This four-part series proposes a mechanism-level, computable program for cross-scale unification based on an Elementary Energy-Quantum Sea (EP-sea): a collision-driven statistical background whose recursive phase transitions generate stable phase-membrane defects and their effective dynamics. Rather than treating geometry or symmetry groups as primitive, the series emphasizes a free-energy/response ledger and event-statistical closure that connect gravity, electromagnetism, nuclear interior phenomenology, and quantum measurement within a single effective-theory dictionary. Falsifiability pack (minimal must-hit constraints):(1) Double-slit visibility scaling under phase diffusion: η(t) ≈ exp[−γ_dec t] with leading-order γ_dec ∼ α_env Θ / ħ_eff.(2) Born statistics as hazard-rate counting: λ(x,t) = Γ(x)|ψ(x,t)|^2 and consistency with absorbing-potential norm loss.(3) Aharonov–Bohm phase calibration: Δφ_AB = (q/ħ_eff)∮A·dl, with q/ħ_eff fixed per tested species in laboratory regimes.(4) Spin-1/2 + Pauli coupling with tree-level g = 2 from SU(2) rotor (tethered-defect) + minimal coupling.(5) (Optional interface) Barrier crossover: activation exp(−ΔW/Θ) vs tunneling exp(−S_E/ħ_eff) with τ_* ~ ω_b^−1 at a quadratic barrier top. Key mechanisms / claims (overview):1) Gravity as a bulk–boundary free-energy response: mass is associated with a defect free-energy gap ΔF, inducing an effective potential Φ_eff through background stress/response gradients.2) Casimir and gravity as two limits of the same free-energy ledger: boundary-constrained fluctuations vs bulk gradients.3) Light speed vs sound speed: two mode identities. Sound is longitudinal (stiffness/inertia), while light is a transverse Maxwell-sector response with c^2 = (ε0 μ0)^−1 in vacuum-like regimes (c ≠ c_s), avoiding a macroscopic preferred frame.4) Operational charge and potentials: charge as boundary flux asymmetry; Aμ as effective response variables; AB phase as a topological consequence of minimal coupling.5) Quantum probability and measurement: |ψ|^2 is interpreted as event-density; measurement is modeled by thresholded absorption/nucleation with hazard Γ(x)|ψ|^2; Born statistics emerges as a frequency limit of Poisson/SDE event dynamics.6) “Collapse” is replaced by (i) absorbing norm loss and (ii) dynamical decoherence via phase diffusion.7) Spin-1/2 from tethered-defect topology (belt-trick): 2π rotation induces a sign change while 4π restores the full configuration (SU(2) double cover as a geometric constraint).8) Tree-level g = 2: once SU(2) rotor structure is in place, minimal coupling forces the Pauli term; deviations (g−2) are assigned to higher-order backreaction/noise-spectrum effects.9) Nuclear interior as a phase-transition landscape: a core–shell (χ1, χ2) closure yields two-scale kernels (e.g., double-Yukawa structure), saturation, and R ∝ A^(1/3), with decays treated as rare events.10) Unifying tunneling and activation: WKB and Kramers/Freidlin limits are related at the exponent level via intrinsic barrier timescales.11) Polarization and Malus’s law: polarization is a geometric projection of two transverse degrees of freedom; Malus’s law follows from deterministic projection plus intensity ∝ amplitude^2. Series structure:Paper I: Gravity and bulk–boundary free-energy closure (including Casimir interface).Paper II: Electromagnetism as transverse response; constitutive closure; why c differs from c_s.Paper III: Nuclear interior (tier-2) closure; two-scale kernels; saturation and rare-event decays.Paper IV: Quantum interface: ψ/|ψ|^2 closure, hazard-rate measurement, AB phase, spin/Pauli sector, decoherence scaling. Status and scope:This release is intended as a coherent, test-driven framework (effective-theory level) with explicit interfaces for numerical templates and data confrontation. Precision QED/GR-level matching is treated as follow-up work guided by the falsifiability pack above.
