arXiv subjects

Karl Svozil

Publications and source records attributed to Karl Svozil.

At least 19 recordsLinked to original sources

arXiv2026

Pseudocontexts forced by finite context hypergraphs

A context is a complete set of mutually exclusive outcomes whose probabilities sum to one. We define a pseudocontext as two disjoint groups, with no mutually exclusive pair within either group, whose total probabilities must nevertheless be equal solely because of how the contexts overlap. We give an exact finite test for this property and show that the equality is independent of the chosen coordinates and probability model. Applying the test in three dimensions, we obtain a 15-outcome real example with groups of three and a 20-outcome complex example with groups of two. Under this definition, the sharp minimum number of outcomes in each target group is two over the complex field and three over the real field.

quant-ph↗

arXiv2026

The Logic of Partitions and Partition Logics: Ore's Correspondence, Contextual Pasting, and Direct-Sum Decompositions

The term ``partition logic'' denotes two constructions at different levels. In automaton and generalized-urn models, selected partitions generate Boolean event algebras whose contextwise union forms a concrete pasted event structure; in Ellerman's framework, whole partitions are classifications governed by refinement and partition operations. For a finite set $U$, Ore's correspondence maps each generator $\pi$ to its Boolean algebra $\BA(\pi)$, but it neither identifies the pasted carrier with $\Part(U)$ nor makes pasting a partition operation. It yields $\BA(\pi\wedge\sigma)=\BA(\pi)\cap\BA(\sigma)$ and $\BA(\pi\vee\sigma)=\langle\BA(\pi)\cup\BA(\sigma)\rangle_{\rm BA}$, where $\langle\cdot\rangle_{\rm BA}$ denotes Boolean-algebra generation. Thus meet captures the common event algebra, whereas join gives the ambient Boolean closure. Chinese-lantern, Firefly, and triangular examples distinguish shared events, atomic intertwining, and inherited concrete order. Ellerman's direct-sum decompositions (DSDs) provide a vector-space analogue: component projections of an orthogonal DSD resolve the identity and encode exclusive outcomes, but its components are not equivalence classes of vectors. Gleason and Kochen--Specker applications require globally context-consistent valuations on those projections.

quant-ph↗

arXiv2026

Which Classicality? Incidence, Simplex, and Product-Rule Tests in Finite Quantum Logics

Finite quantum-logical constructions can appear classical or nonclassical depending on which structure is retained. We distinguish incidence tests based on valuations, colorings, and partition representations; simplex-embedding tests for specified prepare-and-measure fragments; and operator-functional tests imposing spectral and product rules. We show that the collective GHZ joint measurement is a single Boolean context and becomes nonclassical only when a common assignment of local factors, together with product preservation, is required. For selected labelled ray fragments, we compute state-depolarizing thresholds for a restricted projector-cone factorization and for a specified vector-generated operational closure, separating exact primal--dual certificates from numerical estimates. These values are properties of the stated fragments and noise model, not invariants of the underlying hypergraphs or a universal ordering of contextuality.

quant-ph↗

arXiv2026

Operational Shadows of Hilbert-Space Probabilities

At one frozen setting, the probabilities observed in a sharp quantum context are indistinguishable, as detector-click statistics, from ordinary probabilities on the atoms of a classical partition. But an actual analyzer usually comes with a calibrated knob: a tangible handle on the apparatus. If the measurement configuration is co-varied continuously through this physical parameter, the operational object is no longer one point of a simplex but a response curve. Classical linear responses, Malus-type Hilbert-space responses, softmax links, non-homomorphic parameter transcriptions, and discontinuous threshold limits are different maps from settings to probabilities. Continuity, calibration, and preservation of the physical composition law are then part of the experimental meaning of the knob. Such comparisons distinguish specified, calibrated response models; by themselves they do not constitute a classical-versus-quantum impossibility theorem. The static operational coincidence can also persist for two intertwined contexts: if the common outcomes receive the same probabilities, the remaining masses can always be coupled by a classical joint distribution. Genuine multi-context nonclassicality begins when a family of local shadows cannot be glued into one nonnegative global distribution or one simplex factorization. Farkas' lemma gives the exact alternative: either the classical extension exists, or a separating linear inequality certifies its impossibility.

