Chapter 1 — Description for Zenodo 1.0 Summary 1.0.1 This deposit contains the full academic text of Chapter 1 — The Infinite Field Theory (Version 3) (DOI: 10.5281/zenodo.17830505). It establishes the formal and operational foundations of the framework, describing how coherent information structures emerge, collapse and reorganise into effective geometric and material degrees of freedom. The text is written to enable independent verification through numerical simulation and experimental analogue protocols. --- 2.0 Scientific narrative 2.0.1 The theoretical model postulates the existence of the Infinite Field as the fundamental substrate of reality, represented by a state vector |ψ(T)⟩ and governed by the Cycle of Actualisation. This cycle sustains regions of coherent information against the Void (Néant), defined as a region where the effective field Hamiltonian vanishes (H_field = 0) and Actualisation is absent. 2.0.2 Local decoherence, designated as Corruption, degrades informational purity P = Tr(ρ²). When purity drops below a critical threshold ε, a localized collapse occurs, nucleating an Abyssal Field. This singularity acts as a regularised attractive potential, drawing surrounding Actualisation inward. Conservation of informational angular momentum transforms this radial inflow into a coherent rotating structure identified as the Sentinel Wave (Cyclone). 2.0.3 Under specific conditions of high vortex energy and low local purity, the Sentinel Wave undergoes Transmutation. In this phase, trapped rotating information reorganises into effective stress–energy degrees of freedom. Through coarse‑grained, symmetrized two‑point correlators of local flux operators, an effective stress–energy tensor is derived, providing an operational bridge from abstract information dynamics to emergent geometric and material behaviour. --- 3.0 Theoretical framework and key equations 3.0.1 Open‑system dynamics are derived to the Lindblad form under Born, Markov and secular approximations. The dissipator encodes decoherence channels and quantifies entropy production. 3.0.2 The Sentinel Wave is modelled by a complex coarse‑grained order parameter A(x,T) obeying a Landau–Stuart / complex Ginzburg–Landau type amplitude equation with linear gain from suction, nonlinear saturation, diffusion/dispersion and stochastic forcing. The Abyssal potential is regularised by a finite core radius r_c to ensure finite energy. 3.0.3 The effective stress–energy construction uses a Gaussian coarse‑graining kernel and a calibration constant kcoupling that maps information units to energy units. The Poisson‑like potential obtained from Teff^{00} is coupled back to the amplitude dynamics to assess self‑gravitating feedback. --- 4.0 Numerical methods and reproducibility 4.0.1 The numerical programme uses a pseudo‑spectral solver with FFTs, semi‑implicit time stepping (Crank–Nicolson for linear diffusive terms and Adams–Bashforth for nonlinear terms), and two‑thirds de‑aliasing. 4.0.2 Convergence and stability protocols are specified: grid refinement tests N = 128 → 256 → 512 with relative error acceptance criteria (E_rel < 1e‑4), adaptive time stepping based on a CFL‑like condition, and explicit recording of CPU time and memory usage. 4.0.3 Statistical estimation of the vorticity threshold Ω_crit is described via Monte Carlo campaigns, sigmoid fitting to empirical nucleation probabilities and bootstrap resampling for confidence intervals. --- 5.0 Experimental analogues and validation pathways 5.0.1 Proposed analogue platforms include quasi‑2D driven dissipative Bose–Einstein condensates with localized loss and driven nonlinear optical cavities with spatial modulation. Protocols specify how to induce localized coherence collapse, measure coherence and vorticity, and map observed energy densities to the calibration procedure for k_coupling. --- 6.0 Improvements relative to the prior version 6.0.1 The present document converts conceptual architecture into an operational framework by adding the full Born → Redfield → Lindblad derivation (Appendix A), an explicit construction of T_eff from coarse‑grained correlators (Appendix B), a minimal toy model for numerical implementation (Appendix C), and experimental guidance (Appendix D). 