This paper develops a phase-centered tunneling framework that is deliberately positioned as a bridge theory rather than a claimed final unification of quantum theory and relativity. The starting point is a PWD-inspired background phase field whose gradient defines a null causal skeleton. The missing ingredient is the forbidden-region sector: under a barrier, real classical trajectories fail, the eikonal must complexify, and attenuation becomes unavoidable. The central move of the paper is therefore to place a minimal complex-action fluctuation sector on top of the null background, while keeping a strict separation between the background phase gradient Kµ = ∇µΘ and the physical fluctuation momentum Pµ = ∇µS − qAµ. An auxiliary null direction defines a screen-space geometry in which attenuation can be written as a covariant closure without opening a new causal cone.The conceptual claim is narrow but strong. The relativistic contact is not a literal identification between an imaginary Lorentz factor and an imaginary tunneling momentum. It is the structural statement that both relativistic edge cases and forbidden-region quantum dynamics require a complex phase-action description once a naive real-trajectory picture collapses. This immediately yields a1local-universality/global-selectivity principle: the local Airy/Stokes machinery near simple turning points remains standard, whereas genuinely PWD-selective content should first appear in globally organized multi-turning-point observables such as resonance shifts, linewidth modulation, and phase-memory effects.The manuscript is tested at three levels. First, exact one-dimensional Schrodinger and Klein-Gordon barriers recover the expected large-thickness attenuation slope and the expected dominance of the imaginary under-barrier wavevector, establishing consistency rather than novelty. Second, the paper formulates an explicit empirical protocol for deciding whether a putative PWD signal is real: penalized model comparison, parameter identifiability, holdout stability across neighboring resonances or geometry sweeps, digitization-perturbation robustness, and negative controls that should return vanishing correction coefficients. Third, the paper includes exact source-level operational comparisons on two publisher-plate target-corpus panels aligned with the theory’s predicted first battlefields: a Kobos linewidth panel and a Schmidt geometry/asymmetry panel. In both cases, a minimal phase-organization proxy outperforms the corresponding baseline under RMSE, MAE, AIC, and BIC. These results do not yet constitute the final low-parameter direct δΦPWD /δAPWD theory fit, but they move the proposal beyond a purely future-facing benchmark plan.The resulting picture is disciplined. The framework isolates a mathematically coherent contact surface between null causal organization and forbidden-region attenuation, embeds that contact surface in a screen-supported complex-action EFT, and identifies precise observables on which the theory can fail. What remains open is equally explicit: the attenuation sector is still a leading-order effective closure rather than a completed microscopic derivation, higher-order coefficients remain to be fixed, and decisive empirical status requires direct low-parameter fits that survive robustness and holdout tests. The strongest defensible claim is therefore that a falsifiable bridge framework has been constructed and partially anchored at the exact source level, not that a completed final unification has already been achieved.
This paper develops a phase-centered tunneling framework that is deliberately positioned as a bridge theory rather than a claimed final unification of quantum theory and relativity. The starting point is a PWD-inspired background phase field whose gradient defines a null causal skeleton. The missing ingredient is the forbidden-region sector: under a barrier, real classical trajectories fail, the eikonal must complexify, and attenuation becomes unavoidable. The central move of the paper is therefore to place a minimal complex-action fluctuation sector on top of the null background, while keeping a strict separation between the background phase gradient Kµ = ∇µΘ and the physical fluctuation momentum Pµ = ∇µS − qAµ. An auxiliary null direction defines a screen-space geometry in which attenuation can be written as a covariant closure without opening a new causal cone.The conceptual claim is narrow but strong. The relativistic contact is not a literal identification between an imaginary Lorentz factor and an imaginary tunneling momentum. It is the structural statement that both relativistic edge cases and forbidden-region quantum dynamics require a complex phase-action description once a naive real-trajectory picture collapses. This immediately yields a1local-universality/global-selectivity principle: the local Airy/Stokes machinery near