quant-ph↗

arXiv2026

Chromatic Completeness and the Independence of Geometric Obstruction

We establish a strict logical separation between two distinct phenomena in orthogonality hypergraphs: chromatic completeness, the possibility of assigning a single globally consistent nondegenerate spectrum to all contexts, and geometric coordinatizability, the existence of a faithful orthogonal representation by rays. A strong chromatic number larger than the Hilbert-space dimension obstructs only the former. It does not, by itself, obstruct the existence of a faithful orthogonal representation. We make this separation explicit by comparing two three-dimensional examples with the same strong chromatic number. A completed 25-ray version of the Yu-Oh configuration has strong chromatic number four and nevertheless possesses an explicit faithful orthogonal representation in R^3. Conversely, Greechie's G_{32} hypergraph also has strong chromatic number four, and has a separating and unital set of two-valued states, but we give an elementary algebraic proof that it admits no faithful orthogonal representation in C^3. The obstruction in G_{32} is therefore not chromatic but projective-geometric: the incidence relations force two distinct atoms to collapse onto the same ray.

quant-ph↗

arXiv2026

Local Softmax and Global Weights in Non-Boolean Event Structures

Softmax and related normalized response functions are widely used in choice theory, machine learning, and cognitive science. In non-Boolean event structures with overlapping contexts, however, local normalization does not automatically yield a global probability weight. We show that imposing single-valuedness on shared atoms -- equivalently, no-disturbance or consistent connectedness -- collapses generalized softmax rules to coordinate parametrizations of the strictly positive part of the admissible-weight polytope. Any strictly positive admissible weight can be represented in this way, while boundary weights arise as limits. Exotic weights that exceed classical or quantum bounds are therefore properties of the event structure and the chosen weight, not of the normalizing link. The resulting hierarchy separates local normalization, cross-context gluing, Cauchy--Gleason linearity, and physical or cognitive realizability.

quant-ph↗

arXiv2026

Answer Partitions and Oracle Access Determine Quantum Query Complexity

An answer partition specifies which oracle instances share an output, while query complexity also depends on how those instances are accessed. We formulate exact one-query answer-partition resolution as block discrimination of a unitary oracle family. Applied to Deutsch's problem with a controlled response unitary V, the criterion shows that one query suffices if and only if -1 is an eigenvalue of V; cyclic addition in odd response dimension therefore raises the exact quantum cost to two queries, matching the classical cost while preserving the same computational-basis point values. Holding the standard Boolean point oracle fixed, we further show that balanced answer partitions with equal-sized cells can have different exact classical and quantum query complexities. A complete exact classification is given for all 35 balanced three-bit partitions, while the unresolved four-bit cases are reported explicitly as numerical candidates. These results separate the combinatorial specification of an answer from the oracle-dependent distinguishability that determines query complexity.

quant-ph↗

arXiv2026

Double-Exponential Quasi-Orthogonality: The Geometry of Decoherence

A composite system of N local q-level factors has dimension D=q^N. Although at most D vectors can be exactly orthogonal, a fixed squared-overlap tolerance \eps permits M_\eps(D)\gtrsim\exp(c_\eps D) mutually quasi-orthogonal directions. Consequently M_\eps(q^N)\gtrsim\exp(c_\eps q^N): the dimension grows exponentially in N, but its quasi-orthogonal capacity grows doubly exponentially. L\'evy's lemma explains the accompanying concentration of regular observables, and Johnson--Lindenstrauss scaling gives the complementary finite-set account of exponential capacity. For Haar-random pure states the sharper exact law is \mathbb P(|\langle\phi|\psi\rangle|^2\geq\eps)=(1-\eps)^{D-1}, while typical Fubini--Study angles lie within O(D^{-1/2}) of \pi/2: capacity explodes as angular structure homogenizes. We turn these facts into simultaneous overlap and trace-distance bounds for finite decoherence branch families, including mixed environments and collective weak coherences. The results are conditional on typical relative environmental dynamics. They neither select a pointer basis nor identify coherence suppression with readable or redundant records.

quant-ph↗

arXiv2026

No Trading Strategy Can Win on Every Price Path: Computability, Randomness, and the Limits of Universal Trading