This four-part series proposes a mechanism-level, computable program for cross-scale unification based on an Elementary Energy-Quantum Sea (EP-sea): a collision-driven statistical background whose recursive phase transitions generate stable phase-membrane defects and their effective dynamics. Rather than treating geometry or symmetry groups as primitive, the series emphasizes a free-energy/response ledger and event-statistical closure that connect gravity, electromagnetism, nuclear interior phenomenology, and quantum measurement within a single effective-theory dictionary. Falsifiability pack (minimal must-hit constraints):(1) Double-slit visibility scaling under phase diffusion: η(t) ≈ exp[−γ_dec t] with leading-order γ_dec ∼ α_env Θ / ħ_eff.(2) Born statistics as hazard-rate counting: λ(x,t) = Γ(x)|ψ(x,t)|^2 and consistency with absorbing-potential norm loss.(3) Aharonov–Bohm phase calibration: Δφ_AB = (q/ħ_eff)∮A·dl, with q/ħ_eff fixed per tested species in laboratory regimes.(4) Spin-1/2 + Pauli coupling with tree-level g = 2 from SU(2) rotor (tethered-defect) + minimal coupling.(5) (Optional interface) Barrier crossover: activation exp(−ΔW/Θ) vs tunneling exp(−S_E/ħ_eff) with τ_* ~ ω_b^−1 at a quadratic barrier top. Key mechanisms / claims (overview):1) Gravity as a bulk–boundary free-energy response: mass is associated with a defect free-energy gap ΔF, inducing an effective potential Φ_eff through background stress/response gradients.2) Casimir and gravity as two limits of the same free-energy ledger: boundary-constrained fluctuations vs bulk gradients.3) Light speed vs sound speed: two mode identities. Sound is longitudinal (stiffness/inertia), while light is a transverse Maxwell-sector response with c^2 = (ε0 μ0)^−1 in vacuum-like regimes (c ≠ c_s), avoiding a macroscopic preferred frame.4) Operational charge and potentials: charge as boundary flux asymmetry; Aμ as effective response variables; AB phase as a topological consequence of minimal coupling.5) Quantum probability and measurement: |ψ|^2 is interpreted as event-density; measurement is modeled by thresholded absorption/nucleation with hazard Γ(x)|ψ|^2; Born statistics emerges as a frequency limit of Poisson/SDE event dynamics.6) “Collapse” is replaced by (i) absorbing norm loss and (ii) dynamical decoherence via phase diffusion.7) Spin-1/2 from tethered-defect topology (belt-trick): 2π rotation induces a sign change while 4π restores the full configuration (SU(2) double cover as a geometric constraint).8) Tree-level g = 2: once SU(2) rotor structure is in place, minimal coupling forces the Pauli term; deviations (g−2) are assigned to higher-order backreaction/noise-spectrum effects.9) Nuclear interior as a phase-transition landscape: a core–shell (χ1, χ2) closure yields two-scale kernels (e.g., double-Yukawa structure), saturation, and R ∝ A^(1/3), with decays treated as rare events.10) Unifying tunneling and activation: WKB and Kramers/Freidlin limits are related at the exponent level via intrinsic barrier timescales.11) Polarization and Malus’s law: polarization is a geometric projection of two transverse degrees of freedom; Malus’s law follows from deterministic projection plus intensity ∝ amplitude^2. Series structure:Paper I: Gravity and bulk–boundary free-energy closure (including Casimir interface).Paper II: Electromagnetism as transverse response; constitutive closure; why c differs from c_s.Paper III: Nuclear interior (tier-2) closure; two-scale kernels; saturation and rare-event decays.Paper IV: Quantum interface: ψ/|ψ|^2 closure, hazard-rate measurement, AB phase, spin/Pauli sector, decoherence scaling. Status and scope:This release is intended as a coherent, test-driven framework (effective-theory level) with explicit interfaces for numerical templates and data confrontation. Precision QED/GR-level matching is treated as follow-up work guided by the falsifiability pack above.
