| ORCID | https://orcid.org/0009-0002-4317-5604 |
| ResearchGate | https://www.researchgate.net/profile/Rowan-Quni |
| Resume | https://doi.org/10.5281/zenodo.17176733 |
| QWAV Computing | https://qwav.tech |
Rowan Brad Quni-Gudzinas
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tl;dr: cross-ratios (related to tensor networks)
OK so I don't love my wording on this post (these brainstorms are useful testbeds for research, so I am glad it got attention). Here's where I'm at as of now: https://www.researchgate.net/publication/403845735_Quantum_Laws_of_Form_A_Syntactic_Foundation_for_Physics_From_The_Calculus_of_Distinction_to_Ultrametric_Cosmology
Syntactic token calculus is a universal language for describing relational patterns. It embodies the “pattern that connectsˮ that Gregory Bateson sought—a meta‑pattern that explains why patterns recur across disparate domains. https://doi.org/10.5281/zenodo.19547736
SYNTACTIC TOKEN CALCULUS: From the Logic of Distinction to the Coordinate-Free Cosmos
The Syntactic Token Calculus proposes a fundamental re‑conception of physical reality as a web of pure distinctions governed by two reduction rules and one identity property. This monograph develops the complete framework across seven chapters, beginning with the primitive mark and void, progressing through projective geometry and ultrametric topology, deriving particle generation and gauge symmetries, explaining cosmological dynamics, and culminating in an adelic unification that reveals reality as pure relation. The calculus builds all physical phenomena—from quantum particles to cosmic expansion—from syntactic operations alone, without assuming pre‑existing space, time, or substance. Each chapter adheres to a strict seven‑sentence paragraph blueprint that ensures clarity, epistemic humility, and logical progression, while lexical anti‑repetition maintains narrative dynamism. The resulting synthesis demonstrates that the universe is not a collection of objects but a single, self‑referential syntactic structure whose laws are the laws of distinction itself. The work establishes that the two reduction rules—Calling (idempotence) and Crossing (involution)—plus the void identity property suffice to generate all dynamical behavior. Projective invariants emerge as the only measurable quantities, ultrametric hierarchies explain quantum state spaces, stable normal forms correspond to elementary particles, gauge forces arise as syntactic automorphisms, and cosmological evolution reflects the geometry of adelic quotients. By consistently applying the principle that reality is syntactic, the calculus achieves a coordinate‑free description of physics that unifies number theory, geometry, and fundamental interactions. The ultimate conclusion is an adelic ontology in which every physical phenomenon maps to an arithmetic invariant, completing the vision of a universe built from nothing but distinction.
Quantum information is not intrinsically fragile; we have been measuring it incorrectly. https://www.researchgate.net/publication/403845735_Quantum_Laws_of_Form_A_Syntactic_Foundation_for_Physics_From_The_Calculus_of_Distinction_to_Ultrametric_Cosmology
Current critical literature often dismisses Large Language Models (LLMs) as statistical parrots operating via mere stochastic approximation, yet their capacity for cross-lingual zero-shot inference suggests the internalization of deep, invariant topological rules. This study establishes that semantic memory inherently relies on ultrametric topologies, and that true comprehension requires invariant structural mappings. https://doi.org/10.5281/zenodo.19564091
Projective Geometric Frameworks for Semantic Structures: Addressing the Gap Between Statistical Approximation and Formal Invariants in Large Language Models
Current critical literature often dismisses Large Language Models (LLMs) as statistical parrots operating via mere stochastic approximation, yet their capacity for cross-lingual zero-shot inference suggests the internalization of deep, invariant topological rules. This study establishes that semantic memory inherently relies on ultrametric topologies, and that true comprehension requires invariant structural mappings. To resolve this tension, we developed a computational methodology utilizing synthetic hierarchical semantic vectors, subjected to Ward’s minimum variance clustering and subsequent continuous Möbius transformations. By extracting the geometric null-space and enforcing strict cross-ratio equivalence calculations, we isolated the underlying mathematical invariants governing token representations. The computational results validate our extraction pipeline, revealing that synthetic semantic spaces can be mapped into rigid ultrametric hierarchies. Furthermore, when subjected to severe projective transformations, the analogical cross-ratio of these semantic nodes remained stable. These findings confirm that semantic proportions are geometrically immune to projective re-indexing, scaling theoretically to multidimensional tensors. The results address implications for the development of provably correct AI and critical gaps in algorithmic auditing and alignment. By demonstrating that hallucination is fundamentally a geometric error—a measurable deviation from an invariant manifold—we provide the mathematical foundation for ballistic transport on Bruhat-Tits trees. This framework shifts AI safety from opaque statistical alignment to transparent, spatial verification.
The results address implications for the development of provably correct AI and critical gaps in algorithmic auditing and alignment. By demonstrating that hallucination is fundamentally a geometric error—a measurable deviation from an invariant manifold—we provide the mathematical foundation for ballistic transport on Bruhat-Tits trees. This framework shifts AI safety from opaque statistical alignment to transparent, spatial verification.
While unifying gravity with standard gauge groups typically requires 11-dimensional string theory, syntactic token calculus achieves unification by rendering gravity a macro-cocycle condition rather than a gauge field. https://www.researchgate.net/publication/403737213_Computational_Syntax_of_Reality_Addressing_the_Continuous-Discrete_Tension_via_Syntactic_Token_Calculus
No experiment will ever detect a spin‑2 graviton as an asymptotic state. Gravitational waves are not composed of gravitons but are collective excitations of the webʼs geometry.
The fundamental division between fermions and bosons derives entirely from their syntactic behavior under cross-ratio exchange. Calculating the exchange symmetry of bosonic topologies yields the identity element, mirroring integer spin interactions. https://doi.org/10.5281/zenodo.19528343
Computational Syntax of Reality: Addressing the Continuous-Discrete Tension via Syntactic Token Calculus
The persistent reliance on continuous, substance-based ontologies in theoretical physics has precipitated a crisis of non-renormalizable infinities, demanding a radical shift toward discrete relational foundations. By shifting to an epistemic foundation built entirely on a finite substrate of relational boundaries, the Syntactic Token Calculus (STC) organically replaces these problematic geometries. This manuscript formally establishes that physical reality is derived not from pre-existing scalar fields, but from the binary syntax of the ‘Mark’ and the ‘Void’, aligning seamlessly with multiway hypergraph models. By applying universal rewrite rules—Calling, Crossing, and Void elimination—we establish a strictly normalizing, confluent Church-Rosser system. Extracting mass parameters from this discrete web requires the application of the cross-ratio metric, which acts as a non-commutative projective polynomial evaluating topological depth. Our findings computationally prove the topological necessity of the Standard Model while definitively eradicating gravitational infinities. Simulation of the mass cross-ratio maps effectively to empirical observations. Furthermore, the universal crossing rule explicitly forces the hypothesized graviton token to cancel to the Void, proving that gravity is mathematically prevented from existing as a localized particle. Addressing profound gaps in predictive mapping, the STC model strictly forecasts per-mille fractional deviations in Higgs couplings at future lepton colliders and log-periodic oscillations within the CMB angular power spectrum.