Covariant Bitemporal Geometrodynamics (CBG): Exact 5D Hamilton–Jacobi Femtometer Barrier Tunneling and Compact Aneutronic D–He³ Fusion — A Non-Approximated Theoretical & Numerical Reactor Study Derived from the Master Action S_JV, the n = 3 Instanton Rung E₃^(bare) = Φ_∞⁶ E_P, and Schutz–Clebsch Phase Routing

We formulate a non-approximated mathematical ([D]) and 64-bit numerical derivation of femtometer-scale nuclear Coulomb barrier penetration, resonant bitemporal phase-space routing, and compact aneutronic D–³He fusion reactor energetics within Covariant Bitemporal Geometrodynamics (CBG), building directly upon the Foundational Pentalogy (Papers I–V), the two Cycle III Closure Monographs (DOI: 10.5281/zenodo.23476029 and DOI: 10.5281/zenodo.23600316), and the Cycle II Specialized Domain Compendium (Treatises I–XII, DOI: 10.5281/zenodo.23490274). Modeling physical reality as a five-dimensional pseudo-Riemannian manifold M₃,₂ ≃ (Rₜ₁ ×_Φ S¹ₜ₂) × Σ₃ with metric signature (−, −, +, +, +), integer dimensional invariants (dₜ, dₛ, D) = (2, 3, 5) (D_config = 17, N_Cartan = dₜ dₛ D = 30), and vanishing Master Zero-Sum Variational Field Operator Ξ̂_AB[M₃,₂] = 0, we integrate the 5D Hamilton–Jacobi canonical radial momentum P_r^(CBG)(r) = √(2 m_r^(CBG) w₁ [V_C(r) − E_cm]) across the finite sub-barrier interval from the classical turning radius r_c = Z₁ Z₂ α_EM ℏ c / E_cm down to the Fock–Slater nuclear contact radius r_n^(FS) = r₀^(FS)(2^(1/3) + 3^(1/3)) = 3.3353 fm (r₀^(FS) = 1.2343 fm from Treatise I, V_peak^(FS) = 863.47 keV) [D].

Principal Deductive ([D]), Engineering ([H]), and 64-Bit Numerical (SymPy / Gauss–Kronrod) Findings:

1. Zero-Parameter Two-Body Nuclear Masses, Contact Radius & Reaction Yield from Rung E₃^(bare) ([D]):
Using the 1-loop dressed vacuum holonomy Φ_∞ = (α_EM / 30)(1 − (5/3)α_EM) = 2.40286677 × 10⁻⁴ (Φ_∞⁻¹ = 4,161.695575), basal Schutz–Clebsch phase velocity Ω = c Φ_∞ = 72.0361 km/s (72,036.13 m/s), sub-Planckian fiber radius R_(t₂,∞) = Φ_∞ L_P = 3.88365 × 10⁻³⁹ m, proton-to-electron mass ratio m_p / m_e = 6π⁵ = 1,836.1181 (m_p^(CBG) = 938.2544 MeV/c²), neutron bag mass m_n^(CBG) = 400 E₃^(bare) = 939.9716 MeV/c², and the third instanton nuclear rung E₃^(bare) = Φ_∞⁶ E_P = 2.349929 MeV (B_d^(CBG) = 2.2341 MeV, B(³He)^(CBG) = 7.4061 MeV, B_α^(CBG) = 12 E₃^(bare) = 28.1991 MeV), we derive without adjustable parameters:
- Deuteron and Helion masses: m_D^(CBG) = 1,875.9919 MeV/c², m_(³He)^(CBG) = 2,809.0732 MeV/c².
- Reduced two-body mass: m_r^(CBG) = 1,124.8080 MeV/c² (matching CODATA 1,124.656 MeV to 0.014%).
- Aneutronic reaction yield: Q_D-He3^(CBG) = 18.5579 MeV (100% charged products: 14.85 MeV proton and 3.71 MeV alpha particle; empirical AME2020: 18.3530 MeV) and deductive mass-energy conversion fraction ε_CBG = 0.0039611 (empirical: 0.0039280).