We develop a quantum-interface closure for the EP-sea program by integrating out sub-observable degrees of freedom into an effective background term B that injects a finite set of response/noise parameters into the observable tier. Within this setting, the relativistic constant c is identified with the transverse Maxwell-sector characteristic speed, c 2 = (ε0µ0) −1 in homogeneous vacuum-like regimes, while longitudinal compression modes obey a distinct sound-law c 2 s = (∂p/∂ρ)s governed by stiffness-to-inertia, thereby avoiding any macroscopic preferred-frame reintroduction. Matter is modeled as a stable observable-tier phase-membrane defect whose rest energy is a free-energy gap E0 = ∆F, so that defining m ≡ ∆F/c 2 yields E0 = mc2 and the associated relativistic dispersion. On the quantum side, the complex amplitude ψ is not postulated as a prior wavefunction; it emerges as a phase-locked envelope variable of a tethered defect, where complex structure packages two orthogonal transverse/rotor degrees of freedom and an SU(2) double-cover constraint provides a geometric origin for spin-1/2. Probability and measurement are treated operationally: |ψ| 2 is an event-density (absorption/nucleation flux) whose continuity follows from stochastic defect dynamics with ℏeff ≡ 2mD(B); Born statistics arise as a frequency limit of Poisson/SDE detection events with rate Γ(x)|ψ(x, t)| 2 . The framework is falsifiable through (i) double-slit visibility scaling with environment noise Θ and detector coupling, (ii) Aharonov–Bohm phase consistency under minimal coupling, (iii) spin-1/2 (4π) behavior and the Pauli term with tree-level g = 2, and (iv) a mechanism-level interface to Lamb-shift/backreaction spectroscopy. Constancy of ℏeff in tested laboratory regimes imposes a leading-order scaling constraint on the background diffusion strength, e.g. D(B) ∝ 1/m for fixed species.
Evidence Paper VII of the Existence Equation series. The Gross-Pitaevskii equation governs Bose-Einstein condensates, superfluids, and superconductors — one of the most successful equations in condensed matter physics. This paper demonstrates that it is not an independent theory but the non-relativistic, low-energy limit of the Existence Equation: (1/c²)∂²Ψ/∂t² = ∇²Ψ + λΨ − α|Ψ|²Ψ When the relativistic term (1/c²)Ψ̈ becomes negligible, the ED equation reduces to the time-dependent Gross-Pitaevskii equation. The Josephson effect — the hallmark of macroscopic quantum coherence — then emerges as a direct structural consequence of a barrier potential, with no phenomenological input and no GP assumption. Input: 4 items. Nothing else. # Input Description 1 ED equation (1/c²)Ψ̈ = ∇²Ψ + λΨ − α|Ψ|²Ψ 2 1D lattice 512 points, periodic boundary 3 Barrier potential Localized λ suppression (width=2.0, depth=85%) 4 Chemical potential Δμ Split-operator phase kick (standard technique) No GP equation. No Josephson relations. No condensate order parameter. No phenomenological coupling. Output: Three tests, all passed. Test Phenomenon Prediction Result Metric A. DC Josephson Supercurrent ∝ sin(Δφ) J = J_c sin(Δφ) Sin fit across 31 phase points R² > 0.99 B. AC Josephson Phase rate ∝ Δμ dΔφ/dt = Δμ (NR limit) Linear regression, 6 values Δμ (0.03–0.30) R² > 0.99 C. f_Φ̇ channel Temporal phase gradient force No GP counterpart (relativistic) Junction-localized force, ΔΦ̇/Δμ ≈ 1 Ratio ≫ 1 Why this matters: Tests A and B reproduce textbook Josephson physics from the ED equation alone. Test C goes beyond GP: the temporal phase gradient ∂_t(arg Ψ) generates an independent force channel that exists only because the ED equation is second-order in time — a relativistic term that the first-order GP equation cannot contain. This is a falsifiable prediction: any system where GP fails at high frequency should exhibit the f_Φ̇ channel. When does GP break down? The ε-regime map: The validity of GP is controlled by a single dimensionless parameter ε = k²/(4λ) = c²k²/(2μ²_ED), where μ_ED = c√(2λ) is the intrinsic Higgs gap of the ED equation. Where ε ≪ 1, GP is exact. Where ε ~ O(0.1–1), ED corrections become measurable — and where ε ~ O(1), GP is structurally inapplicable: the antiparticle channel and the amplitude inertial mode (Higgs sector) become dynamically active. Physical system μ_ED (estimate) ε (estimate) Regime SC Josephson, V ≪ Δ_gap Δ_gap (~meV) ~10⁻⁶ GP exact BEC Bragg, low k healing freq. ~kHz ~10⁻³ GP exact ULDM / fuzzy scalar dark matter m_φ ~ 10⁻²² eV ~10⁻⁴⁰ GP exact BEC Bragg, high k healing freq. 0.05–0.2 ED correction (5–20%) SC Josephson, V ~ Δ_gap Δ_gap 0.1–1 ED required Neutron-star superfluid core pairing gap O(0.1–1) ED required QCD chiral condensate f_π O(1) ED fundamental Bold entries mark regimes where GP-ED deviations are experimentally or observationally accessible. At ε ~ 0.1, systematic 5–20% deviations appear in dispersion observables. At ε ~ 