation is semantic. Under explanatory realism, physical magnitudes must denote under an admissible semantics, and dynamics must be semantically closed on their ontic domain. Continuum ontology exhibits two independent instabilities. On the domain side, unbounded fine-scale structure permits lawful dynamics to force dependence on unbounded collections of independent contingencies, producing non-denoting magnitudes and loss of semantic closure. On the range side, continuum ontology admits distinctions among real-valued magnitudes that no bounded-input-dependent interface can stably track. In particular, computability is not a physically meaningful predicate at fixed finite resolution, since computable and noncomputable reals are both dense. Such distinctions are semantically inert as ontology. CWFR enforces the required stability conditions via three postulates: (I) a Lorentz-invariant spectral band-limit bounding independent fine-scale degrees of freedom; (II) amplitudes restricted to Type-2 computable complex numbers, aligning the range of magnitudes with admissible semantics; and (III) evolution by finitely specified, oracle-free successor maps that are total on the resulting configuration space. Within this finite-information setting, decoherence yields finite packet partitions and finitely branching successor structure, with Born weights defined over finite packet partitions, while the continuum Hilbert-space formalism survives only as semantic scaffolding for symmetry and approximation. Full constructions and proofs appear in the CWFR manuscript and companion papers.
This deposit contains two companion technical notes developing a finite-dimensional semantic state algebra for unresolved readings, classical decisions, and order-sensitive semantic operations. The first note separates semantic states from their response formats. A response format is defined as an alphabet together with a prescribed resolution map. For a two-reading construction, four selector-polarity states are distinguished explicitly. The polarity-only yes/no map is proven non-injective, whereas the full selector-polarity map is bijective. A separate rank-nullity theorem establishes the corresponding global obstruction for linear maps from higher-dimensional semantic spaces into lower-dimensional decision spaces. A real two-dimensional space is sufficient for storage; under the additional requirements of associative and commutative multiplication, a unit, and division by every nonzero element, the unique two-dimensional real extension is the complex field. The classical real sector is embedded conservatively. The second note extends this framework to semantic operators. Questions and contextual updates generate a unital complex operator algebra, while order dependence is represented exactly by commutators and the associated derived Lie algebra. State-dependent and global order-sensitivity measures are introduced. Complex dimension two is shown to be minimal for noncommuting complex-linear dynamics, while terminal binary decisions remain separate real-valued readouts. Operator complexification preserves sums, composition, identities, and commutators. The construction is structural rather than empirical. It assumes neither quantum ontology nor a Born rule and does not claim a complete formal semantics of natural language.
We formulate a mathematical framework for validating candidate carrier-based physical computations. Logical continuation is kept distinct from compilation, physical preparation, open-system evolution, restricted observation, and decoding. For every finite boundary/future relation we construct a diagonal positive-semidefinite penalty Hamiltonian whose zero-versus-positive ground-energy class equals existential continuation. To connect this extensional static representation to candidate physical dynamics, we introduce a typed driven-dissipative architecture motivated by superconducting bosonic hardware. The generator is separated into a hardware-stabilization layer and an instance-dependent semantic problem layer. We define the fixed-point, protected-manifold, and no-spurious-state conditions required for exact dissipative compatibility. Protected violation-removal corrections are required to admit uniform synthesis and to preserve the encoded manifold. A Penalty-Lyapunov condition yields exponential decay of the expected excess penalty above the ground energy and, together with explicit fixed-point and convergence hypotheses, identifies the semantic ground sector as the terminal stationary set. For Hamiltonians differing only by a global scalar shift, normalized state data are identical in the absence of an operational energy reference. We therefore formulate a reference-coupled microwave decoding criterion: if calibrated measurement distributions remain uniformly separated under declared reference perturbations, a classical decoder achieves a quantified worst-case error bound. A four-level hierarchy separates static semantic representation, exact dissipative compatibility, efficient convergence, and robust physical readout, so that mathematical representation remains distinct from scalable physical synthesis.