simple turning points remains standard, whereas genuinely PWD-selective content should first appear in globally organized multi-turning-point observables such as resonance shifts, linewidth modulation, and phase-memory effects.The manuscript is tested at three levels. First, exact one-dimensional Schrodinger and Klein-Gordon barriers recover the expected large-thickness attenuation slope and the expected dominance of the imaginary under-barrier wavevector, establishing consistency rather than novelty. Second, the paper formulates an explicit empirical protocol for deciding whether a putative PWD signal is real: penalized model comparison, parameter identifiability, holdout stability across neighboring resonances or geometry sweeps, digitization-perturbation robustness, and negative controls that should return vanishing correction coefficients. Third, the paper includes exact source-level operational comparisons on two publisher-plate target-corpus panels aligned with the theory’s predicted first battlefields: a Kobos linewidth panel and a Schmidt geometry/asymmetry panel. In both cases, a minimal phase-organization proxy outperforms the corresponding baseline under RMSE, MAE, AIC, and BIC. These results do not yet constitute the final low-parameter direct δΦPWD /δAPWD theory fit, but they move the proposal beyond a purely future-facing benchmark plan.The resulting picture is disciplined. The framework isolates a mathematically coherent contact surface between null causal organization and forbidden-region attenuation, embeds that contact surface in a screen-supported complex-action EFT, and identifies precise observables on which the theory can fail. What remains open is equally explicit: the attenuation sector is still a leading-order effective closure rather than a completed microscopic derivation, higher-order coefficients remain to be fixed, and decisive empirical status requires direct low-parameter fits that survive robustness and holdout tests. The strongest defensible claim is therefore that a falsifiable bridge framework has been constructed and partially anchored at the exact source level, not that a completed final unification has already been achieved.
Q Quantum Theory is formulated here at the foundational and quantum-mechanical level. Its basic postulate is that the physical quantum entity, denoted by Q, is the whole quantum state rather than an independently real material point whose unknown position is described by a secondary probability cloud. In a one-Q sector admitting a local amplitude representation,\begin{equation} Q(x)=\sqrt{\rho(x)}\,e^{i\theta(x)}Z(x),\end{equation}where x is a spacetime point, ρ is the Born response weight, θ is the phase, and Z is a normalized internal structural direction. A dagger denotes the Hermitian adjoint and ∂μ differentiates with respect to xμ. The decomposition has a local rephasing redundancy. This is a redundancy of the local factorization of the complete Q amplitude, not the physical electromagnetic U(1) gauge symmetry. The associated decomposition-invariant phase-orientation one-form is\begin{equation} \kappa_\mu=\partial_\mu\theta-iZ^\dagger\partial_\mu Z =\frac{\operatorname{Im}\langle Q,\partial_\mu Q\rangle}{\rho}, \qquad \rho>0.\end{equation}In Schr\"odinger correspondence sectors this structure yields exact probability-current and momentum identities, including the standard Abelian gauge-covariant current. In that audit the electromagnetic connection is a correspondence variable; its Q-level interpretation as a local representation of inter-Q relational comparison geometry is developed in the companion manuscript Paper II-A. Klein-Gordon and Dirac audits show that relativistic currents and stress-energy depend on the Lorentz representation: κμ carries phase-orientation translation structure, while amplitude gradients and internal orientation can contribute independently to energy and stress. The standard Hilbert-space probability calculus is retained. Interference, tunnelling, entanglement, localized detection and cloud-chamber tracks are interpreted as properties or records of whole-Q states rather than as evidence for hidden point trajectories. Entanglement is represented by a nonfactorizable joint Q state; standard Bell correlations and no-signalling are retained without identifying correlation with a superluminal physical signal. Boundaryless state support is distinguished from the propagation of a newly generated disturbance, which is required to obey retarded relativistic causality. For stable relativistic sectors, invariant mass is treated as a derived characterization of the translation spectrum: timelike Q states possess a rest frame and rest energy, whereas null Q states do not. The foundational structure does not specify a unique interaction action or establish ultraviolet finiteness. Finite-response dynamics requires a separate construction.