1, the Ψ̈ term cannot be dropped — the antiparticle channel and Higgs sector become active, and GP is no longer a valid description. Four falsifiable predictions are identified: (1) high-momentum Bogoliubov dispersion shift in BEC Bragg spectroscopy, (2) asymmetric AC Josephson response at gap-scale voltages, (3) deep Shapiro delay correction, and (4) condensate fragmentation near ω ~ 2μ_ED. Capstone of the Evidence Program: The same equation that produces quantum scars (EP I), fractional quantum Hall states and anyon braiding (EP II), helical chirality (EP III), non-commutative algebra (EP IV), galaxy rotation curves from topological phase persistence (EP V), and the Tsirelson bound (EP VI) also contains macroscopic quantum coherence as its low-energy sector. Seven phenomena. One equation. No postulates beyond "existence = deviation; deviation smooths." Evidence Program — Complete Summary: EP ED mechanism What emerges Key result I α|Ψ|²Ψ strong-coupling → binary occupation; ∇²Ψ → nearest-neighbor exclusion PXP Hamiltonian (not assumed, derived) ‖T − H_PXP‖ = 0 II Same exclusion on 2D torus; spatial phase closure → winding number sectors Topological degeneracy (without Coulomb interaction); anyon braiding q-fold at ν = p/q; 2π/q phase (0.0% error) III ∇²Ψ + (1/c²)Ψ̈: simultaneous spatial and temporal phase closure Helical scars with spontaneous chirality Chirality 1.78 × 10⁻¹⁵ IV α ≠ 0 → amplitude–phase feedback; commutative operators projected onto constrained subspace Non-commutative algebra with integer eigenvalues j_max = ⌊L/2⌋ (exact) V ½A²|∇Φ|² (phase energy) persists where |∇A|² (amplitude) has decayed Topological phase persistence as structural origin of dark matter ⟨v_θ·r⟩ = 2.0000 ± 0.0003 VI Axiom 1.1 (discreteness) → ±1 projection of continuous phase; 2 axes × √2 diagonal Tsirelson bound S = 2√2 without Hilbert space Exact (analytic + numerical) VII (1/c²)Ψ̈ → 0 (NR limit): ED reduces to GP; ε = k²/(4λ) controls validity boundary Josephson effect (DC + AC); GP as low-energy ED; f_Φ̇ force channel (no GP counterpart) DC: R² > 0.99; AC: R² > 0.99; 4 falsifiable predictions at ε ~ 0.1 All code : https://github.com/Galileo-leo/existence-equation Part of the Existence Equation Evidence Paper series (EP I–VII).Parent work: The Existence Equation: The Grammar of Persistence (doi:10.5281/zenodo.18639317)
In der vorliegenden Arbeit erforschen wir Netzwerke von Vielteilchen-Quantensystemen, um neue, durch die Wechselwirkung der individuellen Knoten entstehende Quanten- und topologische Phasen zu beschreiben. Alle betrachteten Netzwerke beruhen auf dem semi-klassischen Lipkin–Meshkov–Glick-Model, und die Kopplungen zwischen den Netzwerk-Knoten werden mit entweder einer oder zwei Kopplungskonstanten beschrieben. Es wurde gezeigt, dass die uniforme anisotropische y–y Kopplung vier Quantenphasen ergibt (wenn sowie positive, als auch negative Werte für Kopplungskonstanten berücksichtigt werden), die sich in den Mean-Fields und der Entartung der Grundzustände unterscheiden. Für schwache Kopplungen befindet sich das Netzwerk in der paramagnetischen Phase. Wird es jedoch von der Selbstwechselwirkung dominiert, so wird der Grundzustand exponentiell entartet. Für starke Kopplungen ist der Grundzustand zweifach entartet und weist eine Fernordnung auf. Über die Mean-Field-Approximation hinausgehend, erhielten wir analytische Ausdrücke für die Dispersionsrelationen der Energie für ein eindimensionales Netz mit periodischen Randbedingungen. Für relativ kleine Netzwerke rechneten wir die Grundzustandsenergie durch direkte Diagonalisierung des Hamiltonians aus. Das Effekt der Einführung einer zweiten Kopplungskonstante wurde auf dem Beispiel der eindimensionale Kette (eine Erweiterung des SSH-Models auf Vielteilchensysteme) betrachtet, und die grundsätzliche Frage war die Untersuchung vom Wechselspiel zwischen den topologischen und Quantenphasen. Es wurde gezeigt, dass die Sprungkopplung zwischen Knoten fünf Quantenphasen ergibt, wenn sowie positive, als auch negative Werte für Kopplungskonstanten berücksichtigt werden. Die Analyse von der Quantenfluktuationen um die Mean-Field-Lösungen zeigte, dass es für dieses Model topologisch triviale und nicht-triviale Phasen gibt, die durch den Wert der symplectischen Polarisation voneinander abweichen. Die Bulk--Grenzen-Beziehung wurde auf dem Beispiel einer endlichen Kette mit offenen Randbedingungen getestet, und es wurde bestätigt, dass die Anzahl der lokalisierten Randzustände proportional zum Wert der symplectische Polarisation ist. Weitere Analyse zeigte, dass ein zusätzliches Paar von Randzuständen in der selbstwechselwirkungdominierten Quantenphase erscheint, das keinen Zusammenhang mit der Topologie hat. Außerdem, wenn eine von den Kopplungen stark wird, werden topologische Randzustände von Bulk-Bänden abgefangen und dadurch seine Lokalisation verlieren.
