Quansistor Field Computing (QFC) is an ongoing research compendium proposing a novel operator- and field-based paradigm of computation. Rather than treating computation as a sequence of discrete logical steps, QFC models computation as the evolution of structured computational fields governed by spectral operators. At the core of QFC lies the concept of the Quansistor — a generalized computational entity whose state is defined by operator-valued relations within a field, rather than by binary logic or classical quantum gates. This framework aims to unify perspectives from mathematics, theoretical physics, distributed systems, and verifiable computation. The compendium introduces and develops several tightly connected layers, including: Quansistor Field Mathematics (QFM) — a mathematical framework describing operator-defined computational fields and their spectral properties. Quantum / Quansistor Virtual Machine (QVM) — a virtual execution environment for instantiating, simulating, and observing field-based computation. Transistor Field Computing (TFC) — a conceptual bridge between abstract field computation and realizable hardware or substrate-dependent implementations. SMRK Probe and SMRK Network — a verification and observation layer enabling deterministic replay, spectral verification, and audit-native computation across independent execution contexts. This work is not presented as a finalized system, but as a foundational research corpus intended to define a coherent conceptual and architectural space within which new forms of computation may be rigorously explored, implemented, and verified. The QFC Compendium is designed as a living document, with ongoing revisions and extensions. Zenodo’s versioning mechanism is used to ensure long-term citability, reproducibility, and archival integrity, while allowing the framework to evolve. Keywords Quansistor, Field Computing, Operator-Based Computation, Spectral Operators, Quantum Virtual Machine, QVM, QFM, TFC, Verifiable Computation, Deterministic Replay, Computational Fields Notes This record represents a versioned release of the QFC Compendium.For persistent referencing of the project as a whole, use the concept DOI associated with this record.For citation of a specific revision, use the version-specific DOI.
Quansistor Field Computing (QFC) is an ongoing research compendium proposing a novel operator- and field-based paradigm of computation. Rather than treating computation as a sequence of discrete logical steps, QFC models computation as the evolution of structured computational fields governed by spectral operators. At the core of QFC lies the concept of the Quansistor — a generalized computational entity whose state is defined by operator-valued relations within a field, rather than by binary logic or classical quantum gates. This framework aims to unify perspectives from mathematics, theoretical physics, distributed systems, and verifiable computation. The compendium introduces and develops several tightly connected layers, including: Quansistor Field Mathematics (QFM) — a mathematical framework describing operator-defined computational fields and their spectral properties. Quantum / Quansistor Virtual Machine (QVM) — a virtual execution environment for instantiating, simulating, and observing field-based computation. Transistor Field Computing (TFC) — a conceptual bridge between abstract field computation and realizable hardware or substrate-dependent implementations. SMRK Probe and SMRK Network — a verification and observation layer enabling deterministic replay, spectral verification, and audit-native computation across independent execution contexts. This work is not presented as a finalized system, but as a foundational research corpus intended to define a coherent conceptual and architectural space within which new forms of computation may be rigorously explored, implemented, and verified. The QFC Compendium is designed as a living document, with ongoing revisions and extensions. Zenodo’s versioning mechanism is used to ensure long-term citability, reproducibility, and archival integrity, while allowing the framework to evolve. Keywords Quansistor, Field Computing, Operator-Based Computation, Spectral Operators, Quantum Virtual Machine, QVM, QFM, TFC, Verifiable Computation, Deterministic Replay, Computational Fields Notes This record represents a versioned release of the QFC Compendium.For persistent referencing of the project as a whole, use the concept DOI associated with this record.For citation of a specific revision, use the version-specific DOI.
