ADDED 14th of August 2026 Cosmological Phase Transport Hierarchy = revision of previous work A Unified Framework for Phase Clock Dynamics, Spatial Texture, and Sector‑Dependent Response Edwin Jean‑Paul Vening (2026)This revised manuscript presents the fully revised architecture of cosmological phase transport, consolidating three major conceptual discoveries that fundamentally reshape the earlier framework. The scalar field Θ(x) is no longer treated as a transport medium but as a universal phase reference whose temporal and spatial structure is sampled differently by photons, neutrinos, gravitational waves, spinor fields, and orbital systems. 1. Endpoint Identity → Cosmological Phase Clock The revision establishes that for an exact gradient background, ∫C∂μΘ dxμ=Θo−Θe, phase accumulation is an endpoint quantity, not a path‑dependent transport law. This discovery reframes cosmological phase effects as historical sampling of a scalar phase function. Redshift becomes a direct coordinate of the phase clock, enabling reconstruction of Θ(t) from multi‑messenger observations. 2. Clock–Texture Decomposition The scalar field is decomposed into Θ(x,t)=Θˉ(t)+δΘ(x,t), revealing two distinct physical roles: Θˉ(t) — the homogeneous cosmological phase clock, producing isotropic, redshift‑organized phase signals. δΘ(x,t) — the inhomogeneous phase texture, generating directional structure, dipoles, multipoles, and macro‑helicity correlations. This resolves the earlier contradiction: a homogeneous FLRW field cannot define a cosmic axis, but a spatial texture can. 3. Universal Field, Sector‑Dependent Response The v9 framework replaces universal coupling with a sector‑response hierarchy: ΔΦs=gsKs ΔΘ. Different messengers respond differently to the same cosmological phase history. This enables: frequency‑independent cosmic birefringence (photons) helicity‑dependent oscillation modulation (neutrinos) parity‑asymmetric propagation (gravitational waves) axial phase shifts (spinor systems) orbital phase offsets (classical periodic systems) This structure makes the theory falsifiable through multi‑messenger phase‑closure tests. Unified Cross‑Scale Framework The v9 manuscript integrates microscopic, mesoscopic, macroscopic, and cosmological phenomena under one derivative‑controlled phase structure. The scalar field Θ(x) acts as a universal phase reference whose temporal evolution and spatial texture generate coherent, helicity‑dependent geometric phases across: quantum interference optical propagation neutrino flavor‑helicity evolution gravitational‑wave polarization planetary and stellar macro‑helicity orbital action‑angle transport pulsar timing and spacecraft ranging The result is a covariant, testable, and observationally constrained theory linking geometric phase, axial coupling, cosmological symmetry, and cross‑scale coherence. Significance Version 9 represents the first fully consistent formulation of cosmological phase transport: mathematically integrable FLRW‑compatible sector‑modular observationally falsifiable cross‑scale coherent geometrically grounded axion‑like but non‑exotic compatible with anomaly structure and hypersurface‑orthogonal flows It transforms the original proposal into a structured theoretical programme capable of guiding multi‑messenger astrophysics, neutrino phenomenology, precision interferometry, and cosmological polarization studies. Cosmological Axial Phase Transport: Helicity–Dependent Geometric Phase Across Scales (Neutrino, Optical, and Orbital Propagation) Description / Abstract: This work presents a unified framework for cosmological axial phase transport, exploring how helicity-dependent geometric phase evolves consistently across physical scales—from microscopic neutrinos to optical waves and macroscopic orbital systems. It introduces a covariant scalar field Θ(x) as a universal cosmological phase potential, whose gradient aligns with large-scale energy flow in the universe, establishing a directional ordering field that all propagating systems sample. Photons, neutrinos, and periodic orbital systems no longer accumulate phase independently; instead, their evolution is coherently guided by the same cosmological ordering structure. Helicity-dependent couplings generate subtle geometric phase shifts analogous to axial vector backgrounds in the Standard-Model Extension, spin-connection effects in curved spacetime, and refractive potentials in matter-induced oscillations. These shifts, while small, produce detectable interference patterns, directional anisotropies, and coherence modulation correlated across distinct physical systems. Key implications and predictions include: Helicity-suppressed neutrino oscillation modulation, potentially measurable in long-baseline experiments such as DUNE, Hyper-Kamiokande, or IceCube-Gen2. Cosmic dipole–aligned directional anisotropy observable in optical and gravitational wave propagation. Phase-coherence correlations in macroscopic orbital systems, detectable via pulsar timing or precise spacecraft ranging. A cross-scale principle of phase transport, providing a physically meaningful, covariant measure of phase accumulation that links microscopic, mesoscopic, and macroscopic regimes. This framework frames phase as a transportable, physically motivated quantity rather than a