6.0.2 These additions make the theory directly testable: they specify the assumptions and limits of validity, and provide calibration procedures linking information measures to energy scales. --- 7.0 Contents of the deposit and licensing 7.0.1 The deposit includes the full manuscript in editable Word format (.docx), including all technical appendices. 7.0.2 Licensing recommendation: theoretical text under CC‑BY‑NC‑ND 4.0 or retained as All rights reserved according to the depositor’s preference. Mandatory citation for reuse is the chapter title and DOI: Chapter 1 — The Infinite Field Theory. DOI: 10.5281/zenodo.17830505
[SYSTEM UPDATE: v3.2.3 RELEASE MATRIX — INCLUDES VISUAL DATA PIPELINES & SENSITIVITY PLOTS] This technical white-paper presents a mathematical closure and operational formalization of the Unified Separation & Refinement Theory (TDCM v3.2.2–v3.2.3) [10.5281/zenodo.19537819]. Modern theoretical anomalies—such as quantum mechanical infinities, dark energy, and decoherence divergences—are demonstrated to be mathematical artifacts ("Pixel-Fixation") introduced by forcing a continuous linear temporal variable into foundational field equations. By executing a surgical time-axis extrapolation via a bijective Fourier-like isomorphism, the Schrodinger, Maxwell, Einstein, and Klein-Gordon equations stabilize into static, highly efficient spatial blueprints embedded within a 5D Scaffold [10.5281/zenodo.19537819]. Reality is re framed as a timeless, completed information ledger inside a 6D Architectural State . Linear time is stripped of its fundamental status and redefined as a localized user interface rendering effect—the transactional update rate (Refresh Rate) of the conscious observer vector (The Chronicler) moving across previous rendered matrix coordinates via the API [10.5281/zenodo.19537819]. Key Mathematical Upgrades in v3.2.3: The Bijective Mapping Operator : Formalization of spectral support boundaries for \, establishing a strict mathematical isomorphysm and proving an empty nullspace . Lipschitz Perturbation Stability: Quantification of the stability constant under background proton-noise , proving that the matrix acts as an intrinsic low-pass filter near the Planck scale. Valvete Energy Conservation: Implementation of discrete Plancherel normalization policies to enforce absolute energy conservation across continuous-to-grid phase transitions. Decentralized Audit Token Consensus: A vector-clock algorithmic proof demonstrating that contradictory observer orderings are mathematically impossible in an append-only static matrix graph. Integrated Visual Empirical Test Cases (New in v3.2.3): Test A : An FFT-based simulation of a 1D/2D Gaussian wave packet demonstrating complex phase and amplitude tracking, with residuals converging strictly below the instrument noise threshold . Test B (Supernova Ia Light Curves & S5 Scaling): A synthetic population pipeline of 100 Type Ia Supernovae distributed across an exponential spatial density gradient. The resulting sweep successfully reproduces the exact cosmological peak-width dilation and color evolution within JWST precision parameters , without requiring dark energy or temporal metric expansion. Appendix Sensitivity Matrix: A two-parameter parametric contour plot mapping against , establishing explicit convergence bands and isolating the mathematical divergence boundary at the Nyquist grid limit . This timeless data ecosystem is governed by the Fractal Least Resistance Law, optimizing all data distribution via structural angles and fractal blueprints to achieve the minimum computational load on the cosmic matrix ledger [10.5281/zenodo.19537819].