Abstract We establish a complete geometric reconstruction framework in which quantization, symplectic structure, and infrared curvature emerge from the discrete phase overlaps between low-energy eigenstates of the spectral vacuum Hessian H. This work provides a rigorous derivation of Planck's constant ℏ as a measurable geometric quantity rather than a fundamental postulate. Key Results: 1. Emergent Symplectic Structure: From discrete phase overlaps θₐᵦ = arg⟨ψₐ|ψᵦ⟩, we construct a closed, non-degenerate 2-form: ω = Σ_{⟨ab⟩∈𝒩} (dθₐᵦ ∧ dλₐ) / √(ΔₐΔᵦ) satisfying the symplectic condition dω = 0 and rank(ω) = 2n, providing the first principles derivation of Hamiltonian dynamics from spectral data. 2. Geometric Origin of ℏ: We prove that Planck's constant emerges as the minimal symplectic area of a phase-space cell in the reconstructed manifold: ℏ ≈ ∮_{∂Σ} θₐᵦ dλ ≡ Area_ω(cell) linking quantization to the topological density of the spectral graph. 3. Topological Phase Invariants: We demonstrate that the discrete phases θₐᵦ converge to the Berry curvature and the Aharonov-Bohm phase shift in the continuum limit, where the magnetic flux is recovered as a spectral holonomy: Φ_AB = ∮_Γ 𝒜_Berry · dl establishing the framework as a discrete U(1) gauge theory on eigenvalue space. 4. Infrared Curvature Scaling: We show that the spectral gap Δ of the vacuum Hessian dictates the large-scale (IR) curvature of the emergent manifold: R_curv ~ 1 / √Δ offering a natural resolution to the infrared divergence problem and linking the cosmological constant to spectral stability. 5. Phase-Space Crystallization: We introduce the concept of Phase-Space Crystallization: quantization as a phase transition from continuous (classical) to discrete (quantum) phase space, with the spectral gap Δ acting as the order parameter: Δ = 0 → ℏ_eff = 0 (liquid/classical) Δ > 0 → ℏ_eff > 0 (crystal/quantum) exhibiting critical scaling ℏ_eff ~ (τ - τ_c)^(1/4) near the transition, where quantum mechanics emerges as the 'solid phase' of spectral geometry. Verification and Implementation: The framework is verified via a Discrete Exterior Calculus (DEC) pipeline through 10-seed Monte Carlo simulations confirming: • Symplectic closure: |dω| < 10⁻¹⁴ (machine precision) • Phase coherence: ⟨|δθ|⟩ < 10⁻³ • ℏ_eff stability: σ/⟨ℏ_eff⟩ < 5% • IR residual: R_IR/R* = 1.02 ± 0.02 with full Python implementation provided for reproducibility. Significance: This work completes the SVM foundation by showing that: • Quantization is geometric, not axiomatic • Planck's constant ℏ is a derived quantity from phase overlap structure • Symplectic geometry emerges from Berry phase curvature • Gauge theory (U(1)) arises from spectral holonomy (Aharonov-Bohm equivalence) • Quantum mechanics is a 'crystalline phase' of spectral geometry thereby unifying quantum mechanics, gauge invariance, and emergent gravity under a single spectral principle, with no external postulates. Keywords: Spectral vacuum mechanism, phase geometry, Berry phase, Aharonov-Bohm effect, symplectic reconstruction, discrete exterior calculus, emergent quantization, Planck constant derivation, phase-space crystallization, infrared curvature, spectral gap Other works by the author on a related topic: [1] M. Nemirovsky, Spectral Vacuum Mechanism — Part XXIX: Spectral Yang–Mills Dynamics: Field Equations, Running Coupling, and Confinement from Vacuum Geometry, Zenodo. DOI: 10.5281/zenodo.18624234 (2026). [2] M. Nemirovsky, Spectral Vacuum Mechanism — Part XXX: Emergent Geometry from Spectral Flow, Zenodo. DOI: 10.5281/zenodo.18636847 (2026). [3] M. Nemirovsky, Spectral Vacuum Mechanism — Part XXXIV: Quantum Spectral Flow and Vacuum Stability, DOI: 10.5281/zenodo.18704453 (2026). [4] M. Nemirovsky, Spectral Vacuum Mechanism — Part XXXV: Spectral Strings and Emergent Worldsheet Dynamics, DOI: 10.5281/zenodo.18726006 (2026). [5] M. Nemirovsky, Spectral Vacuum Mechanism — Part XXXVI: Spectral Derivation of String Tension and Confinement from Stable Vacuum Structure, DOI: 10.5281/zenodo.18749131 (2026).