system-specific parameter. It offers a testable echo of Mach’s principle, suggesting that the universe’s energy-flow structure directly influences coherent evolution across all scales. It also opens new possibilities for multi-modal observational tests, unifying optical, quantum, gravitational, and orbital datasets under a single predictive scheme. Author: Edwin Jean–Paul Vening (Utrecht, The Netherlands, 2026)Acknowledgments: Analytical assistance from a structured computational reasoning system (synthesis and formal exposition). license:Creative Commons Attribution 4.0 International (CC BY 4.0) t7_transport_002_2026-03-02_vening2026.pdf t7_transport_002_2026-03-02_vening2026_short_introduction.pdf Cosmological Axial Phase Transport: Helicity–Dependent Geometric Phase Across Scales (Neutrino, Optical, and Orbital Propagation) This manuscript develops a unified, covariant framework for cross-scale phase transport, introducing a cosmological scalar field, Θ(x), that defines a universal phase structure throughout spacetime. Its gradient aligns with the large-scale cosmological energy flow, establishing a directional ordering medium sampled coherently by photons, neutrinos, gravitational waves, and classical periodic orbits. Helicity-dependent couplings produce directional geometric phase shifts analogous to axial-vector backgrounds in the Standard-Model Extension, spin-connection phases in curved spacetime, and refractive potentials in matter-induced oscillations. Phase accumulation along trajectories produces observable interference effects without altering local dynamical laws, providing a physically motivated, testable principle of cross-scale coherence. Introduction Phase accumulation governs wave propagation, quantum flavor-helicity evolution, and periodic orbital motion. Traditionally treated within separate frameworks, these phenomena share a universal principle: coherent phase transport along trajectories embedded in spacetime relative to the cosmic energy flow. We introduce the covariant scalar field Θ(x) as a cosmological phase potential. Its gradient aligns with the local energy-flow four-vector $u^\mu$, establishing a directional ordering field for all physical systems. Accumulated phase depends only on the trajectory through this background, leaving local equations of motion intact while enabling coherent, system-spanning effects. Optical Propagation Photon trajectories follow standard null geodesics, but the eikonal phase receives an additive contribution from Θ: S_eff = S + Θ This generates directional geometric holonomies, producing subtle, long-baseline interference effects aligned with the cosmic energy flow. Potential experimental verification includes high-precision interferometry, cosmological polarization surveys, and laser ranging experiments. Neutrino Flavor-Helicity Evolution Neutrino oscillation phases acquire helicity-dependent contributions: Δφ_ij(h) = Δφ_ij^std + h ∫ v^μ ∇_μ Θ dλ, h = ±1 where v^μ is the neutrino four-velocity, λ parameterizes the trajectory, and h is the helicity. Observable signatures include: - Directional anisotropy: sky-dependent oscillation patterns correlated with the cosmic dipole or bulk flow.- Helicity asymmetry: opposite-signed phase shifts for left- and right-helicity components.- Coherence modulation: visibility enhanced or suppressed depending on alignment with Θ. These structured, small effects can be tested in long-baseline neutrino experiments (DUNE, Hyper-K) and in astrophysical neutrino observatories (IceCube, IceCube-Gen2). Orbital Action-Angle Transport Periodic orbits accumulate phase relative to the cosmological potential: Θ_orb = ∮ Ω u_μ dx^μ This produces weak, coherent modulations in orbital phases detectable in precision timing systems such as pulsars, planetary radar, and spacecraft ranging experiments. These effects offer a novel window into cosmological-scale ordering phenomena observable in classical systems. Unified Cross-Scale Implications Θ(x) provides a coherent, testable phase-ordering structure linking microscopic (neutrino flavor), mesoscopic (optical waves), and macroscopic (orbital) systems. Observable consequences include: - Helicity-suppressed neutrino oscillation modulations.- Directional anisotropies aligned with cosmic dipole or bulk flow.- Environment-dependent coherence affecting optical and orbital propagation. All predictions remain falsifiable while preserving the integrity of local relativistic equations of motion, making this framework both scientifically rigorous and experimentally approachable. Conceptual Significance Phase becomes a covariant, physically meaningful geometric quantity connected to the universe’s energy-flow structure. Optical, quantum, and orbital systems no longer evolve independently; they sample the same cosmological ordering field. This framework establishes a modern, testable echo of Mach’s principle, unifying cross-scale phase accumulation in a single, covariant, and empirically accessible formalism. The potential implications span fundamental physics, cosmology, neutrino phenomenology, precision astronomy, and even quantum-classical coherence studies. Author: Edwin Jean-Paul Vening (Utrecht, The Netherlands, 2026) Analytical Assistance: Structured computational reasoning system for synthesis and formal exposition