Every universal-trading claim pairs a trader with a market---a path, generator, or law. For any total deterministic computable trader, its code yields a fixed computable countermarket with proportional price moves opposing its positions; hence no such trader wins on every computable path. Gold-style learning cannot identify every computable binary market rule from history. Separately, Turing-universal generators make certification of unbounded-future events undecidable; Busy-Beaver growth defeats every computable description-size waiting schedule. A passive Martin-L\"of-random record is incompressible and prevents effective test-capital processes from becoming unbounded; no-arbitrage supplies a distinct financial boundary. Together these results form an expository taxonomy: repeatable success requires a market restriction, benchmark, risk premium, or informational advantage, while time reversal supplies a simple stress test.

q-fin.TR↗

arXiv2026

Complementarity in Social Measurement: A Partition-Logic Approach

Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually incompatible coarse-grained modes of observation. We show that this structure arises in a range of social-science settings by constructing six explicit examples from personnel assessment, survey framing, clinical diagnosis, espionage coordination, legal pluralism, and organizational auditing. For each case we identify the latent state space, the observational contexts as partitions, and the shared atoms that intertwine contexts, yielding instances of the $L_{12}$ bowtie, triangle, pentagon, and automaton partition logics. These examples make precise a notion of social complementarity: different modes of inquiry can be incompatible even though the underlying system remains fully value-definite. Complementarity in this sense does not entail contextuality or ontic indeterminacy. We further compare the classical probabilities generated by convex mixtures of dispersion-free states with the quantum-like Born probabilities available when the same exclusivity graph admits a faithful orthogonal representation. The framework thus separates logical structure from probabilistic realization and suggests empirically testable benchmarks for quantum-cognition models.

physics.soc-ph↗

arXiv2026

Quantum Structures as Generative Scores: Partition Logic, Generative Logic, and Aesthetic Form

We connect partition logic with Generative Logic by translating finite partition logics into Prolog-based Simple Generative Logic Grammars. As a proof of concept, we use the five-atom V-logic L_{12} to generate a modular visual artifact, the \emph{Quantum Square}. The approach separates logical structure from its visual, textual, or sonic realization. This makes partition logic useful both as a generative design resource and as a tool for communicating complementarity.

quant-ph↗

arXiv2026

Dirac's Dilemma of the Economy of Inheritance: Parental Care, Equality of Opportunity, and Managed Inequality

In a brief reflection on the principles of human society, P. A. M. Dirac articulated a structural tension between two widely affirmed norms: that it is good and natural for parents to improve the prospects of their own children, and that justice requires that all children have equal opportunities in life. These principles, each compelling on its own, cannot be fully realized together. This paper reconstructs Dirac's dilemma, connects it to the dynamics of compounding advantage and inheritance, and situates it within the broader history of political philosophy, including the work of Rawls, Dworkin, Cohen, Brighouse and Swift, Nozick, Murphy and Nagel, and others. The paper argues that attempts to eliminate the resulting injustices entirely risk damaging the non--zero--sum structures that generate general prosperity, and defends a position of "managed inequality": a robust social floor and real mobility, combined with limits on extreme dynastic accumulation and an explicit acceptance of some residual, but constrained, inherited advantage.

physics.soc-ph↗

arXiv2025

Certified Private Relational Time from Entanglement

We introduce an ``entangled clock'' in which time is defined operationally by discrete measurement registrations on a singlet state. Locally, each party's tick rate is fixed by the unbiased marginals. The nontrivial resource is the relational (coincidence-tick) stream: because the singlet's information budget is entirely exhausted by joint properties, the only definite temporal structure resides in the correlations between the two parties. Operationally, after exchanging time tags and outcomes, Alice and Bob identify synchronized events (that is, the $++$ channel) and thereby obtain a joint tick record. Comparing the $++$ coincidence rate R(\theta)=P_{++}(\vec a,\vec b) to Peres' isotropic bomb-fragment local-hidden-variable model (yielding R_{\mathrm{cl}}(\theta)=\theta/(2\pi)), we find that for obtuse analyzer separations the quantum prediction exceeds this natural classical benchmark, with a maximal relative excess of about 13.6\% near \theta\approx 140.5^\circ. We emphasize that this ``faster ticking'' refers to the rate of identified coincidence ticks under a specific operational convention, not to an improved local clock rate, precision, or stability. Finally, by using multiple settings and a Bell test, we outline ``Certified Private Time'': a device-independent certification of unpredictability/privacy of the relational time-stamp record against adversaries lacking foreknowledge of the settings, analogous to certified randomness generation.

