Vacuum Information Density as the Fundamental Geometric Scalar: The Covariant Four-Pillar Architecture of the Yang-Mills Mass Gap (UIDT v3.9.8)
Description
The Unified Information-Density Theory (UIDT) presents a constructive proposed theoretical framework that explores geometric connections between Quantum Field Theory and General Relativity via information-geometric methods. Version 3.9 consolidates the Four-Pillar Architecture by combining a rigorously verified QFT core with a covariant scalar-field extension, a lattice-torsion model, and a photonic analog platform. Canonical parameters are obtained self-consistently within the UIDT framework using the Extended Functional Renormalization Group (FRG) and a Banach fixed-point construction for the Yang–Mills sector. The analysis yields a numerically stable vacuum solution characterized by the spectral gap Δ = 1.710 ± 0.015 GeV, coupling ratio κ = 0.500 ± 0.008, the self-coupling λS := 5κ²/3 (exact RG fixed-point definition), and the phenomenological invariant γ = 16.339. The kinetic vacuum expectation value is v = 47.7 MeV [A]. These parameters exhibit numerical closure with residuals below 10⁻⁴⁰ in the constructive core and are consistent with continuum-extrapolated lattice-QCD results where applicable. The invariant γ = 16.339 is phenomenologically calibrated from the kinetic vacuum expectation value (Category A⁻) rather than derived from renormalization-group first principles in UIDT v3.9. A recent algebraic analysis identifies a candidate expression γbare = (2Nc+1)²/Nc = 49/3 ≈ 16.333 from SU(3) Casimir structure, matching the canonical value to 0.037%. The physical dressing shift δγ ≈ 0.006 from the bare to the calibrated value remains under investigation via momentum-dependent FRG vertex flows (Limitation L4, Category D). Version 3.9 completes the synthesis of the Four-Pillar Architecture: the QFT foundation (Pillar I), lattice topology and torsion binding energy (Pillar II), spectral expansion and thermodynamic noise thresholds (Pillar III), and macroscopic isomorphism with nonlocal optical media (Pillar IV). Within UIDT, the lattice torsion binding energy ET = 2.44 MeV is defined as an entropic scale that parametrizes a torsion-related binding contribution in the hadronic sector and is explicitly classified as a quantitative Category D prediction. Within this structure, the framework implements a multi-stage suppression mechanism for the effective vacuum-energy density, combining the non-perturbative spectral gap, the invariant scaling factor γ, and an empirically defined 99-step renormalization-group cascade (N99). The N99 cascade represents a leading-order phenomenological scaling rule; a next-to-leading-order correction yields N ≈ 94.05, and both are documented in the canonical audit with their respective precision bounds.
Files
Steps to reproduce
UIDT v3.5.6 — Reproduction Protocol Runtime: Python ≥3.10 Dependencies: numpy Objective: Deterministische Verifikation von Mass Gap Δ, Gamma‑Invariant γ und DESI‑kalibrierter Kosmologie. --- Proof 1 — Environment Initialization ```bash git clone https://github.com/badbugsarts-hue/UIDT-Framework-V3.2-Canonical.git cd UIDT-Framework-V3.2-Canonical pip install -r requirements.txt sha256sum -c reproduction_manifest_v3.5.6.sha256 ``` --- Proof 2 — Mathematical Closure (Pillar I) ```bash python UIDT-3.6.1-Verification.py ``` Criteria: Residuals < 1e‑14 (3 coupled equations) Target: γ ≈ 16.339 | Δ ≈ 1.710 GeV --- Proof 3 — Lattice QCD Simulation (HMC) ```bash python Supplementary_Scripts.for.Simulation/UIDTv3.6.1_HMC-MASTER-SIMULATION.py ``` Note: GPU/CuPy empfohlen für >20k Schritte. --- Proof 4 — Cosmic Simulation Dependencies: numpy, matplotlib ```bash python Supplementary_Scripts/uidt-cosmic-simulation.py ``` Validation: 1. Flache Rotationskurven (JWST high‑z) 2. Kausaler Horizont > physikalische Skala vor Δ‑Transition 3. Asymptotische Vakuumdichte‑Konvergenz --- Phase 5 — Data Clay Audit Dependencies: numpy, pandas, mpmath 5.1 Grand Audit ```bash python Supplementary_Scripts/uidt_clay_grand_audit.py ``` Pass: L < 1.0, Residual = 0.0 Artifacts: Supplementary_Data_Clay_Audit/3.6.1-grand/UIDT_v3.6.1_Audit_*_Audit_Certificate.txt 5.2 Canonical Audit ```bash python Supplementary_Scripts/uidt_canonical_audit.py ``` Pass: Banach‑Konvergenz <50 Iterationen Artifacts: Supplementary_Data_Clay_Audit/3.6.1-canonical/Audit_Log_v3.6.1.txt --- Cross‑Verification Hash‑Abgleich mit reproduction_manifest_v3.5.6.sha256 bestätigt konsistente Δ‑Konvergenz. --- Validation Gates Residuals < 1e‑14 HMC R̂ ≤ 1.1 Casimir‑Anomalie +0.59% ±0.05% @0.66 nm Δ = 1.710 ±0.015 GeV H₀ = 70.4 ±0.16, S₈ = 0.757 ±0.002 --- Result Summary (v3.6.1) Scalar Mass 1.70496 GeV, VEV 47.7 MeV (corrected), γ = 16.2866. Vacuum density 1.08e‑49 GeV⁴, hierarchy reduction 10¹²⁰ → 3.3%. Status: Clean State, mathematisch geschlossen. Evidence: Supplementary_Results/Verification_Report_v3.6.1.md SHA‑256: 13e9f5e4a7c629d26aecb8c517fe3d54784e588d0c368d59cb0cb318b285bf24