How a finite real cycle acquires a complex structure and a rule for composition Quantum theory uses a common imaginary unit when individual systems become a composite. This framework constructs that compatibility from finite real source histories. On the complete contrast sector of a three-cycle, the forward and backward comparisons give J=3P−P2,J2=−I The complex structure appears after the real comparison is specified. At a qualified unmarked boundary, opposite reference shifts select QAB=2I−JA⊗JB The range is the balanced complex tensor product. Its many-source composition is associative. A finite controlled contact supplies a nonfactorizable complex-linear operation, and exact residual bounds quantify departure from the selected sector. A source model that produces the contact A reversible controller compares operation orders on 24 proper signed frames. Its ordered, arrow-insensitive axis detector produces the retained cyclic response. The contact algebra gives [[G,G],[G,G]][G,G]≅C3. The construction prints the controller, scratch cleanup, full contrast probes, admissible operations and refusal states. A triaxial real response tensor realizes the detector and provides an explicit map between material contrasts and event-count contrasts. A record must survive the test of future operations A present tensor can hide a material marker that a later operation reveals. The framework derives independent force-gradient calibration and a delayed odd-field release. With a nonzero release field, energy and vector torque reconstruct the entire marker change: DU=−Δp⋅E,Dτ=Δp×E.Δp=∣E∣2E×Dτ−DUE The test includes shared calibration errors, stray fields, finite release pulses, marker relaxation and a complete operation inventory. It distinguishes detection of a retained record from agreement with its frozen prediction and from discrimination between physical theories. From proved structure to existing experiments The paper adds a conditional probability-correspondence theorem for the balanced composite, examines independent-source quantum-network experiments, and reproduces all eight measured rows of a public torque dataset. These supply composition benchmarks and demonstrated apparatus capabilities. Their published significances are kept attached to the hypotheses they actually test. The calibrated material release law is also a conventional electrostatic prediction; it is not presented as a QTT-exclusive signal. One material coefficient, two readouts A new archival calculation transfers a published same-particle libration calibration to a separate precession measurement. In the qualified rotor regime, the cross-readout relation is Ξ=ωlib2EpωsΩElcosϕl=alibaprec. An unchanged dipole-to-inertia coefficient gives unity. The calculation yields a slope of 2.909 from the libration calibration, compared with the published precession slope of 2.950, a central difference of 1.4135%. This shared electrostatic consistency relation eliminates the separate dipole and inertia; unequal field gains, dynamical corrections and shared uncertainty remain explicit. Reversal and long-term dipole-stability observations identify complementary laboratory capabilities. The complete matched-tensor delayed-release test remains an experimental target. When do two descriptions differ in any future experiment? The finite-reference extension follows a controlled source contact through shared references, fresh references, inverse operations, intermediate measurements and feedback. Its complete order-three response is gn=∑k=02pkζkn,ζ=e2πi/3,g3=1,g2=g1. A finite observable-span algorithm tests two fully specified models across every permitted future word. It either certifies agreement or returns the preparation, operation sequence, terminal outcome and exact probability difference. In the populated compatible-instrument benchmark, the complete quantum representation gives the same records without an additional target fit. A source-selected physical coupling or preparation remains a distinct route to predictive value. The framework includes nine vector figures, the retained source proofs and countermodels, complete reference-history benchmarks, calibration and vector-reconstruction theorems, runnable exact and numerical checks, published-input receipts, a data assessment and an experimental packet specification. The introduction defines the QTT terms needed to follow the construction without prior familiarity with the corpus. The probability-interface theorem, finite-memory bounds and covariance-weighted witness specify which further laboratory comparisons can distinguish physical models. Source anchors QTT Main Book, especially pp. 56, 248-250, 352 and 827-829; Artian's Completed-Event Four-Capacity Theorem; Frame-cycle derivation map, completed-event lexicon, and Artian's Universe and laboratory readout. Stable citation: 10.5281/zenodo.22882084.
It was proposed recently that the Schrödinger wave function can be reconstructed exactly from a discrete superposition of classical action branches weighted by associated classical densities, without semiclassical approximations. We examine this construction for quantum tunneling through finite potential barriers and for quantum phase phenomena. Although formally consistent when the Hamilton-Jacobi equation admits globally defined real branches, the construction breaks down in classically forbidden regions where no real classical action exists. Using rectangular and Coulomb barrier tunneling in alpha decay and nuclear fusion, we show that the wave function requires either a non-vanishing quantum potential or complex-valued action. The growing barrier component fixed by global boundary conditions is essential for transmission and cannot arise from local real classical trajectories alone. Berry phase, flux quantization, Josephson tunneling, and dc SQUID interference likewise impose global phase constraints absent from local classical action transport.
