Lance R. Williams

Replication time is among the most important components of a bacterial cell's reproductive fitness. Paradoxically, larger cells replicate in less time than smaller cells despite the fact that assembling a larger cell requires collecting and combining increased quantities of raw materials. This feat is accomplished through the prodigious use of parallel processing, chiefly the translation of mRNA into protein by tens of thousands of ribosomes acting in parallel. The massive over-expression of ribosomes permits protein synthesis, the limiting step in replication, to occur at a rate and scale that would be otherwise impossible. In computer science, spatial parallelism is the distribution of work across the nodes of a distributed-memory multicomputer system. Despite the fact that a non-negligible fraction of artificial life research is grounded in spatially parallel substrates, there have been no examples of artificial organisms that exploit spatial parallelism to replicate in less time than smaller organisms. This paper describes artificial cells defined in a combinator-based artificial chemistry that replicate in less time than smaller cells. This is achieved by employing extra copies of programs implementing the limiting steps in the process used by the cells to synthesize their component parts.

The preferred basis problem has resisted resolution because it is doubly ill-posed. First, it seeks an ontological solution to a structural problem: every proposed solution encounters the same difficulty, indicating that its source is architectural rather than interpretive. Second, it demands an answer in the language of orthonormal bases, presupposing that classical alternatives must correspond to orthogonal decompositions of a state space. They need not. Classical worlds require only logical incompatibility of stabilized distinctions, not linear-algebraic orthogonality. This paper develops refinement geometry, a theory-neutral structural framework that reframes rather than solves the preferred basis problem by identifying its root cause. Physical histories are partially ordered by prefix extension. Stability predicates are existential claims over history prefixes, necessarily monotone since what has occurred cannot be uncertified by later extension, and admissible only if their truth sets are open under finite variation. Monotonicity and admissibility together induce a directed refinement structure admitting a canonical maximal partition. The root cause is then identifiable: purely synchronic refinement cannot reproduce maximal refinement structure because admissible stability predicates are defined over history prefixes and carry monotone certification semantics that no instantaneous state description can fully encode. A synchronic procedure powerful enough to recover the canonical maximal partition must implicitly reconstruct and traverse the prefix order, collapsing into diachronic refinement in disguise rather than achieving a genuinely synchronic result. In contrast, diachronic refinement, accumulating certified distinctions monotonically along histories, converges to the canonical maximal partition without basis selection or orthogonality. Significantly, quantum interference requires no special treatment: non-singleton partition blocks represent histories not yet separated by any certified distinction. Decoherence generates the stability predicates that resolve such blocks; classical worlds are the limit of that resolution. Persistence of distinctions, irreversibility, and absence of merging follow from predicate semantics alone, independent of dynamical law and without presupposing Hilbert-space structure or ontological commitments.

This paper establishes a general semantic constraint on physical ontology in continuum theories under explanatory realism and finite-information access. Working in the framework of represented state spaces, we show that ontic predicates must satisfy bounded input dependence: once true, their truth must persist under sufficiently small perturbations of state. This requirement forces the extension of any ontic predicate to be open in the representation topology. As a consequence, predicates defined by exact equalities, lower-dimensional subspaces, digit-level conditions, or algorithmic properties are structurally non-denoting, even though they are mathematically well defined. Ontic structure in continuum physics must therefore take the form of open stability regions, not sharp boundary conditions. The result is theory-agnostic and applies to any physical framework whose states are modeled in continuum spaces and accessed through finite procedures, including classical field theories, dynamical systems, and quantum models. The theorem clarifies the boundary between mathematical structure and ontological structure in continuum descriptions and connects denotation to operational discrimination constraints.

Refinement geometry defines a directed subdivision structure over history-prefix spaces generated by admissible stability predicates. This paper analyzes the effective realizability of that structure within represented-space semantics. Stability predicates are formalized in uniformly semi-decidable witness form, yielding certified fact sets that evolve monotonically under refinement. A partitioning functional Pi maps finite-information access to a history into the corresponding directed family of refinement partitions. We prove that Pi is Type-2 computable: every finite portion of refinement structure depends on only finitely many oracle interactions. Refinement asymmetry arises as a direct consequence of witness-based predicate semantics. Certified distinctions accumulate monotonically and are never revoked, establishing irreversibility at the level of refinement structure independent of dynamical assumptions. We further show that the canonical maximal partition induced by admissible predicates is computably generable through directed refinement of finite certification stages. Worlds, defined as blocks of the canonical maximal partition, therefore form a recursively enumerable set. Worldhood need not be decidable, and maximality is not finitely certifiable, yet every world arises through effective generation of finite refinement prefixes. In the effective setting, each refinement stage induces a computably presented equivalence relation on a countable domain of names, and branching corresponds to monotone contraction of indistinguishability rather than enlargement of the underlying history space. These results provide a computability-theoretic classification of refinement geometry, establishing constructive generation of maximal distinction structure under finite-information semantics and clarifying the effective consequences of stability-based refinement.

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.

We formalize a general semantic constraint on physically admissible procedures: discrete outcomes must exhibit bounded input dependence, meaning that determinate outcomes are supported by finite stability margins in the underlying state space. We prove that any such procedure can discriminate only properties corresponding to open regions of state space. Properties whose truth sets are topologically thin, having empty interior with dense complement, are operationally unresolvable under admissible physical semantics. This limitation is structural rather than computational. It arises from topological constraints induced by stability at the semantic interface and applies uniformly across continuum ontologies. Stability is shown to be preserved under lawful continuous dynamics, implying that thin distinctions cannot be amplified into operational differences by finite physical evolution followed by admissible readout. Computability provides a canonical representative example. Computable and noncomputable elements form interwoven dense subsets of continuum domains, so computability is not a topological property of states but a property of representation structure. As such, it cannot be operationally extracted by bounded-input-dependent procedures. Restrictions motivated by bounded input dependence thus express ontological parsimony: they eliminate distinctions incapable of supporting stable physical discrimination. The result provides a semantic foundation for aligning ontological commitments with structurally admissible distinctions in realist physical theories.

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.

Computable Wavefunction Realism (CWFR) is an ontological framework for quantum theory grounded in the semantic requirements of explanatory realism. Standard continuum ontology violates two stability conditions: domain instability, in which well-posed dynamics can map admissible states to states with non-denoting magnitudes; and range instability, in which predicates defined on topologically thin sets cannot ground stable physical distinctions. CWFR enforces the minimal corrections via four structural postulates: Lorentz-invariant spectral band-limitation; restriction to computable ontic states; admissible successor dynamics closed on the ontic domain; and predicate admissibility requiring open truth sets. The continuum Hilbert-space formalism is retained as semantic scaffolding rather than ontological furniture. Classical worlds emerge from refinement geometry as maximal diachronic threads through stability-predicate certifications, dissolving the preferred basis problem by identifying classical alternatives as history-dependent objects rather than components of an instantaneous state decomposition. Branching irreversibility follows as a logical consequence of witness-based certification, not a dynamical postulate. Probability operates on finite Boolean event algebras at every refinement stage, rendering standard frameworks for recovering the Born rule applicable without measure-theoretic idealization. This primer is self-contained and accessible to graduate students in physics, mathematics, and the philosophy of physics.

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.