Étude de l’effet des interactions élastiques et électroniques dans les théories de champs en basse dimension Cette thèse explore l'effet des interactions dans plusieurs théories des champs de basse dimension à l'aide de techniques analytiques perturbatives et non perturbatives de la théorie des champs. Nous nous concentrons principalement sur les systèmes planaires de la physique de la matière condensée et leurs transitions de phase, thermiques ou quantiques, induites par les interactions. Ces dernières sont caractérisées par des dimensions anormales, ou de manière équivalente des exposants critiques, qui sont des observables physiques universelles calculables avec les techniques de diagramme de Feynman multi-boucles. Une première partie est consacrée à l'étude des fluctuations élastiques dans plusieurs théories statistiques des champs associées à la phase plate des membranes polymérisées, omniprésentes en physique. Nous explorons leurs propriétés mécaniques critiques, en particulier la rigidité anormale induite par les corrélations à longue portée que nous calculons à un ordre en boucles élevé. Une variante incluant du désordre est aussi considérée par la technique des répliques, dévoilant une nouvelle transition de plissement vers une phase de verre. Une deuxième partie examine plusieurs théories de jauge abéliennes en basse dimension, qui sont particulièrement utiles pour décrire les systèmes quantiques fermioniques planaires fortement corrélés comme le graphène à basse énergie. Nous considérons également une extension minimalement supersymétrique en relation avec un potentiel supergraphène. Pour ces modèles, nous calculons les exposants critiques, par un développement en boucles ou Nf, et abordons la possibilité d'une transition de phase métal isolant par la génération dynamique d'une masse pour l'électron.
GRUT Programatic ToE v6: Constitutive Response Theory from the CTP Effective Action GRUT v6: Constitutive Response Theory from the CTP Effective Action derives a unified response framework from the closed-time-path (Schwinger-Keldysh) effective action S_CTP and extracts an effective constitutive response equation τ dz/dt + z = z_target[z] in the relevant sectoral limits. The target functional z_target[z] is not postulated — it emerges from the variation δS_CTP/δz_a = 0, with the noise kernel N(x,x') emerging from the second variation δ²S/δz_a² = iN. These are two outputs of one CTP action: the deterministic response and the stochastic fluctuations. The constitutive projection (replacing d²/dt² with (1/τ)d/dt) has sector-dependent status: it is exact in sectors with first-order underlying dynamics (the Schrödinger equation is already first-order; the decoherence rate comes from the noise kernel, not the constitutive equation), and is a heuristic effective projection in sectors with second-order dynamics (gravity, cosmology, QG). The framework's sharpest predictions — the decoherence plateau and QM recovery — do not depend on the constitutive projection. The normalization τ_I = ℏ/2 is a definition (selecting the Keldysh convention that recovers quantum mechanics), not a physical axiom, reducing the framework to two axioms (CTP doubling, directed response) plus one definition. Four sectoral limits are developed in detail. Sector 1 (Quantum Mechanics): the nonrelativistic limit of the CTP variation gives the Schrödinger equation exactly, with the ground state as the fixed point z = z_target[z]. 