Covariant Bitemporal Geometrodynamics (CBG): Bitemporal Holonomic Telescopes, S¹ₜ₂ Polarimetric VLBI & Fabry–Pérot Gravitational-Wave Comb Observatories, and 47.10 μm Terahertz Dilaton / Casimir–Yukawa Quantum Microscopes

We formulate a parameter-free mathematical ([D]) and 64-bit numerical engineering design architecture for a new class of astronomical telescopes and quantum microscopes derived from Covariant Bitemporal Geometrodynamics (CBG)[cite: 7, 14, 22, 32, 41, 48, 57]. Because physical reality on the 5-dimensional manifold M₃,₂ ≃ (Rₜ₁ ×_Φ S¹ₜ₂) × Σ₃ with metric signature (−, −, +, +, +) and integer invariants (dₜ, dₛ, D) = (2, 3, 5) (N_Cartan = 30, D_config = 17, Ξ̂_AB[M₃,₂] = 0) connects the ultraviolet Planck scale (L_P = 1.616255 × 10⁻³⁵ m) to the infrared Hubble horizon (rH,0 = 1.372497 × 10²⁶ m) through the 1-loop holonomy invariant Φ_∞ = (α_EM/30)(1 − (5/3)α_EM) = 2.4028667690 × 10⁻⁴ (Φ_∞⁻¹ = 4,161.695575) and the UV/IR mirror fulcrum λ_micro = √(L_P rH,0) = 47.0989 μm[cite: 7, 41, 48], instruments engineered solely within (3+1)-dimensional physics discard the primary phase, polarization, and resonance channels of the compact temporal fiber S¹ₜ₂. Principal Deductive ([D]) and 64-Bit Numerical Instrumentation Designs & 24-Benchmark Discovery Program: 1. Achromatic S¹ₜ₂ Birefringence Tomographic Telescopes ([D]):Multi-band polarimetric arrays cooled to T_micro = 48.6187 K that separate astrophysical Faraday rotation (∝ ν⁻²) from the frequency-independent Berry–Kaluza–Klein holonomy rotation β_CBG(z) = 180° Φ_∞ ln(1 + z) (slope c_β = 0.043252°/e-fold)[cite: 32, 36], functioning as direct geometric cosmological rangefinders from local galaxy clusters (Coma z = 0.023, β = 3.54″; Bullet Cluster z = 0.296, β = 40.37″) to cosmic reionization (z_re = 7.70, β = 0.093567° = 336.84″) and CMB recombination (z_* = 1089.80, β = 0.302531° = 1,089.11″, Stokes EB/EE = 1.055952 × 10⁻²)[cite: 14, 32, 36]. 2. Berry-Phase VLBI Photon Sub-Ring Correlators (Δχ_n = n × 49.5627″) ([D]):Cross-hand space-ground VLBI correlators locked to the quantized EVPA holonomy step Δχ_n = n Φ_∞ rad = n × 49.5627″ and universal Lyapunov flux demagnification ratio Iₙ₊₁/I_n = exp(−π) = 0.04321392 across spatial baselines u_n ∈ {15.00, 72.16, 347.11, 1,669.77} Gλ to project out direct accretion emission and image the r_crit = r_s + L_P signature-flip boundary of Sgr A* and M87*[cite: 24, 27]. 3. Fabry–Pérot Gravitational-Wave Quantum Comb Observatories ([D]):Phase-locked matched-comb filter banks tuned to the tortoise cavity [r_s + L_P, 3r_s/2] (Δt_echo = 53.97 ms, Δf_comb = 18.5286 Hz for 30 M_☉; 132.43 ms, 7.5510 Hz for spinning GW150914; peak enhancement 12.2611×, peak-to-trough contrast 151.14 : 1)[cite: 22, 24, 26, 27], achieving a 50-harmonic coherent SNR boost of 24.76×–24.78× across LIGO/Virgo/KAGRA, Einstein Telescope, DECIGO, and LISA (10 M_☉ to 10⁶ M_☉). 4. 47.10 μm Terahertz Dilaton Near-Field Microscopes (SNOM-CBG) & Casimir–Yukawa Cryogenic AFM Microscopes ([D]):Near-field THz microscopes operating at the bitemporal dilaton carrier ν_dil = 1.013048 THz (mχΦc² = 4.189632 meV, T_micro = 48.6187 K)[cite: 7, 41, 43] with super-diffractive holonomy pitch Δx_SNOM = √Φ_∞ λ_micro = 730.09 nm to map Cooper-pair dimensionality domains ν_eff ∈ {4/5, 2, 9/4, 13/5, 14/5, 3} up to Tc,max = 145.8560 K[cite: 41, 44], paired with cryogenic Casimir–Yukawa AFM cantilevers whose force-gradient sensitivity kernel S_grad(x) = x² e^(−x) peaks at d_opt = 2λ_micro = 94.1978 μm (α_Yuk = 20 Φ_∞ = 4.805734 × 10⁻³)[cite: 7, 9]. 5. Levitated Optomechanical Diósi–Penrose–CBG Collapse Probes & 24-Item Discovery Program ([D]):Levitated nanomechanical probes at the critical holonomy mass m_crit = Φ_∞ M_P = 5.2297 ng (τ_col = 0.6833 μs for SiO₂, 0.6095 μs for Si₃N₄, 0.5845 μs for diamond NV, 0.5608 μs for sapphire, and 0.3313 μs for Au), accompanied by a master table of 24 quantitative CBG benchmarks and new physical phenomena to test and discover[cite: 7, 14, 22, 32, 41, 48, 57]. 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 numerical simulation scripting (verify_cbg_C4_paper3.py), and editorial drafting. All bitemporal quantum computing figures represent mathematical and engineering explorations of the postulated geometric axioms.