Release V1.0 This preprint is the second part of the time-core series in the Gamma–Dynamic Geometry (Gamma-DG) programme.In Time-Core I (Kawanishi, 2025), time was treated as a structural object equipped with three basic roles—absolute, relative, and undefined—and organised into layers, Brūri regions, gates, and clock layers over a core time axis TcoreTcore. That framework provided an axiomatic backbone for multi-layer time, including a minimal “arrow of time’’ derived from monotone role levels along gate chains. Time-Core II: Brūri Regions and Branching Traces extends this architecture by introducing internal state spaces, dynamics, and state-annotated traces on time layers. Each layer is enriched with an abstract state space and a local time-evolution relation, and gates are equipped with state-transition relations. On top of this, the paper defines state-annotated traces that follow a single event through time and across layers while respecting the original gate axioms. Within this extended setting, Brūri regions—points where multiple layers are simultaneously visible—naturally support branching families of traces that emanate from undefined layers and end in different absolute layers. This yields a minimal, structural model of “measurement-like’’ behaviour without committing to any specific physical or probabilistic interpretation. The paper also presents relativistic-style Rel–Rel configurations (e.g., Earth vs.\ ISS viewpoints) and uses them as conceptual templates for gravitational and multi-clock scenarios. Finally, the work sketches Spin-like labels and measurement-like selection on families of branches, preparing the ground for fully fledged Spin/Brūri structures in future parts of Gamma-DG. Time-Core II should be regarded as a time-core foundations layer: a template designed to host concrete models for intuition, quantum/relativistic/gravitational viewpoints, and number-theoretic applications (such as Collatz and Goldbach) in subsequent work.
Release V1.0 This preprint is the second part of the time-core series in the Gamma–Dynamic Geometry (Gamma-DG) programme.In Time-Core I (Kawanishi, 2025), time was treated as a structural object equipped with three basic roles—absolute, relative, and undefined—and organised into layers, Brūri regions, gates, and clock layers over a core time axis TcoreTcore. That framework provided an axiomatic backbone for multi-layer time, including a minimal “arrow of time’’ derived from monotone role levels along gate chains. Time-Core II: Brūri Regions and Branching Traces extends this architecture by introducing internal state spaces, dynamics, and state-annotated traces on time layers. Each layer is enriched with an abstract state space and a local time-evolution relation, and gates are equipped with state-transition relations. On top of this, the paper defines state-annotated traces that follow a single event through time and across layers while respecting the original gate axioms. Within this extended setting, Brūri regions—points where multiple layers are simultaneously visible—naturally support branching families of traces that emanate from undefined layers and end in different absolute layers. This yields a minimal, structural model of “measurement-like’’ behaviour without committing to any specific physical or probabilistic interpretation. The paper also presents relativistic-style Rel–Rel configurations (e.g., Earth vs.\ ISS viewpoints) and uses them as conceptual templates for gravitational and multi-clock scenarios. Finally, the work sketches Spin-like labels and measurement-like selection on families of branches, preparing the ground for fully fledged Spin/Brūri structures in future parts of Gamma-DG. Time-Core II should be regarded as a time-core foundations layer: a template designed to host concrete models for intuition, quantum/relativistic/gravitational viewpoints, and number-theoretic applications (such as Collatz and Goldbach) in subsequent work.
13-Apr-2026(V1.0): Gamma-DG and the Quantum–Spacetime Bridge: Toward a Unified Structural Theory This paper develops an original structural framework, Gamma-DG, for the quantum–spacetime bridge. The central problem is not merely how to connect a quantum-primitive foundational layer and a relativistically readable spacetime layer, but how to describe a controlled, admissible, and structurally coherent passage between these distinct regimes. The paper formulates a unified perspective in which bridge formation, bridge validation, and bridge culmination are treated as successive aspects of a single theoretical program. Core I and Core II provide the foundational basis of the framework, while the present paper focuses on the minimal structural ideas needed for the current synthesis.