12/12 tests pass. Sector 2 (Electroweak/SM): the Standard Model Lagrangian is imported as S_classical in the CTP action — the framework hosts it, does not derive it. 13/13 tests. Sector 3 (Gravitational Decoherence): the noise kernel becomes the Diósi gravitational self-energy functional, yielding Λ_grav = Gm²S(l/R)/(ℏl) with zero free parameters. The corrected benchmark uses a gold microsphere (R = 1 μm, m = 80.8 pg, l = 1 μm) giving 689 Hz with 1.5 ms coherence time. Earlier benchmarks (10 pg, R = 50 nm) were physically inconsistent. The full Lindblad master equation is documented and verified (max population error 1.4 × 10⁻⁶ vs Boltzmann). Momentum diffusion gives a heating rate of 4.7 × 10⁻⁶⁸ W — safe by over 60 orders of magnitude, though a complete heating analysis has not been performed. Six discriminating signatures distinguish this prediction from all tested alternatives. 14/14 tests. Sector 5 (Cosmology): a 10-step derivation chain (7 computed, 3 structural) produces the vacuum expansion rate H_∞ = (2 − R_anomaly)/(S × τ_0) = 1.885 × 10⁻¹⁸ Hz as an absolute prediction independent of H₀. The structural steps (linearity from single 3-loop insertion, CTP boundary conditions, dimensional assembly) constrain the formula to a unique form but do not constitute a derivation from a Lagrangian. The implied Ω_Λ is H₀-dependent: 0.2% accuracy at H₀ = 70, 8.1% at Planck H₀ = 67.4. The standard perturbative loop expansion cannot reach this result because it hits the cosmological constant problem at 1-loop; the structural route uses scheme-protected anomaly coefficients. A 329-era non-perturbative discrete map with exact retarded memory kernel produces three-phase expansion with 100% robustness and zero fitting. Linearized tensor gravity (Sector 12) yields a graviton propagator G_R(k,ω) = −16πG/[(ω² − k²c²)(1 − iωτ_grav)] that is massless (same pole as GR), ghost-free (imaginary pole is dissipative), UV-improved (1/ω³ vs 1/ω² in GR), and recovers classical GR to 10⁻¹⁰ at LIGO frequencies. Black hole information is resolved through the constitutive memory kernel K(t) = (1/τ_grav)exp(−t/τ_grav), which controls information correlation between the interior and outgoing Hawking radiation via the overlap factor η(M) = exp(−t_infall/τ_grav). The τ₀ branch (τ_grav = 41.9 Myr) gives η = 1 for all astrophysical masses, yielding 99.94% information recovery during evaporation with a Page-like turnover at the halfway point — non-thermal, unitary, constitutively correlated radiation. The T_Planck branch gives end-stage release only. This achieves 5/5 quantum gravity closure conditions for the τ₀ branch (graviton, UV completion, backreaction, BH information, classical GR) and 4/5 + end-stage for the T_Planck branch. The branch choice is a discriminable prediction, not an ambiguity. Neither resolution is available in standard GR, which has no metric memory kernel. Dark matter (Sector 9) is addressed through a gauged extension: the global Z₂ symmetry of the double-well potential is promoted to a local U(1)_dark gauge symmetry, fixing λ = g²_dark/2. Two routes determine g_dark: RG running from the Planck scale via the one-loop U(1) beta function (λ = 0.42, M = 2.1 × 10⁹ GeV) and anomaly extraction from CTP coefficients (λ = 3.83, M = 2.3 × 10⁸ GeV). Both give natural λ, viable σ/m (10⁻³–10⁻² cm²/g within Bullet Cluster bounds), and superheavy soliton masses in the 10⁸–10⁹ GeV range. The dark sector spectrum includes a massive dark photon (m_A' = g_dark v ≈ 387 MeV, sub-GeV, not yet excluded) and a dark Higgs at the pion scale. The extension class is finite and viable; unique branch selection within the window has not been achieved. 8/8 gauged tests pass. Additional mapped sectors include QCD confinement (threshold at 0.81 GeV, Wilson loop area-law confirmed), flavor hierarchy (Koide formula at 0.005%), coupling unification (f_self = 0.93), neutrino masses (near-zero fixed point, seesaw as threshold crossing), baryogenesis (3/3 Sakharov conditions structural), and neural gamma resonance (40 Hz from two independent routes: 39.9 Hz gravitational, 41.7 Hz network topology, 20/20 tests). The primary falsification test is the gravitational decoherence plateau — if no plateau is observed, Λ_grav is wrong, the USL constants lose their grounding, the cosmological formula loses its inputs, and the framework is falsified at its core. The structural mappings in other sectors are independently testable and do not logically depend on the plateau measurement. The document is explicit about what is not claimed: mechanism for subjective experience, observable GW/QNM modifications (dead at ~10⁻³⁹ rad), resolution of the Hubble tension, exact fermion masses, and "decoherence is undefined" in the Lindblad sense (only the constitutive driving term is zero at the fixed point). All computations are reproducible via the grut_solver package (github.com/ryangrvr/GRUT-RAI-v1.0). 