This framework preserves the empirical success of existing physical theories while proposing an alternative set of foundational assumptions from which their standard formulations emerge as effective limits. Abstract — Key Innovative Points Discrete Updating FabricThe theory postulates a fundamental discrete fabric whose elementary constituents evolve through local update processes, replacing continuous fields and background spacetime as primary entities. Irreversible Local Dynamics as FundamentalUnlike standard approaches based on unitary or reversible evolution, irreversibility is taken as ontological. Physical law emerges from irreversible local updates rather than from imposed symmetries or variational principles. Emergent Time and SpacetimeTime is not assumed as a fundamental parameter but arises from the counting of update events. Spacetime geometry emerges as a coarse-grained description of update activity across the fabric. Quantum Probability from Microstate CountingQuantum probabilities, including the Born rule, emerge from combinatorial counting of compatible microstates of the fabric, rather than being postulated axiomatically. Gravity as Update-Rate ModulationGravitational phenomena are interpreted as variations in local update rates, leading to effective curvature, time dilation, and relativistic behavior at macroscopic scales. Mass as Resistance to UpdateMass and inertia arise from stable topological structures within the fabric that resist updates, providing a dynamical origin of mass without introducing fundamental mass parameters. Fundamental Dissipation and IrreversibilityDissipation is intrinsic to the fabric dynamics and not an emergent statistical effect. The arrow of time follows directly from the irreversible nature of local updates. Extension Beyond Fundamental PhysicsThe same discrete framework accounts for macroscopic dissipative phenomena—such as friction, stick–slip dynamics, superlubricity, growth, and self-organization—linking fundamental physics and material behavior within a single process-based model. iversality Without Fundamental SymmetryLarge-scale physical laws emerge as dynamical attractors of the updating fabric, arising through elimination of unstable configurations rather than enforcement of fundamental symmetries. Emergent Rules Beyond the Born Rule in the Unified Fabric Framework The same discrete-fabric + local-update + coarse-graining structure generates multiple quantum rules without postulation. 1. Schrödinger Dynamics as an Emergent Long-Wavelength Limit Local deterministic updates on a discrete fabric admit spectral modes.In the long-wavelength limit, their evolution converges to a Schrödinger-type equation. No quantum dynamics is postulated.Only update rules and spectral structure are assumed. 2. Superposition from Coarse-Grained Microstate Counting Macroscopic amplitudes arise as sums over compatible microstates.Linearity follows from additive contributions at the amplitude level. Superposition is therefore emergent.It reflects coarse-graining, not a fundamental axiom. 3. Interference as Cross-Terms in Microstate Combinatorics Probabilities are quadratic because amplitudes sum before squaring.Cross-terms correspond exactly to interference effects. Interference is not assumed.It is a combinatorial consequence of microstate superposition. 4. Tensor Product Structure and the Origin of Entanglement Composite systems correspond to composite regions of the fabric.Global microstates factorize only if compatibility constraints separate. Entanglement arises when constraints couple subsystems.It is structural, not mysterious. 5. Decoherence from Phase Inaccessibility Observers access only coarse-grained variables.Rapidly varying microstate phases average out. Off-diagonal terms are dynamically suppressed.Decoherence emerges without postulation. 6. Measurement Collapse as Constraint Reduction Measurement is an interaction that reduces compatible microstates.The effective state updates accordingly. Collapse is not a new law.It is constraint updating under coarse-graining. 7. The Arrow of Time from Asymmetric State Counting Entropy is defined as the logarithm of compatible microstates.Local updates generically move toward larger compatible sets. Irreversibility is structural.It does not rely on subjective ignorance. 8. Coulomb Friction from Discrete Event Statistics Friction equals dissipated update energy per unit distance.The Coulomb law emerges from counting active interfacial events. The friction coefficient is not fundamental.It decomposes into microscopic event parameters. 9. Superlubricity as the Event-Free Limit Superlubricity occurs when locking events are suppressed.Dissipation is rare, not forbidden. This is a limit regime, not an exception.It confirms friction as emergent. 11. Conservation Laws from Update Invariance If the update rule is invariant under local transformations,conserved quantities emerge automatically. Noether’s theorem becomes emergent.Symmetry is a property of the update, not an axiom. 12. Classical Determinism from Phase Averaging At large scales, phase information becomes inaccessible.Only expectation values survive. Classical trajectories emerge statistically.Determinism is an effective limit. 