Modern theoretical physics rests on two highly successful but conceptually distinct frameworks: quantum mechanics and general relativity. While both theories are experimentally confirmed to high precision within their respective domains, they rely on fundamentally different starting points. General relativity takes spacetime as a primitive geometric structure, whereas quantum mechanics is formulated in terms of abstract state spaces without intrinsic spacetime meaning. Most approaches to quantum gravity attempt to reconcile this tension by modifying, quantizing, or discretizing spacetime itself. Even in approaches where spacetime is said to be “emergent,” it typically remains the primary conceptual backdrop on which physical processes are defined. Despite extensive efforts, there is no consensus on whether spacetime should be regarded as fundamental or derivative. In this work, a more radical starting point is explored. Rather than modifying spacetime or its geometry, we ask whether spacetime can be excluded entirely from the fundamental layer of the theory and recovered only at a later, operational stage. The central question is not how spacetime behaves, but whether the notion of “what lies between physical objects” must be spatial or temporal at the most fundamental level. We propose a framework—referred to here as Super Relativity (SR)—based on a single pre-geometric postulate: the existence of a monotonically expanding set of possible quantum configurations, referred to as the flux. Formally, this flux is represented as a monotone, σ-finite family of capacity measures on a common configuration space (introduced in Section 2). This postulate deliberately refrains from assuming spacetime, time ordering, metric structure, causality, or dynamics. Within this pre-geometric core, two derived, dimensionless notions are introduced: utilization, describing the realization of configurations, and saturation, defined as the ratio between utilized and available configurations. A central structural element of SR is the strict separation between a core layer and an interface layer. In the core layer, all quantities are pre-geometric and dimensionless, and no reference is made to space, time, motion, energy, or interaction. Only at the interface layer are operational notions introduced, including clocks, rulers, and signal propagation. Spacetime, in this construction, is not a dynamical entity but an effective bookkeeping structure that encodes relative rates of change once a calibration to physical units is performed. Within this framework, gravitational phenomena do not originate from spacetime curvature taken as fundamental. Instead, they arise from variations in saturation that, at the interface level, manifest as uniform rescalings of physical processes. When expressed in geometric language, these rescalings reproduce the standard predictions of general relativity, including gravitational time dilation and the equivalence between gravitation and acceleration. The invariant local speed of light is not postulated but follows as a derived consequence, since both clock rates and signal propagation are affected identically by the same underlying saturation mechanism. The aim of this paper is not to introduce new empirical predictions beyond those of general relativity, nor to present a complete theory of quantum gravity. Rather, the objective is foundational: to demonstrate that the mathematical structure of general relativity can be reconstructed from a single pre-geometric postulate without assuming spacetime as part of the fundamental ontology. In this sense, SR should be understood as a reconstruction and reinterpretation of known physics, rather than as a competing dynamical theory. An extended and fully explicit formulation of the framework, including all intermediate steps, is available in a companion preprint (version V12) deposited on Zenodo. The present paper restricts itself to the minimal conceptual and mathematical structure required to establish logical consistency and to demonstrate the emergence of general-relativistic behavior at the interface level.
A Time-Role Audit of Foundational Physics: Clock-Language Mapping Across Quantum, Classical, and Gravitational Equations (v1) This preprint presents a structural audit — a time-role decomposition — of established physical equations across quantum, classical, relativistic, and gravitational domains. All results are obtained through algebraic substitution and role labeling of existing variables. No new dynamics are introduced and no empirical predictions are altered. The paper identifies three structurally distinct roles for the variable t (background evolution, internal oscillation, propagation travel time) and maps which roles govern which physical domains across the Dirac equation, Schrödinger equation, hydrogen atom energy, de Broglie relations, Newtonian mechanics, and the Schwarzschild metric. This is Version 1 of an ongoing audit series. Open questions and failed derivation paths are explicitly documented.
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.
