Grand Responsive Universe Theory: Theory of Everything Candidate Framework

GRUT (Grand Responsive Universe Theory) is a candidate Theory of Everything built on one premise: the gravitational vacuum is a viscoelastic medium with finite relaxation time τ₀ = 41.9 Myr and finite impedance α = 1/3. A single closed-time-path (Schwinger-Keldysh) effective action S_CTP produces a constitutive response equation whose sectoral limits yield quantum mechanics, general relativity, gravitational decoherence, dark matter, dark energy, baryogenesis, and the observer's classical definiteness — all from the same parent action evaluated at different scales. Four constants (τ₀, α, S = 108π, R = √(4/3) ≈ 1.15470) govern phenomena across roughly sixty orders of magnitude in frequency without running with energy or epoch. "Zero free parameters" throughout means: zero adjustable parameters given the α = 1/3 postulate and the τ₀ cosmic-baseline anchoring — these two inputs are named, audited, and traceable, not fitted to downstream predictions. The framework is presented for adversity testing and module-by-module specialist review. It is not presented as an established theory.

The document is structured as a 14-chapter book with six appendices, covering the foundational picture (Part I: Chapters 1-4), recovered physics and the predictive backbone (Part II: Chapters 5-11), and the research frontier (Part III: Chapters 12-14 — SM Closure Program, cosmic history, and the complete falsification ledger). The framework has rigorous claim governance: 109 registered claims across six tiers (61 computed, 15 anchored, 3 conjectural, 18 open negative, 2 foundational, 10 meta), each traceable to the GRUT-RAI codebase (DOI: 10.5281/zenodo.18993689) with 2816 passing tests. Every claim carries a tier label, a verification path, and a registry ID. Every correction — 31 to date — is documented with full audit transparency. The v8→v2 cycle (May 2026) closed three previously-blocking open negatives: the constitutive projection Φ_μν is now derived from δS_CTP/δh_a at linearized level with explicit FRW extension; the n_g(ω) cosmological covariance is closed via the MG-EFT-of-dark-energy mapping (μ_GRUT = n_g², γ_GRUT = 1); and T_c provenance is resolved through the two-τ-scale convention distinguishing τ₀ (gravitational, 41.9 Myr) from τ_micro (thermal, ~10⁻¹⁹ s). The canonical derivation of R = √(4/3) is now closed (Gate R, May 2026) via the Weyl-decomposition identification of the gravitational conformal mode as one real conformally-coupled scalar (Duff 1994 a/c = 1/3 exactly).

The framework surfaces near-term falsifiers within reach of current or next-generation experiments. The primary falsifier is the gravitational decoherence plateau at ~689 Hz at the gold benchmark (m = 80.8 pg, l = 1 μm), predicted with zero free parameters and six joint scaling laws that no tested alternative model (CSL, Diósi-Penrose, Adler, GRW) reproduces simultaneously. A GRUT-vs-CSL isotope-pair discriminator (³⁰Si/²⁸Si at 3.8% measurement precision) distinguishes GRUT's m² mass scaling from CSL's linear nucleon-count scaling — within reach of MAQRO-class matter-wave interferometry. Cluster-merger gas-to-lensing offsets follow δ ∝ v × τ₀ with a 1.72% internal scaling residual across four systems. The structural relation H₀√Ω_Λ = 58.16 km/s/Mpc provides a calibration-independent cross-survey test for DESI, Euclid, and Roman. Two v2 falsifiers: the modified-gravity parameter μ − 1 = 1/3 on horizon scales (testable by DESI Y3+ at ~5σ, Euclid 2027 definitively — GRUT uniquely predicts γ = 1, distinguishing it from Brans-Dicke, f(R), and DGP); and Σm_ν ≈ 60 meV with Normal Hierarchy preferred (testable by KATRIN, JUNO, and Euclid lensing).