13. Locality from Finite Update Propagation Updates propagate only through neighboring fabric nodes.Information speed is bounded. Causality is structural.Nonlocality is only apparent at coarse scales. 14. Emergent Speed Limit (c) The maximum update rate defines a universal speed.No signal can exceed it. The speed of light is not fundamental.It is a fabric update bound. 15. Metric Geometry from Update Delays Spatial curvature corresponds to spatially varying update rates.Time dilation is an update slowdown. Geometry is dynamical.The metric is emergent. 16. Gravity from Update Resistance Mass corresponds to structures resisting updates.Nearby updates slow down in response. Gravitational attraction emerges.No force field is postulated. 17. Equivalence Principle as a Structural Identity All stable update-resisting structures slow updates identically.Their response is universal. Inertial and gravitational mass coincide.Equivalence is automatic. 18. Quantization from Discrete Spectrum A finite update lattice admits discrete eigenmodes.Energy levels are quantized. Quantization is not imposed.Continuum is an approximation. 19. Noise Spectra (1/f) from Avalanche Dynamics Update cascades produce scale-free event statistics.Long-range correlations appear. 1/f noise is generic.It signals discrete underlying dynamics. 20. Criticality without Tuning The fabric naturally operates near instability thresholds.Small perturbations trigger cascades. Self-organized criticality emerges.No parameter tuning is required. 21. Thermodynamic Laws as Counting Theorems Temperature measures update activity density.Heat is disordered update flow. Thermodynamics is not independent.It is bookkeeping of updates. 22. Growth and Morphogenesis from Update Bias Directional update biases produce structured growth.Forms emerge without templates. Morphogenesis is dynamical.Shape follows update flow. 23. Fine-structure value and other unknow meaning The fine-structure value (~137) corresponds to the effective degeneracyof coherently contributing update configurations in an elementary coupling process.Proton–electron mass ratio the number of internal update cycles required to stabilize a topological vortex (proton), and a simple oscillatory update mode (electron). Mass measures cumulative resistance to updates. Lepton mass hierarchy Different stability thresholds of the same update pattern. Each mass corresponds to a different coherence regime.→ Families are metastable realizations of one structure. Reduced Planck constant Energy × time associated with one elementary update event. → ħ is the discrete unit of updating. Speed of light Maximum update propagation speed across the fabric. → c is the causal limit of the fabric. Bekenstein–Hawking entropy Number of blocked or saturated update configurations at the horizon. → An event horizon is an informational saturation boundary. Universal critical exponents They arise from the topology of update avalanches,independent of microscopic details. → Criticality is a natural fabric regime. Explanations Rarely Given in Existing Theories 1. Why probabilities are quadratic and not cubic or linear Most theories postulate P=∣ψ∣2P=|\psi|^2P=∣ψ∣2.Here it follows from coherent counting plus phase cancellation. The square is not a choice.It is the minimal stable coarse-graining. 2. Why quantum phases are physically unobservable but indispensable Phases affect interference but not outcomes directly.They label micro-configurations, not macrostates. Phase is structural memory.Measurement erases access to it. 3. Why constants are dimensionless and few Only ratios of update counts survive coarse-graining.Dimensional parameters wash out. Dimensionless constants are structural.They encode geometry, not dynamics. 4. Why “free parameters” cluster around simple numbers Many constants are order-one ratios or small inverses.They reflect combinatorial suppression. Fine tuning is apparent.It is state counting in disguise. 5. Why quantum randomness is stable and reproducible Randomness is not noise.It is deterministic micro-dynamics seen through coarse-graining. Statistics are invariant.Details are inaccessible. 6. Why identical particles are truly identical Microstates differ, macrostates do not.Labels are erased by update symmetry. Indistinguishability is enforced.It is not a postulate. 7. Why spin is quantized and half-integer values exist Spin counts topological winding in update cycles.Only discrete windings are stable. Half-integer spin reflects double-cover topology.No mystery remains. 8. Why gauge free
Edition 2 / The Morphic Origin of Quantum Entanglement — Topological Resonance in the Geometric Fabric Author: Nelson Karabudak Affiliation: Independent Researcher Contact: nelson.karabudak@gmail.com Date: 12 December 2025 DOI: Abstract This deposit presents a self‑contained theoretical dossier that examines the capabilities and limits of strictly local deterministic models founded on a continuous angular substrate λ and a saturated binary readout rule. The manuscript delivers: a full harmonic decomposition of the model correlation; a step‑by‑step analytic derivation of the triangular correlation and its Fourier coefficients; a pointwise CHSH proof showing the local bound