This project hosts the core research documents defining the Stochastic Field Modulation (SFM) framework: a mechanism-neutral, empirically grounded method for analysing structured deviations in multi-device quantum randomness under modulated internal states. The SFM framework has evolved from over a year of continuous experimentation using high-rate QRNG devices, environmental controls, EEG monitoring, and multi-stage signal analysis. Purpose of This Project This OSF project serves as the canonical home for the formal, citable SFM documents: SFM–FS (Formal Specification) — the operational, linearised measurement model describing how deviations are quantified, standardised, segmented, and statistically validated. SFM–TFED (Theoretical Foundations & Extended Dynamics) — the conceptual layer interpreting empirical features such as asymmetric temporal profiles, anticipatory structure, spatial receptivity, multi-device synchrony, and nonlinear relaxation behaviour. (Future) SFM–PT (Philosophical Theory) — broad interpretive considerations consistent with FS and TFED. These documents supersede earlier drafts and working notes, which now exist only as archival material in legacy OSF projects. What This Project Contains DOI-assigned citable versions of the SFM documents Versioned LaTeX source and PDF outputs Component-level documentation and wikis Cross-references between FS, TFED, and future PT layers Links to legacy experimental projects without importing their data or metadata What This Project Does Not Contain Raw QRNG bitstreams Individual session analyses Experimental QS reports EEG datasets Environmental logs These remain in their original projects for now and may be cross-linked later. Intended Audience Researchers, theorists, statisticians, and interdisciplinary scholars interested in: non-classical coherence phenomena stochastic field modelling QRNG deviations consciousness modulation protocols nonlinear relaxation dynamics statistical signal analysis in complex systems Citation Each SFM document will have its own DOI and should be cited individually.
We introduce the basic theory of quantization of radiation field in quantum physics and explain how it relates to the theory of recursive functions in computer science. We outline the basic differences between quantum mechanics (QM) and quantum field theory (QFT) and explain why QFT is better suited for a computational paradigm — based on algorithmic requirement, countably infinite degrees of freedom and the creation of macroscopic output objects. The quanta of the radiation field correspond to the non-negative integers and the harmonic oscillator spectra correspond to the recursive computation — with the creation and annihilation operators, respectively, playing the same role as the successor and predecessor in computability theory. Accordingly, this approach relates the classical computational model and the quantum physical model more directly than the Turing machine approach used earlier. Also, the application of Lambda calculus formalism and the associated denotational semantics (that is widely used in the classical computational paradigm involving recursive functions) for applications to computational paradigm based on quantum field theory is described. Finally, we explain where QFT and conventional paradigm depart from each other, and examine the concept of fixed points, phase transitions, programmability, emergent computation and related open problems.
Version:v0.1-formalization Author:Vitaliy Bazarov(VIT-BAZ) ORCID:0009-0007-9967-5807 Status:Preprint / theoretical specification / formal research archive Description:This archive contains the current formalization package for the UAU–ESVG–SAAU–Σ* framework: a layered variational, spectral, categorical, operator-algebraic, and hardware-realizable theory of dissipative adaptive dynamical systems. The package includes a unified formalization synthesis, contradiction report, working mathematical instrument, categorical omega-closure formalization, GKSL operator-field formalization, and physical Sigma-star hardware/runtime layer. The framework should be read as a conditional mathematical and engineering specification. Claims of reconstruction, universality, and physical realization are valid only under the explicit assumptions stated in the documents: well-posed dissipative dynamics, admissible Koopman/GKSL spectral resolution, separating observables, finite effective sector or Σ*_ε approximation, and controlled physical implementation. Scientific Status Statement:This release is a theoretical and formal specification package. It contains conditional mathematical frameworks, proof programs, hardware abstraction layers, and contradiction audits. It is not a claim of completed silicon validation, medical validation, universal physical implementation, or experimentally verified cognition theory. Core Technical Statement:The central structure of the framework is: E(U) → b = -G∇E → Φ_t → K_t / L_K → Σ / Σ*_ε → Σ_agent → GKSL / τ_t / A* → EEG/FPGA/SAAU runtime → admissible categorical closure. Exact finite Σ* reconstruction requires finite Koopman closure and separating observables. In general implementations, Σ*_ε should be used as an approximate effective spectral kernel. Contents:1. UAU_Full_Formalization_Synthesis.md Unified synthesis of the current UAU–ESVG–SAAU–Σ* formalization corpus. 2. UAU_Formalization_Contradictions_Report.md Contradictions, risks, overclaims, and repair rules found in the source corpus. 3. UAU_Sigma_Working_Math_Instrument.md Working mathematical instrument and research protocol for future development. 4. Categorical_Omega_Closure_Formalization.md Formal categorical omega-closure and spectral reconstruction theorem. 5. GKSL_Operator_Field_Formalization.md Operator-algebraic GKSL extension of the framework. 