Quantum theory universally represents a physical history by a phase of the form exp(iS/ℏ), adds amplitudes across unresolved alternatives, and assigns probabilities through the Born rule. These structures are empirically successful but are ordinarily introduced only after a quantum state space has been assumed. This article develops a conditional reconstructional account of their common origin. The premetric reconstruction domain contains neither fields, action, amplitudes, nor quantum probabilities; a quantum platform arises only through constitutive read-out. On a connected platform whose persistent sectors descend from one neutral parent, Indefinite Reconstruction Stability requires locally readable primitive returns to agree on overlaps. Under compact connected scalar return, faithful overlap comparison, common orientation, and smooth-holonomy bridges, the local return data form one global U(1) phase structure. A continuous composition-preserving representation of additive post-read-out action then has the form Θ[γ]=exp(iS[γ]/a0). If the platform supplies one total action for joint histories and no additional action-calibration field, common-parent and overlap compatibility require the same a0 in every physical sector; empirical calibration identifies it with ℏ. The resulting invariant is an action period 2πℏ, not a minimum positive action. IRSP saturation retains every inequivalent admissible alternative, while an explicitly declared linear-composition bridge produces coherent history amplitudes. Positivity, normalization, orthogonal additivity, and a Hilbert-space event read-out then give the Born representation conditionally. The construction yields parameter-free falsification relations: equal action-to-phase slopes across sectors, one total-action phase for mixed-sector histories, invariance under observationally equivalent history refinements, and vanishing genuine third-order interference. A nonzero residual identifies which bridge fails. Previously reported constants, particle ratios, and law-selection results provide cross-sector motivation but are not premises. The construction does not derive Hilbert space or linear composition from IRSP alone; its bridges, inherited ingredients, and failure conditions are separately audited.
Null-Directional Kinematics (NDK) begins with a statistical ensemble of invariant-speed propagation directions rather than massive particle trajectories as primitive. Previous work showed that a small set of compositional axioms uniquely selects the Bhattacharyya coefficient as a statistical clock affinity and that its binary reversal sector reproduces the Lorentz clock factor. A companion closure result further showed that this statistical clock law, together with the inertial and null-direction structural inputs of NDK, closes the kinematic sector to the proper orthochronous Lorentz group. A subsequent construction connected the local geometry of the same statistical structure to nonrelativistic Schrödinger dynamics. The present paper asks a stronger question. Can the clock sector itself constrain a relativistic quantum dynamics? It is shown that the invariant proper occupation associated with the null-direction current is exactly the extensive form of the same Bhattacharyya overlap that defines the NDK clock. Within the local, derivative-free class of Lorentz-scalar transport actions that are extensive in occupation, this proper occupation fixes the free clock action up to the normalization of the inertial mass. Its exact quadratic auxiliary representation introduces a positive scalar density q that classically coincides with the proper occupation. The clock action then fixes the phase block of the local (q,S) geometry, while compatibility with the inherited density-phase two-form uniquely fixes the reciprocal Fisher density block within the stated local symmetry class. The natural complex coordinate Ψ=qeiS/κ and the linear Klein-Gordon equation are not assumed separately. Within that class, they follow from the inherited density–phase geometry. The quantum correction enters through the relationn=qmM,where M is the local invariant mass parameter, relating proper occupation to amplitude density while leaving the kinematic NDK clock ratio unchanged. Its nonrelativistic limit recovers the previously obtained Madelung-Fisher structure, while its first relativistic correction has the standard scalar mass-velocity coefficient. With standard external electromagnetic minimal coupling, the theory also reproduces the exact Klein-Gordon Coulomb spectrum. The Klein-Gordon equation, Fisher geometry, and auxiliary-field methods are established results and are not claimed as new. The proposed foundations result is the chain connecting a uniquely selected null-direction clock overlap to a relativistic scalar quantum dynamics. In this construction, the relativistic clock does more than share a statistical representation with quantum mechanics. It helps determine the form of the relativistic quantum transport theory.
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.