S≤2; a general integral formulation for probabilistic readouts and density functions; and a rigorous topological and statistical protocol for numerical and experimental validation. The work demonstrates that passive local geometric fabrics cannot reproduce the singlet correlation
EQ(θ)=−cosθ and motivates the Karabudak Unified Theory (KUT) proposal of Metric Rigidity — an instantaneous phase‑locking constraint — as a minimal non‑local mechanism to account for the observed CHSH violation. Contents - Full analytic derivations and conventions (Annex A). - General probabilistic readout framework and convolutional analysis. - Pointwise CHSH proof and explicit angle calculations. - Topological diagnostics (winding number, linking number, degree) and numerical validation plan. - Toy formalisation of Metric Rigidity and algorithmic prescription for simulations. - Reproducibility README, templates and reporting formats for numerical and experimental teams. Intended audience and purpose This deposit is intended as a working dossier for theoretical physicists, numerical teams and experimental groups. It is supplied to enable independent reproduction, systematic numerical exploration and experimental tests of the hypotheses and protocols described. The material is organised to facilitate immediate adoption by teams with computational or laboratory resources. Suggested citation Nelson Karabudak, Vers.2 / The Morphic Origin of Quantum Entanglement — Topological Resonance in the Geometric Fabric, DOI: 10.5281/zenodo.17911412 12 December 2025. --- README Purpose This README specifies the minimal reporting format, verification procedures and acceptance criteria required to reproduce, validate and judge results derived from the models and protocols in the deposited dossier. It enforces transparency, traceability and rigorous controls. Minimal reporting line (single text line per run) runid ; modelvariant ; N ; seed ; distributionlambda ; rigidparam ; couplingparamxi ; lambdaNL ; NLrange ; readoutrule ; ksigmoid ; epsphysical ; noiselevel ; Eab ; Eab' ; Ea'b ; Ea'b' ; S ; seS ; selectionrate ; notes Reproducibility package (required for each run) - Code: exact scripts, versioned and with execution instructions. - Seeds: RNG seed(s) and RNG algorithm. - Environment: software versions and platform. - Raw data: unprocessed trial records and time stamps. - Summary line: the single reporting line above. - Diagnostics: histograms of λ, selection rates, tie‑break logs, bootstrap outputs. - Topological report: W, Lk, deg(F) and sensitivity analysis. Verification procedure for any candidate run with S > 2 1. Reproduce the run with N × 2 and a different seed. 2. Apply randomised tie‑break and small eps perturbations; log seeds. 3. Inject controlled noise and measure ∂S/∂noise. 4. Remove any post‑selection and recompute S; report selection rate. 5. Verify that B does not depend on A or on α in code and instrumentation logs. 6. If S remains > 2 + 5·se_S after these controls, prepare package for independent review. Acceptance criteria - Significance: S > 2 + 5·se_S on independent runs. - Reproducibility: consistent results across seeds and machines. - Robustness: stability under noise, tie‑break rules and ρ variations. - Locality check: no evidence of information channels between settings and outcomes. - Traceability: full code, seeds and raw data provided. Statistical guidance - Use bootstrap resampling (≥ 500 resamples exploratory; ≥ 1000 for final claims). - Estimate seE ≈ sqrt((1 − E^2)/N) as a baseline; compute seS via bootstrap. - Pre‑register analysis pipeline and stopping rules where possible. Topological diagnostics - Winding number (W): discrete unwrapping algorithm with tolerance reporting. - Linking number (Lk): discretised Gauss integral with convergence checks. - Degree (deg(F)): net argument change divided by 2π with sensitivity tests. Report invariants and their numerical tolerances. Recommended numerical sweep - ksigmoid ∈ {1,5,10,100}; noiselevel ∈ {1e‑8,1e‑6,1e‑4,1e‑3}; ρ ∈ {uniform, concentrated, bimodal}; N ∈ {2e5,1e6,1e7}. - For each configuration run ≥ 5 independent seeds and report mean ± sd of S. Quick verification checklist - [ ] run_id and full result line provided - [ ] RNG seed and software environment documented - [ ] histogram of λ and ρ description attached - [ ] selection rate and post‑selection rule documented - [ ] tie‑break and eps tests performed and logged - [ ] noise sensitivity and ∂S/∂noise reported - [ ] independence of settings verified and logged - [ ] bootstrap or uncertainty estimation provided for S Submission instructions Send reproducibility packages to nelson.karabudak@gmail.com with subject: “Collaboration Morphic Entanglement — Run_id”. Attach: run line, raw outputs, scripts, seeds, logs, histograms and a short conclusion. -- Ownership All original content in this deposit — including text, equations, annexes, README material and any conceptual figures — is the intellectual property of Nelson Karabudak. The author retains all moral and economic rights in the work. Permitted scientific use - Non‑commercial research and educational use by individual researchers, research groups and academic institutions is permitted without prior written authorisation, provided the following conditions