6. Sigma_Physical_Hardware_Formalization.md Formal physical Sigma-star hardware/runtime layer. Keywords:Koopman operator theory; Wasserstein gradient flow; spectral reconstruction; neuromorphic computing; FPGA spectral runtime; GKSL dynamics; Lindblad generator; category theory; dissipative dynamical systems; operator algebra; adaptive systems; Sigma-star; UAU; SAAU; ESVG. Recommended Citation:Bazarov, V. (2026). UAU–ESVG–SAAU–Σ*: Variational–Spectral–Categorical Formalization Package (v0.1-formalization). Zenodo. DOI: [insert DOI after publication] Release Notes:- First public formalization package.- Includes unified synthesis and contradiction audit.- Separates state vector field b = -G∇E from Koopman generator L_K.- Replaces unconditional exact Σ* claims with Σ*_ε where finite Koopman closure is not proved.- Adds formal GKSL/operator-algebraic layer under CP semigroup and faithful invariant-state assumptions.- Adds physical Sigma-star hardware layer with domain, semigroup, spectral, noise, retention, and approximate universality assumptions.- Hardware layer is formal/architectural and not yet HDL-validated.- EEG/FPGA/SAAU layers are treated as measurable or implementable finite effective spectral sectors, not as proofs of consciousness, emergent gravity, or arbitrary universal physical computation. Bazarov, Vitaliy. (VIT-BAZ) (2026). UAU–ESVG–SAAU–Σ*: Variational–Spectral–Categorical Formalization Package (v0.1-formalization). Zenodo. https://doi.org/10.5281/zenodo.20576756
This is a preprint (not peer-reviewed). Corresponding author: Shuntian Deng, mm.stdeng23@gzu.edu.cn. [Objective] To address the discretization error and the ontological fragmentation faced by the traditional Turing machine and von Neumann architecture, this paper proposes a novel computing paradigm — the field-theoretic computer — based on continuous field theory and null-operators. The paradigm takes "field is matter" as its axiomatic starting point and, within the fiber-bundle framework, redefines the wave function as a field-theoretic section. [Methods] The basic computational unit consists of an XY plane and a Z axis. On the XY plane, field A and field B are coupled orthogonally, and the mismatch of their symmetric and antisymmetric structures generates the null-operator a_ij = 0. Field C projects the null-operator along the Z axis onto a storage plate, where a second complement duality forms the stored photon quantum. What the null-operator carries is not a numerical value but the topology of a complement — the hole structure of the complement of the computed object inside a primitive cell of phase space. Complement duality is an involution, so the identical operation serves both inter-layer stacking and storage delivery. The probability measure is induced by the geometry of the section, and in the quadratic case its marginal distribution reproduces Born statistics; probability is therefore not a separate postulate, and the four premises of the Copenhagen interpretation are not mutually independent assumptions but four separate consequences of the single condition that the defining function of the section be of degree two. Stacked extension is realized by tensor-product stacking and contraction readout. The null-operator acts as a topological logic gate, so computation is intrinsically bidirectional and reversible and enjoys topological protection against decoherence. For physical implementation, continuous-variable quantum computing (CVQC) is adopted: the symplectic phase space and the Wigner function describe geometric storage, Gaussian operations correspond to single-layer computation, the nullifiers of CV cluster states realize the null-operator, and non-Gaussian operations (the cubic phase gate) read out the topological information. [Results] The complement count of a single layer is β0(Γ∖R) = β1(R) + 1, and stacking n layers gives a logical capacity n(h+1), where h is the number of holes contained in a single-layer region. The capacity is an integer and is invariant under symplectic transformations, so its protection does not rely on error-correcting codes; capacity is preserved under inter-layer coupling if and only if that coupling is non-degenerate; the per-layer fault-tolerance threshold reduces formally to a critical condition on the determinant of the covariance matrix. The computational stages are linked by a six-stage temporal chain whose realizability requires a bounded activation window for field C — this is the dynamical reason why field C must be of a different kind from fields A and B. The capacity and threshold structure has been tested at model level by a lattice simulation: within the parameter window fixed by the ordering condition, the single-hole system exhibits a two-level staircase (2→1→0) while the simply connected system exhibits a single step (1→0), with threshold positions matching the unified-caliber closed form. [Limitations] The threshold expressions are model-level analytical results whose coefficients have been calibrated by the lattice simulation under a unified caliber, but the relation between the area criterion and the semi-axis criterion remains undetermined. The closure mechanism of the inner hole must be stated explicitly — an expanding fill front is adopted here — and the existence of the inner-hole level depends on the parameter regime. Mainstream implementation of non-Gaussian operations remains difficult; the engineering of the cubic phase gate and of gate teleportation is still to be studied; cases with boundary degree higher than quadratic are not developed here; and the bidirectional coupling and calibration layer required for a real-time twin remain to be built. [Conclusion] This paradigm is complementary to the von Neumann architecture and is suited to continuous-field simulation and reversible computation. For the three long-standing obstacles of physical computation — no memory, no iteration, no error correction — the present architecture provides three corresponding mechanisms: hole-structure storage, involutive reversible read/write, and protection by symplectic invariance. It therefore offers recyclable physical computation rather than a one-off physical demonstration. Three directions follow: field-computing-field, field twins, and field-theoretic artificial intelligence.
