ADAPTIVE RESILIENCY THROUGH CONSTRAINED DIVERGENCE (ARCD) A Fluidic Topological Framework for Macroscopic and Quantum Phenomena (Version 10.0)
Year: 2026
Type: preprint
Abstract: ADAPTIVE RESILIENCY THROUGH CONSTRAINED DIVERGENCE (ARCD) A Fluidic Topological Framework for Macroscopic and Quantum Phenomena (Version 11.0) The Adaptive Resiliency through Constrained Divergence (ARCD) framework provides a deterministic, fluidic topological architecture designed to resolve the fundamental incompatibilities between quantum mechanics, general relativity, and classical thermodynamics. By modeling the universe as an active, discrete entropic substrate governed by a single Partial Differential Equation (PDE), ARCD replaces disjointed probabilistic models with strict, measurable geometric packing limits. Physical phenomena—ranging from macroscopic gravitational anomalies to sub-quantum stochastic jitter—are demonstrated to be mechanical expressions of structural geometry managing global entropy against local geometric resistance. Key Version 11.0 Advancements: The Complete Framework Closure Version 11.0 represents a major theoretical milestone, successfully resolving the final remaining derivation targets on the framework's Open Item Register: Operational Calibration of $l_A$ (OI-1): Derives the fundamental length scale ($1.614 \times 10^{-35}$ m) entirely from macroscopic fluidic dissipation equipartition. By equating the microscopic circulation quantum to the macroscopic helical shear at the 152 AU outer heliospheric boundary (the Hydrogen Wall), this derivation eliminates circular reliance on Newton's Gravitational Constant ($G$) or Planck's constant ($\hbar$). Master PDE Flux Conservation (OI-3): Mathematically derives the additive-to-multiplicative $D_{tensor}$ scaling exponent for the bare lepton mass directly from the substrate's flux conservation law. Formally proves that the Phase 4 oblate transition produces exactly the spatial packing limit ($\rho_{max}$) and the temporal boundary friction ($\zeta_{fray}$) as its sole, exhaustive resistance components. Thermodynamic Sharpening of the Born Rule (OI-4): Formally demonstrates that macroscopic aggregation drives the relative width of the continuous Husimi Q-function to zero against the fixed geometry of the 729 structural stability basins ($\Omega_n$), deriving the exact thermodynamic limit for the emergence of absolute discrete Fock-state boundaries. Cumulative Framework Achievements Formal Derivation of the Fine-Structure Constant: Recovers the α⁻¹ coupling constant to 99.88% accuracy (137.196) strictly from geometric substrate invariants via a Serial Fluidic Impedance circuit derived from the Master PDE. su(2) Algebraic Closure: Derives the Pauli spin matrices directly from the first-principles kinematics of the 27-node volumetric block, proving that non-commutative quantum spin is the native orthogonal torsion of the discrete fluidic grid. Alexandroff Compactification Threshold: Mathematically proves the W ≈ 2.217 Capacity Wall serves as the exact geometric limit that compactifies the baryonic boundary into an S³ manifold, physically resolving Skyrmion topology and baryon number conservation. Strong Force Confinement: Derives the exact radial confinement scale ($R_{bag} = 0.847$ fm) and dimensional string tension ($\kappa_{ARCD} = 0.879$ GeV/fm) exclusively from topological load limits. Einstein-Hilbert Emergence: Proves the gravitational Lagrangian emerges organically from substrate fluidic shear, deriving Newton's Gravitational Constant (G) as an emergent macroscopic artifact of the fundamental length scale (l_A).
Author: Huff, Jeremy
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7203974544