183 passing tests. 13 sectors. One CTP action. Key Points: 1. A unified CTP response framework is derived from the Schwinger-Keldysh effective action, with the constitutive equation τ dz/dt + z = z_target[z] and noise kernel emerging as two outputs of one variational principle. The constitutive projection is exact in first-order sectors (QM, decoherence) and a heuristic effective projection in second-order sectors (gravity, cosmology) — the framework's sharpest predictions do not depend on the projection. 2. The Schrödinger equation is derived as the nonrelativistic limit of the CTP variation (exact, 12/12 tests). The gravitational decoherence rate Λ_grav = Gm²S(l/R)/(ℏl) comes from the noise kernel with zero free parameters (exact, 14/14 tests). The corrected benchmark uses a gold microsphere (R = 1 μm, m = 80.8 pg, 689 Hz). The full Lindblad master equation is documented and verified. 3. A 10-step derivation chain (7 computed, 3 structural) produces the vacuum expansion rate H_∞ = 1.885 × 10⁻¹⁸ Hz as an absolute prediction independent of H₀. The structural steps constrain the formula uniquely but do not constitute a conventional derivation. The implied Ω_Λ is H₀-dependent (0.2% at H₀ = 70, 8.1% at Planck). The structural route uses scheme-protected anomaly coefficients, bypassing the cosmological constant problem. 4. The graviton propagator is massless, ghost-free, UV-improved (1/ω³), and recovers classical GR to 10⁻¹⁰ at LIGO frequencies. Black hole information is resolved through the constitutive memory kernel: the τ₀ branch achieves 99.94% information recovery with a Page-like turnover and non-thermal unitary radiation (5/5 QG closures). The T_Planck branch gives end-stage release only (4/5 + end-stage). 5. Dark matter is closed as a gauged extension class: U(1)_dark fixes λ = g²_dark/2 via two routes (RG running: λ = 0.42, M = 2.1 × 10⁹ GeV; anomaly extraction: λ = 3.83, M = 2.3 × 10⁸ GeV). The dark sector spectrum includes a dark photon (~387 MeV) and dark Higgs at the pion scale. Both routes viable; unique branch selection remains open. 8/8 gauged tests pass. 6. τ_I = ℏ/2 is a normalization choice (selecting the Keldysh convention that recovers QM), not a physical axiom. This reduces the framework to two axioms (CTP doubling, directed response) plus one definition, with the mass-dependent conversion c₂ = ℏ²/(4m) providing sector-specific dimensional translation. 7. Six discriminating signatures distinguish the decoherence prediction from all tested alternatives (CSL, Diósi-Penrose point-mass, constant floor, power-law): pressure plateau, geometry dependence, entanglement protection, l-scaling, geometric kink at l = 1.8R, and mass-squared scaling. Heating rate (4.7 × 10⁻⁶⁸ W) is safe by over 60 orders; complete analysis not yet performed. 8. The self-referential fixed point z = z_target[z] organizes all sectoral limits as different expressions of the same CTP action: ground state (QM), gravitational plateau (decoherence), vacuum H_∞ (cosmology), confining vacuum (QCD), broken vacuum (electroweak), and gamma resonance (neural). The threshold is not a separate postulate — it is the constitutive equation's approach to its own fixed point. 9. QCD confinement (0.81 GeV threshold, Wilson loop area-law), flavor hierarchy (Koide at 0.005%), coupling unification (f_self = 0.93), neutrino masses (near-zero fixed point, seesaw as threshold crossing), baryogenesis (3/3 Sakharov structura