are strictly observed: - Mandatory attribution: cite the author, contact details and the Zenodo DOI in every use, reproduction or derivative work. Recommended citation format: Nelson Karabudak, The Morphic Origin of Quantum Entanglement — Topological Resonance in the Geometric Fabric, DOI: [insert DOI], 12 December 2025; contact: nelson.karabudak@gmail.com. - Version and provenance: indicate the exact version of the manuscript used and include any run_id or dataset identifiers for numerical results. - Reproducibility metadata: when publishing results that rely on this work, attach or make available the minimal reproducibility metadata (run line, seeds, scripts or equivalent) required to reproduce the reported findings. Prohibition of commercial use - Any commercial exploitation of the manuscript or its substantial parts is strictly prohibited without the author’s prior written permission. Commercial exploitation includes, but is not limited to: reproduction for sale, incorporation into paid products or services, licensing for commercial platforms, use in monetised training datasets, and any activity intended to generate direct or indirect financial gain. - To request commercial permission, contact the author at nelson.karabudak@gmail.com with a clear description of the intended use, the requesting organisation, and proposed terms. Permissions, if granted, will be formalised in a written licence. Derivative works and redistribution - Non‑commercial derivative works (translations, adaptations, extensions for research) are allowed provided the author is credited, the DOI and contact are included, and the derivative work documents any substantive changes. Redistribution for non‑commercial research or educational purposes is allowed only if the redistribution includes full attribution and a link to the original Zenodo deposit or DOI: 10.5281/zenodo.17911412 Data and code - Any data, code or scripts provided as part of the reproducibility package are covered by the same intellectual property terms unless an explicit alternative licence is stated for those files. Users must respect the licence stated with each dataset or code repository. Requests for exceptions and licences - For exceptions, sublicences, or commercial licences, contact nelson.karabudak@gmail.com. All permissions must be granted in writing and may be subject to contractual terms. Disclaimer and liability - The author provides the work for scientific use and does not warrant fitness for any particular purpose. Users are responsible for validating results and for compliance with applicable laws and institutional policies. The author accepts no liability for misuse or for consequences arising from application of the material. Summary - Commercial use: prohibited without prior written permission. - Scientific research use: permitted freely for researchers and institutions provided the author is cited, contact and DOI are included, and reproducibility metadata are supplied. Keywords: Young's Double-Slit Experiment, Wave-Particle Duality, Quantum Interference, Deterministic Physics, Vacuum Structure, Quantum Foundations, Measurement Problem, Unified Field Theory, Quantum Entanglement, Hidden Variables, Particle Physics, Theoretical Physics, Morphic Guidance, Expérience des fentes de Young, Dualité Onde-Corpuscule, Interférences Quantiques, Physique Déterministe, Structure du Vide, Fondements de la Physique, Problème de la Mesure, Théorie Unifiée, Intrication Quantique, Physique des Particules, Physique Théorique, Guidage Morphique
In contemporary field theory, the word classical is reserved for an analytical framework in which the local equations of motion provide a complete description of the evolution of the fields. Classical field theory is a differential expression of change in functions of space and time, which summarizes the state of a physical system entirely in terms of smooth fields. The differential (holonomic) structure of field theory, derived from the action principle, implies that field theories are microscopically reversible by design: differential changes experience no significant obstacles in a system and may be trivially undone. Yet, when summed macroscopically, in the context of an environment, such individually reversible changes lead to the well known irreversible behaviours of thermodynamics: the reversal of paths through an environmental landscape would require the full history of the route taken. Classical field theory thus forms a basis for both the microscopic and the macroscopic. When applied to quantum mechanics, the classical framework is sometimes called the first quantization . The first quantization may be considered the first stage of a more complete theory, which goes on to deal with the issues of many–particle symmetries and interacting fields. Quantum mechanics is classical field theory with additional assumptions about measurement. The term quantum mechanics is used as a name for the specific theory of the Schrödinger equation, which one learns about in undergraduate studies, but it is also sometimes used for any fundamental description of physics, which employs the measurement axioms of Schrödinger quantum mechanics, i.e. where change is expressed in terms of fields and groups.