The constant R = √(4/3) is now supported by four independent routes. Gate R (canonical): Weyl decomposition → conformal scalar → Duff a/c = 1/3 → R = √(1 + α) = √(4/3), derived with zero free parameters. Osborn (supporting): local RG coefficients with measured SM couplings give ε = 1.15367, agreeing at 0.089%. V5/V6 loop-suppressed matrix (diagnostic): a 9×9 Euler/operator mixing matrix on S⁴ with loop-suppressed off-diagonal elements collapses the dominant eigenvalue from 2.28 to 0.22, making the Euler channel near-pure (projection 0.9688); the Christensen-Duff SM anomaly anchor (a_hat = 1991/720) gives β_eff = 0.12293 vs target 0.1215, a ~1.2% gap classified as higher-order Seeley-DeWitt refinement. The right-handed neutrino extension (N_F: 45→48) worsens the fit by +1.657%, disfavoring RHNs as a vacuum-expansion repair. The 3-loop anomaly quotient route remains an honest negative.

The linear cosmological growth problem (previously reported as D = 1.0 vs required ~2626) has been diagnosed and resolved. The decoupled constitutive equation gives D ≈ 3 because it lacks matter sourcing — a closure gap, not a structural failure. Adding the Poisson source k²Φ = −4πGμ_GRUT a²ρ̄_m δ_m (using the MG-EFT mapping from Correction #26) recovers D_ΛCDM = 2626 at the σ₈ scale exactly, with τ₀H₀ ≈ 0.003 confirming the quasi-static limit. The framework now predicts scale-dependent enhancement of structure formation above ΛCDM: f ≈ 1.0009 at σ₈ (invisible), 1.085 at BAO (8.5% — potentially measurable by Euclid/DESI), 2.024 at CMB low-ℓ (factor 2 — strongly testable), and 2.348 at the CMB horizon. The remaining open work is deriving the Poisson coupling from ∂²S_CTP/∂σ∂ρ_m (first principles), registered as an open negative with the CAMB/CLASS implementation gate no longer blocked.

The cosmological predictions include Ω_Λ ≈ 0.69 within 0.2% of Planck (computed, zero free parameters), H₀ ≈ 68.8 km/s/Mpc from the cosmic-baseline route (zero parameters) or 69.03 km/s/Mpc from Friedmann integration (one parameter — observed cosmic age), both in the Hubble tension gap. The dark matter density Ω_dm = α = 1/3 is derived geometrically from the vacuum's bandwidth integral, giving a gravitational enhancement of order ~30%, consistent with observed phenomenology. Baryogenesis gives η_B = 6.57 × 10⁻¹⁰, within 8% of observed. The MOND acceleration scale a₀ ≈ 1.2 × 10⁻¹⁰ m/s² emerges naturally. Eight independent solar-system GR tests confirm safety factors from 10⁵ to 10³⁵.

The framework dissolves the measurement problem through the Schrödinger-in-the-Box inversion: the observer's own Λ_grav computes their classical definiteness from the same equation that predicts the decoherence plateau and the dark matter density, with zero free parameters and no interpretive stance required. GRUT is the only framework where this dissolution is quantitative rather than philosophical.

The framework is explicit about what is NOT yet derived: the nonlinear gravity ladder is 4/8 rungs complete; the curved-background Φ_μν extension is scaffolded but not fully explicit beyond FRW; the primordial scalar amplitude A_s is rescaling-conditional; the Poisson coupling in the growth equation is borrowed from the MG-EFT mapping, not yet derived from S_CTP; the Standard Model is hosted as S_classical, not derived (Yukawa matrices, CKM/PMNS mixing, and Higgs potential remain open — though neutrino hierarchy is now structurally predicted as NH with Σm_ν ≈ 60 meV, and right-handed neutrinos are structurally disfavored). The S⁴ CTP 3-loop solver infrastructure (Stages 1-7J, 170+ tests) is built and benchmarked but the actual integral evaluation remains open. Chapter 14 contains the complete open-question ledger with closure conditions for each of the 18 open negatives.

This deposit asks the community for adversity testing, module-by-module specialist review, replication of the codebase computations, and engagement with the specific falsifiers and closure conditions documented in Chapter 14 and the companion falsifier paper. The framework's posture is that of a candidate research program with discipline infrastructure that makes its gaps visible rather than concealed. Not more rigorous than other ToE programs — but more adversarial, with six predictions falsifiable on 1-10 year timescales by named experiments.