quant-ph↗

arXiv2025

Irreducible Rules and Equivalence Classes of One-dimensional Cellular Automata

One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric transformations of the lattice induce symmetry transformations on the set of local rules and the set of global maps of cellular automata, resulting in a partitioning of the set of cellular automata into equivalence classes. The concept of an irreducible local rule that depends on all its coordinates is used to analyse the equivalence classes and results on the number of equivalence classes of irreducible binary local rules and binary global maps are presented. Finally, another symmetry operator based on the scaling of neighbourhoods is introduced and the change in the number of equivalence classes is analysed.

nlin.CG↗

arXiv2025

Nuclear Detonations as Probes of Hidden Superluminal Sectors

We propose a highly speculative phenomenological framework in which nuclear detonations and high-energy collisions serve as probes for hidden sectors with effective superluminal propagation. Motivated by analogies between acoustic and electromagnetic phenomena, we stratify the physical description into three layers: a fundamental ``substrate'' layer, hidden-sector fields with extended causal cones, and the emergent Standard Model. We posit that the extreme, macroscopic stress-energy gradients generated by nuclear explosions might excite substrate or hidden modes that remain kinematically inaccessible to standard laboratory probes. This work unifies various exotic proposals -- including extra-dimensional shortcuts and trans-metric shockwaves -- into a single formalism, discussing the constraints imposed by causality and observation while outlining how such distinct high-energy regimes could complement one another in searching for physics beyond the emergent metric.

hep-ph↗

arXiv2025

Causal Rigidity and the Single-Unit Universe: Integrating the Alexandrov-Zeeman and Unruh Clock Scales

We unify two complementary viewpoints on relativistic spacetime and the counting of fundamental constants. Operationally, Matsas, Pleitez, Saa, and Vanzella (MPSV) have recently argued that relativistic spacetime requires only a single fundamental dimensional constant. Mathematically, theorems due to Alexandrov and Zeeman demonstrate that the light-cone structure determines the spacetime geometry only up to a conformal factor. We show that these approaches are mutually reinforcing: the Alexandrov-Zeeman theorems establish the rigid conformal structure of spacetime, while the ``bona fide clock'' required by MPSV serves the necessary mathematical role of breaking the dilation symmetry. We provide a formal derivation proving that the normalization of a single clock worldline is sufficient to select a unique metric from the conformal class, thereby clarifying that the number of fundamental constants is exactly one.

gr-qc↗

arXiv2025

Faithful real embedding of a three-dimensional complex Kochen-Specker configuration

We describe a phase-adjusted realification procedure that embeds any finite set of rays in C^3 into R^6. By assigning an appropriate phase to each ray before applying the standard coordinate-wise map, we can arrange that two rays are orthogonal in C^3 if and only if their images are orthogonal in R^6, so the construction yields a faithful orthogonal representation of the original complex configuration. As a concrete example, we consider the 165 projectively distinct rays used in a C^3 Kochen-Specker configuration obtained from mutually unbiased bases, list these 165 rays explicitly in C^3, and give for each of them its image in R^6 under the canonical realification map. We also note that, because the original 3-element contexts are no longer maximal in R^6, the embedded configuration admits two-valued states even though its realisation with maximal contexts in C^3 is Kochen-Specker uncolourable.

quant-ph↗

arXiv2025

Singlet-Like Correlations: Equal Peak Work, Unequal Robustness

Initial system-environment correlations are a thermodynamic resource, enabling work extraction through their erasure. We compare three representative singlet-like, rotationally covariant correlation laws -- a local classical benchmark, the quantum cosine law, and an idealized stronger-than-quantum step law -- under measurement misalignment. In the binary-outcome, uniform-marginal setting, all three can attain the same peak extractable work, k_{\mathrm B}T\ln 2. Their operational value differs, however, in robustness away from perfect alignment. For the chosen classical benchmark the mutual information degrades as \Theta(\delta\theta\ln(1/\delta\theta)), whereas for the quantum cosine law it degrades as \Theta(\delta\theta^2\ln(1/\delta\theta)). The stronger-than-quantum step law is perfectly flat except at a critical angle. Accordingly, the paper establishes a robustness hierarchy within this restricted comparison class, rather than a no-go theorem for all classical correlations.

quant-ph↗