Dynamically Perturbed Spacetime: From Gravitational Deflection and Spacetime Quantisation to Cosmic Flow and Horizon-Thermodynamic Coupling A Unified Synthesis of Papers I, IV, V, and Crossover Extension Dynamically Perturbed Spacetime Series

This manuscript presents a unified synthesis of four previously independenttexts in the Dynamically Perturbed Spacetime series. The four components areintegrated into a single logically progressive narrative spanning stellar, black-hole,Planck, and cosmological scales. The unifying thread is a hierarchy of consistencyconditions: each level of the hierarchy constrains and motivates the next, andeach level yields at least one falsifiable prediction.Part I (Paper I of the series) derives the modified parallax correction coefficient κ(ξ,φ) for photon deflection by a dynamically varying, anisotropicgravitating source in linearised GR. A new control test—null geodesics in theVaidya metric—proves that spherically symmetric sources produce no first-ordergravitomagnetic deflection (∆αgm = 0 exactly), establishing anisotropy as thenecessary condition for a gravitomagnetic signal. The corrected coefficientκ(ξ,φ) = 4(1 − e−ξ) + K(ξ)βcos2φ supersedes the earlier cotφcscφ form. Aunified parallax equation incorporating SMBH lensing and CMB reference-framecontamination (Sachs–Wolfe and thermal Sunyaev–Zel’dovich effects) yields thefalsifiable prediction that S2 at periastron should exhibit a periastron–apastrondistance asymmetry |δd|/d ∼ 5 × 10−3 detectable by Gravity+.Part II (Paper IV of the series) promotes the TIMER operator to a covariantfour-vector quantisation and imposes the Metric Quantisation Consistency Condition (MQCC): the minimal invariant interval must equal ℓ2P. In Schwarzschildspacetime the MQCC yields ∆reff(r) = ℓP/ 1−rs/r, which diverges at thehorizon—a first-principles derivation of stretched-horizon physics from metric consistency alone. In Kerr spacetime the off-diagonal term gtφ entangles temporaland angular quanta, producing a spin-dependent angular quantum ∆φeff measurable as a phase asymmetry in the photon ring of M87* by the ngEHT. The PlanckConvergence Theorem establishes that ξP = ∆t · c/ℓP = 1 is simultaneouslythe MQCC minimum, the peak of the gravitomagnetic kernel K(ξ), the peak ofthe quantum decoherence kernel I(ξQ), and the minimum of the computationalinformation floor—a structural convergence, not a numerical coincidence.Part III (Paper V of the series) extends the framework to cosmological scales.The vaz˜ao (flow) field V(z) = ∞z j(z′)e−(z′−z)/τdz′ identifies the dark energydensity with the accumulated momentum of stellar isotropic emission acrosscosmic history. The resulting equation of state w(z) = −1 + w1[V(z)/V(0) − 1]recovers w = −1 today by construction and predicts dynamic evolution at0 < z ≲ 2. Calibration against DESI DR2 BAO and eight independent H0environmental measurements yields τ = 4.50, w1 = 1.924, Ωm = 0.319, and αV =0.288±0.056. The model fits DESI DR2 BAO at the level of ΛCDM (χ2 = 102.9versus 104.9). The central empirical finding is that the observed density–H0 slopeis 3.5× weaker than ΛCDM linear perturbation theory predicts, with αV < 1naming this discrepancy. The KBC void explains only 24% of the Hubble tensionunder the calibrated model. A critical slope dH0/dδ = −6.7 km/s/Mpc separatesthe Cosmic Flow prediction from ΛCDM at > 14σ with N > 1000 galaxies fromDESI DR3.Part IV (Crossover Extension) provides a physical mechanism for αV < 1by reinterpreting the stretched-horizon structure of the MQCC as a source ofan informational/entropic reservoir ρI. Injection, dissipation, and saturationof ρI modulate the effective coupling efficiency αcrossV (z,δ), producing falsifiablepredictions for angular relaxation scales in residual H0 sky maps, BH/AGN/spinproxy correlations, and high-|δ| saturation behaviour testable with DESI DR3and large galaxy catalogues.Throughout, the manuscript maintains strict scope discipline: toy-level constructions are labelled as such, calibrated phenomenological results are distinguished from first-principles derivations, and no claim to a complete theory ofquantum gravity or dark energy is made. Papers II and III of the series arereferenced as prior works but are not reproduced in full here