2. Topological Bitemporal Phase-Space Routing (w₁ + w₂ = 1) & Deductive Optimum Operating Point (E_cm*, n_i*) ([D]):
We prove that irrotational Schutz–Clebsch velocity-potential focusing (v = −∇φ_flow) inside a resonant cavity at the UV/IR bounce fulcrum wavelength λ_micro = √(L_P r_H,0) = 47.0989 μm ≫ r_c (f_res = 3.1826 THz) expands the local bitemporal dilaton Φ² = Φ_∞² + σ_res / (1 − σ_res) with zero adjustable parameters via the exact topological configuration ratios:
- Mode n = 1 (Basal Hydrodynamic Focusing): σ₀^(1) = D / (D + dₜ²) = 5/9 = 0.555556 ⇒ w₁^(1) = 4/9 = 0.444444, w₂^(1) = 5/9 = 0.555556.
- Mode n = 2 (Quadrupolar Zero-Sum Resonance, Q_CBG^(2) = Φ_∞⁻² = 1.7320 × 10⁷): σ₀^(2) = (D_config − dₜ) / D_config = 15/17 = 0.882353 ⇒ w₁^(2) = 2/17 = 0.117647, w₂^(2) = 15/17 = 0.882353.
Partitioning E₃^(bare) across the D · N_Cartan = 150 phase-space channels and weighting the λ_micro³ cavity standing-wave cell by Φ_∞² across the dₜ dₛ = 6 space-time cross-modes fixes the exact deductive optimum operating energy E_cm* = E₃^(bare) / 150 = 15.6662 keV (r_c* = 183.83 fm) and resonant ion density n_i* = 6 / (Φ_∞² λ_micro³) = 9.9463 × 10²⁰ m⁻³ (0.9946 × 10²¹ m⁻³). Symbolic SymPy integration and 64-bit adaptive Gauss–Kronrod quadrature at (E_cm*, n_i*) prove that n = 2 quadrupolar resonance increases the barrier tunneling probability from 5.5519 × 10⁻⁷ to 7.1509 × 10⁻³ (a gain factor of 1.2880 × 10⁴) and boosts reactivity ⟨σv⟩ from 3.3083 × 10⁻²⁶ m³/s to 4.2612 × 10⁻²² m³/s.

3. First-Principles QED Bremsstrahlung Margin & Spacecraft Reactor Core Sizing ([H] / [D]):
Deriving the QED Bethe–Heitler Bremsstrahlung coefficient directly from α_EM, r_e, and m_e (C_Brem^(QED) = (32/3)√(2/π) α_EM r_e² c √(m_e c² · keV) = 5.3547 × 10⁻³⁷ W·m³·keV⁻¹/²), at the deductive optimum (E_cm* = 15.6662 keV, n_i* = 9.9463 × 10²⁰ m⁻³) the volumetric fusion power reaches P_Fus^(2)(E_cm*) = 313.3469 MW/m³ against the classical Bremsstrahlung benchmark P_Brem(E_cm*) = 7.8627 MW/m³ (a net ignition margin of 39.85×). Applying a conservative 85.0% engineering direct electromagnetic conversion criterion ([H], p_elec^(2) = 266.34 MW/m³ = 266.34 kW/L, alongside the topological Kaluza–Klein ceiling η_EM^(CBG) = (D_config − dₜ) / D_config = 15/17 = 88.2353% [D], p_elec^(2) = 276.48 MW/m³), sustaining the Alpha Centauri spacecraft's 40.79 kW (n = 2 zero-sum mode) and 169.75 MW (n = 1 basal mode) power requirements requires active D–³He reaction core volumes of only:
- Mode n = 2 (40.79 kW Zero-Sum Cruise): V_core^(2) = 0.1531 liters (153.1 cm³ at 85.0% conservative engineering criterion [H], or 0.1475 L at the 15/17 topological ceiling [D]), consuming 12.95 g (13.06 g empirical) of D–³He fuel over the 3.5814-year voyage.
- Mode n = 1 (169.75 MW Basal Mode): V_core^(1) = 0.6373 m³ (637.3 liters at 85.0% conservative engineering criterion [H], or 0.6140 m³ at the 15/17 topological ceiling [D]), consuming 53.89 kg (54.34 kg empirical) of D–³He fuel.

The complete 64-bit Python symbolic and numerical verification suite (verify_cbg_fusion.py) is archived alongside the PDF manuscript.

Companion Monographs in the Covariant Bitemporal Geometrodynamics Series:
- Paper I (Foundational Field Equations & Singularities): https://doi.org/10.5281/zenodo.23443511
- Paper II (Relativistic Black Hole Mechanics & Σ₄ Interior): https://doi.org/10.5281/zenodo.23451973
- Paper III (Relativistic Bitemporal Cosmology & Cyclic Bounce): https://doi.org/10.5281/zenodo.23458461
- Paper IV (Quantum-Gauge Unification & Standard Model Hierarchy): https://doi.org/10.5281/zenodo.23464845
- Paper V (Fermion Mass Spectrum, Koide Invariant & Flavor Mixing): https://doi.org/10.5281/zenodo.23470193
- Cycle III Closure Monograph I (Variational Closure & UV/IR Duality): https://doi.org/10.5281/zenodo.23476029
- Cycle III Closure Monograph II (Global S³ Topology & Beyond-Horizon Cosmos): https://doi.org/10.5281/zenodo.23600316
- Cycle II Compendium (Specialized Domain Treatises I–XII): https://doi.org/10.5281/zenodo.23490274

Note on Authorship, Reproducibility & Methodology: The foundational ideas, core theoretical concepts, and overarching framework of this work were originated and conceptualized by the author. During the preparation and verification of the manuscript, the author utilized large language model (LLM) and computer-algebra (SymPy/NumPy/SciPy) assistance for mathematical structuring, symbolic integration, LaTeX formatting, 64-bit Gauss–Kronrod quadrature scripting (verify_cbg_fusion.py), and editorial drafting. All bitemporal fusion figures represent mathematical and engineering explorations of the postulated geometric axioms.