12 Key Points

1. One action, one medium, one equation. A single CTP (Schwinger-Keldysh) effective action S_CTP produces a constitutive response equation τ₀ dz/dt + z = z_target[z] + ξ(t) whose sectoral limits yield QM, GR, gravitational decoherence, dark matter, dark energy, baryogenesis, and the observer's classical definiteness.

2. Four constants across sixty orders of magnitude. τ₀ = 41.9 Myr, α = 1/3, S = 108π, R = √(4/3) — unchanged from Planck UV to Hubble expansion. "Zero free parameters" means zero adjustable parameters given these named, audited inputs.

3. Decoherence plateau at 689 Hz. The primary falsifier: zero-parameter gravitational decoherence rate at the gold benchmark, with six joint scaling laws no tested alternative model reproduces simultaneously.

4. Cosmological constant within 0.2% of Planck. Ω_Λ ≈ 0.69, derived as the terminal velocity of a damped conformal instability — not a fitted parameter, not a landscape selection, but the steady-state rate when topological pressure meets viscoelastic resistance.

5. R = √(4/3) from four independent routes. Gate R (canonical, derived): Weyl → conformal scalar → Duff a/c = 1/3. Osborn (supporting): ε = 1.15367 from SM couplings, 0.089% agreement. V5/V6 matrix (diagnostic): SM operator-mixing on S⁴, Euler channel near-pure, 1.2% β_eff gap. 3-loop anomaly quotient (honest negative): not reproduced.

6. Dark matter as vacuum refractive enhancement. Ω_dm = α = 1/3 from the bandwidth integral — no new particles required. Modified-gravity parameter μ − 1 = 1/3 on horizon scales, with γ = 1 (no gravitational slip) — testable by DESI Y3+ and Euclid.

7. Linear growth diagnosed and resolved. The D = 1.0 failure was a closure gap, not a structural failure. With Poisson sourcing: D_ΛCDM = 2626 recovered at σ₈. Scale-dependent GRUT enhancement: +0.09% (σ₈), +8.5% (BAO), +102% (CMB low-ℓ), +135% (horizon). The enhancement is a testable prediction for Euclid and DESI large-scale structure measurements.

8. Measurement problem dissolved quantitatively. Schrödinger-in-the-Box: the observer's own Λ_grav computes their classical definiteness — the only framework where the quantum-classical boundary is a zero-parameter prediction rather than a free parameter or interpretive stance.

9. Neutrino hierarchy predicted: NH with Σm_ν ≈ 60 meV; right-handed neutrinos disfavored. The Z₃ Koide circulant with derived a_ν = 1 selects Normal Hierarchy. The S⁴ operator-mixing matrix shows N_F: 45→48 (adding RHNs) worsens the vacuum-expansion fit by +1.657%. Two independent lines of evidence point toward SM with 45 Weyl fermions, not 48.

10. 109 registered claims with rigorous tier discipline. 61 computed (backed by 2816 passing tests), 15 anchored, 18 open negatives with closure conditions. Three previously-blocking open negatives RESOLVED in v8→v2; Gate R closed; D = 1.0 growth failure diagnosed and resolved; Allen-Jacobson propagator implemented.

11. 31 documented corrections with full audit transparency. Foundational provenance audits, El Gordo reclassification, Genesis-BBN-DM narrative falsification, nine v8→v2 corrections, hard-theory corrections including Allen-Jacobson propagator, V4/V5/V6 matrix audit/repair, RHN falsification, Gate R closure, and linear growth diagnosis — all surfaced and documented.

12. Candidate, not completed. Remaining research packages: nonlinear quantum gravity beyond rung 4 of 8, Standard Model closure (Yukawas, CKM, Higgs potential), Poisson coupling from first principles (∂²S_CTP/∂σ∂ρ_m), curved-background Φ_μν beyond FRW, and the V5/V6 matrix's ~1.2% β_eff gap. The S⁴ CTP 3-loop solver is scaffolded through Stage 7J. The discipline pattern makes these gaps visible. Six near-term falsifiers are documented in the companion adversarial-roster paper.

GRUT ResponsiveAI Software Repository: www.github.com/ryangrvr/GRUT-RAI