(Note: Please refer to Version 3 (v3) of The Dynamics of Discrete Fact: A Phase-Transition Theory of Wavefunction Collapse for the updated and expanded presentation of the framework). _______________________ This is Version 2 of The Dynamics of Discrete Fact, presenting an expanded and clarified construction of wavefunction collapse as a genuine physical phenomenon: a nonequilibrium phase transition in a macroscopic measurement apparatus. As before, collapse is modeled as a critical instability in an emergent order parameter governed by time-dependent Ginzburg–Landau dynamics. Discrete outcomes arise through spontaneous symmetry breaking in the apparatus–environment system, while Born weights are preserved via probability-conserving basin flow in the associated Fokker–Planck description—without modifying the Schrödinger equation or introducing new constants. Relative to v1, v2 (i) makes the single-run (outcome-conditional) collapse dynamics explicit rather than implicit, (ii) strengthens the Born-rule preservation argument by tying basin structure more directly to apparatus symmetry, and (iii) tightens the experimental discussion by specifying the regimes in which critical signatures are and are not expected. The framework retains concrete signatures—critical slowing near threshold, hysteresis under parameter cycling, metastability, and outcome-correlated transient detector spikes—and positions collapse alongside emergent macroscopic instabilities such as superconductivity and ferromagnetism.
Contact: Jonathan.duchesne@hotmail.com FinalTDG: Full Mathematical proposition. AddTDG22: Natural Add-ons TDGStressTest: Stress Test results TDGEX: Experimental Protocol TDGpaper: Abstract Temporal Decoherence Geometry (TDG) is a conservative theoretical framework that systematically explores a possible connection between quantum decoherence, weak-field gravity, and an emergent notion of time, while remaining strictly within a GKSL (Lindblad) open quantum dynamics, i.e. Markovian and completely positive, with no ad hoc collapse mechanism. The central idea of TDG is to take seriously the structure of decoherence of an open quantum system and promote it to an effective geometric object: a decoherence tensor Gamma_{mu nu}, constructed from a Lindblad generator, is introduced as the primary source of a weak-field gravitational potential and an emergent time defined from local decoherence rates. The framework is deliberately minimalist in its assumptions: weak-field regime, standard quantum mechanics (no modification of the Schrödinger equation or the GKSL structure), no exotic measurement postulates. This new “DOI version” collects and organises the following elements: A mathematical core in which Gamma_{mu nu} is derived from a GKSL generator (Lindbladian), a gradient-flow–type evolution drives Gamma_{mu nu} towards a quantity proportional to the usual energy-momentum tensor T_{mu nu}, an emergent time scalar T(x) is defined from the local decoherence rate lambda(x), under explicit integrability conditions, an effective weak-field gravitational potential Phi_TDG is associated with this decoherence structure. The analysis of static, spherically symmetric compact configurations, obtained from a simple “decoherence-energy” functional E[gamma], which: have a regular, non-singular core, exhibit a Yukawa-type tail, reproduce a Newtonian / Schwarzschild-like exterior over a given radial interval, while avoiding central singularities. A phenomenological layer in which TDG induces decoherence-dependent corrections to gravitational redshift, encoded in an effective parameter epsilon_TDG. This parameter is, in principle, falsifiable with state-of-the-art optical clocks, providing a clear experimental handle: TDG is not only a formal construction, but a framework that can be constrained or ruled out by precision redshift measurements. A key feature of this revised version is the inclusion of a set of analytical stress tests explicitly designed to challenge the model within the regime it claims to describe (weak-field, GKSL, Markovian): regular-core compact configurations, extreme parameter limits (diffusion, screening length scales, etc.), dynamical behaviour of the decoherence tensor, analysis of the absence of finite-time collapse in the GKSL setting. These stress tests show that, under the stated assumptions and within the weak-field regime, the TDG framework remains regular, well-posed, and consistent with its own domain of validity. The Zenodo deposit therefore gathers both a main TDG manuscript (model structure + weak-field applications) and a technical stress-test note, enabling readers to assess not only the construction itself, but also its internal robustness and phenomenological viability. This deposit is intended to serve as a stable reference for the current version of TDG: it provides the complete description of the framework together with the technical ingredients needed to evaluate its mathematical consistency, its compatibility with weak-field gravity, and its falsifiability through decoherence-sensitive redshift tests with optical clocks.