Substrate Logistics: The Garbage Collection Threshold

Title: Substrate Logistics: The Garbage Collection Threshold — Compiled Baryonic Scaling, the 4-Channel α-Particle Activation Ceiling, and the Parameter-Free Derivation of the Hubble Rate Author: Marco Lindenbeck Description: The 5σ Hubble Tension (67.4 km/s/Mpc vs. 73.0 km/s/Mpc) represents a fundamental crisis for the empirical standard model. This manuscript resolves the discrepancy by demonstrating that the cosmic expansion rate is a dynamic local function of compiled node density. By evaluating the Global Resting Cover Ledger (Σ0,Ledger = 6.0022 × 10⁻¹⁰ J/m³) across the void cover partition (ΩΛ,void = 0.781726), the global baseline expansion rate is derived parameter-free as Hglobal = 67.42 km/s/Mpc, matching the Planck CMB baseline. Auditing the 10 Mpc Local Volume reveals that only compiled 3D matter (Γ-knots, 3.70 × 10¹² M_) commands active spatial Garbage Collection (g_Ω), while diffuse baryons (WHIM/IGM) are processed passively by the global background cover, resolving the Missing Baryon Problem. Inputting this compiled node density (ρN = 0.03573 nodes/m³) yields a coordinate pointer recycling boost of Δ H = 5.64 km/s/Mpc, predicting Hlocal = 73.06 km/s/Mpc, matching the empirical SH0ES Cepheid/SNe Ia benchmark (73.04 ± 1.04 km/s/Mpc) to within 0.03%. Empirical Catalog Benchmark & Open-Source Pipeline: The manuscript includes direct empirical validation across 451 cataloged galaxies from the Karachentsev et al. (2004) Catalog of Neighboring Galaxies (CNG). Evaluating the 3D density field maps a catalog mean of H̄local = 71.48 km/s/Mpc (σ = 2.27 km/s/Mpc), dynamically scaling from 67.51 km/s/Mpc in deep cosmic voids up to 76.54 km/s/Mpc in dense group cores. This spatial environmental gradient effortlessly reconciles intermediate Tip of the Red Giant Branch (TRGB) values (~ 69.8 km/s/Mpc) with high-density Cepheid/SNe Ia benchmarks (~ 73.0 km/s/Mpc). Furthermore, equating localized mass deletion to the resting vacuum ledger isolates an exact critical node threshold of ρN,GC = 4 nodes/m³ (6.678 × 10⁻²⁷ kg/m³). This threshold is proven to be the exact 4-channel vector saturation ceiling of the metric (4λ̄ₚ), identifying the Helium-4 nucleus (α-particle, 2p+2n = 4 nodes) as the elementary minimal closed-shell spatial lock of the universe. Code & Data Availability: Complete evaluation pipelines, VizieR catalog parsing scripts, and output data tables are open-source on GitHub: https://github.com/LoopBreacher/substrate-logistics-local-expansion-field.