This paper is the thirty-second in a sequence developing an interpretive framework that redescribes physical reality as a causally consistent history of information updates rather than as a collection of independently existing objects. It opens the ninth grouping — the quantum-mechanics–gravity interface trilogy (32 Quantum Geometry → 33 Records Backreacting on Geometry → 34 Causal Structure Without a Global Order) — and is the first paper to cross Gate IV (geometry sensitivity): the metric is no longer a fixed background but a quantum degree of freedom. Papers 8 and 31 localized records relationally but on one fixed geometry, where a frame-change groupoid on the shared space made localization objective. When the geometry is itself superposed there is no physically privileged cross-branch map — a common manifold, if used, is mathematical scaffolding, not a physical identification — so that groupoid has no physical domain, and a tempting shortcut appears: compare the branches on one external background and read "the same event" off coordinate coincidence. The claim is that there is no Global Background. The hole argument's lesson — that a record-formation event is individuated by relational coincidences and what is recorded there, not by a manifold point (Einstein's point-coincidence resolution; Stachel, 2014; Rovelli, 2002) — does not merely survive into the quantum case; it sharpens into a problem no background can solve: across inequivalent geometry branches even the relational strategy must be carried by a declared, admissibility-constrained comparison map. Throughout, an event is a record-formation event, kept type-distinct from the record token and from its provenance; unrecorded events are out of scope. The flagship R-A is a separation, not a denial: there is a two-branch geometry-superposition state for which the background-label map (a presentation artifact identifying events by the external labels used to write the branches down) and the admissible relational/provenance comparison return different verdicts, and only the latter is invariant under relabeling. So event identity is not background-readable; primitive identity gives way to identity under an admissible comparison map, where admissibility requires relabeling/gauge-invariance, a support (witness-neighborhood) condition, provenance preservation, anti-gerrymander, and challenge-openness — and the background-label map is the foil, not one admissible map. A worked finite model — two branches presented as record-coincidence graphs with no shared vertex set, including a harder case with the same labels and same contents but non-isomorphic structure — computes the divergence and the determinate / admissibly-open / incomparable trichotomy. R-B extends Paper 31's localization profile to a geometry-indexed GeoLocProf that strictly generalizes it (Paper 31 is the single-geometry degenerate case), built over an identity fiber rather than treating one event as recurring in several branches. R-C lifts the disposition trichotomy to geometry branches. R-D handles region and local-algebra correspondence as induced-where-possible or declared/deferred. This crosses Gate IV, carries Paper 9's record arrow into the interface as a provenance-compatibility clause, retires the Global Background, and hands backreaction to Paper 33 and causal order to Paper 34. Geometry is quantum; its dynamics is not derived. ALAC Paper 32. First panel of the ninth grouping — the quantum-mechanics–gravity interface trilogy (32 Quantum Geometry Without a Global Background -> 33 Records Backreacting on Geometry -> 34 Causal Structure Without a Global Order). Part of the Consistency-Constrained Information History (Akashic Ledger Architecture Cosmology) series. Presents no new quantum mechanics or gravitation; results are interpretive (L2) on imported physics (L1).
From Phase to Spacetime (Phase Ontology — Part II) develops the central consequence of Part I (Phase Without Ontology): if phase coherence is treated as an ontologically primary layer, then spacetime cannot be fundamental. This paper proposes a conceptual pathway by which temporal order, spatial geometry, and gravitational effects can be understood as emergent structures arising from stable phase relations—without introducing new dynamics or speculative entities. The core move is operational: clocks are oscillators, and what we call “time” is the comparison and synchronization of counted cycles across systems. Temporal order appears where phase relations are stable; divergence in clock rates appears where coherence conditions vary. In this framework, proper time corresponds to a system’s internal phase evolution, and relativistic phenomena (time dilation, gravitational redshift) are reinterpreted as changes in phase evolution induced by coherence gradients. Spatial distance and geometry are treated as doubly derivative: they are inferred through timing relations, synchronization procedures, and stable relational structure across extended systems. Uniform coherence yields an effectively “flat” geometry; varying coherence yields curvature-like behavior. The paper also sketches how inertia and acceleration can be viewed as resistance to reconfiguring phase-locked relations, aligning naturally with the equivalence principle. This work is Part II of a seven-part series that reframes foundational problems—unification, measurement, nonlocality, and the status of time—through the lens of phase coherence. Part III addresses measurement and classical definiteness; Part VII discusses experimental implications and falsifiability.