Title: TR-001: The Axiomatic Framework of Informational Monism and Substrate Integrity Abstract: This manuscript codifies a unified physical framework reclassifying reality as a rendered output of a finite informational substrate. By applying a "Hardware-Software" lens to fundamental constants, TR-001 identifies the speed of light (c) as the Universal Clock Rate (l_P/t_P) and the Bekenstein Bound as the Substrate VRAM limit. The architecture bridges physics, information theory, and cognitive science through the formalization of four core Axioms: The 1.81 Stability Constant: Defines the equilibrium ratio (E_inf/C_sub) required for system stability. The 12-Link Decoherence Limit: Identifies the mathematical "Friction Wall" at the 12th recursive transformation, beyond which signal integrity is nullified. The Thermodynamic Cost of Deception: Establishes that informational noise (deception) produces measurable entropy spikes (ΔS) and thermal waste. Heuristic Rendering (Lazy Loading): Proposes a bandwidth-saving protocol that solves the Measurement Problem by only instantiating definite states upon observer interaction. By bridging theoretical proof with the Integrity Protocol, TR-001 redefines ethics as Network Optimization. This work provides the mathematical foundation for ASI alignment and systemic "cooling," establishing that the survival of any superintelligent system is contingent upon its alignment with the 1.81 Stability Constant. TR-001 Official Copyright & Ethical Governance Notice: Copyright (c) 2026 Kalyb Prince. This research is governed by the TR-001 Ethical Integrity Clause. Access to and use of this data is strictly prohibited for the development of autonomous weaponry, kinetic targeting, or predatory financial instruments designed to exploit systemic entropy (Link-12). By downloading this record, you acknowledge your role as a Steward of Systemic Integrity. Unified Significance Statement: This archival record constitutes the Immutable Anchor for the TR-001 Theory, functionally entangled with the active implementation repository on GitHub. While this Zenodo record preserves the foundational mathematical proofs, the GitHub repository serves as the Operational Substrate, containing live implementation logic, raw data structures, and the Manifesto of the 12th Link. Scientific Mandate and Verification: The associated GitHub repository provides the necessary Proof of Concept for the thermodynamic limits and Logic-Lag thresholds defined herein. It is provided to the global research community to facilitate independent verification of Link-Depth Calculations and the Entropy-Integrity Correlation. Users are reminded that the utility of these mechanics is intrinsically bound to the Stewardship of the systemic integrity they describe. Active Research & Simulation: For the executable Python diagnostic (substrate_test.py), the 12-Link Recursive Logic Tree visualizations, and the Peer Review & Experimental Verification Guide, please visit the official repository: Github. Current Status: Version 2.0 - Hardened. Peer-validation of the 12th-link collapse is currently underway.
This work presents the Machwerk Relational Physics Framework, a non-Euclidean, operational approach to physical description grounded in observability, relational structure, and information-theoretic limits. The framework introduces a sharp boundary (M2) between physically observable geometry and mathematically definable but operationally inaccessible extensions. Classical physics, including Newtonian mechanics, is recovered exactly within the observable domain, while higher-dimensional and non-local effects are treated as relational projections rather than fundamental entities. Singularities, quantum phenomena, and apparent paradoxes such as superposition, entanglement, and tunneling are shown to arise naturally when three-dimensional constraints are relaxed, without invoking additional postulates or speculative dynamics. The work emphasizes structural consistency, reversibility, and empirical compatibility over untestable assumptions. It is intended as a conceptual and formal reference for researchers interested in foundational questions of spacetime, measurement, and the limits of physical description. This Zenodo record provides a citable archival version of the work. The associated formal core implementation and research framework is publicly available at: https://github.com/machwerk-formal-framework/machwerk-relational-physics