The Volumetric Buoyancy–Occupancy Interface Model: A Three-Phase Picture of the Dark Sector, with Falsifiable Threads and Honest Limits

Title: The Volumetric Buoyancy-Occupancy Interface Model: A Three-Phase Picture of the Dark Sector, with Falsifiable Threads and Honest Limits Series: TZPID Gold Spine Series II, Paper XVI of XX Author: Daniel Alexander Trawin Overview Following the findings in Paper XII (The Spartan Dawn Test), which favored a dynamical dark-energy term F (a) but supplied no underlying mechanism, this paper constructs a rigorous mechanical model to account for the term. Rather than relying on conceptual metaphors, the framework introduces a localized physical mechanism while explicitly delineating the model's boundary constraints, falsifiable exposures, and theoretical limitations. Theoretical Framework The model formalizes a three-phase occupancy field bounded by the constraint ₁+ₓ+₄=1, where effective volumes are defined by V₈=ₒ^₃₈dV. Within this framework: Ordinary Matter (₁) acts as a finite-viscosity interface condensate or standard sech² domain-wall kink between immiscible phases. The Topological-Current Phase (ₓ) serves as the candidate dark matter. The Breathing-Volume Phase (₄) serves as the candidate dark energy. Globally, the enclosure seeks a macro-level volumetric equilibrium governed by the master balancing equation: ₕJ B-~ v+~g₄₅₅+ P₄+f₈₍ₓ-=0 Critical equilibrium is established at the Elsasser criticality attractor: ₄=B^2₀1 Falsifiable Handles & Diagnostics The Elsasser Attractor: The empirical attractor ₄1 is testable against active dynamos in rotating conductive systems (laboratory dynamos, planetary cores, and stellar bodies). Breathing Equation of State: The conjecture that the breathing pressure gradient P₄ derives the dark-energy equation of state w (a), aiming for the target parameters w₀-0. 6 and w₀-1. 4 established in Paper XII. The work leverages robust physics components as substance-versus-residual diagnostics, including the Hodge decomposition (=d++H₊), magnetic helicity conservation (H₌=ₕA B~dV), and ⁴ domain-wall soliton profiles. Honest Limits & Demarcation To maintain strict analytical transparency, four explicit theoretical vulnerabilities are detailed: Symbol Collision: Clarifying that the Elsasser number (₄) and the cosmological constant () are physically unrelated variables sharing a glyph. Radiation-like Scaling: Addressing the seductive error of the nested-mode density scaling as ₍ R₍^-4, which behaves like traditional radiation dilution rather than constant dark energy density. Unmet Dark-Matter Bars: Acknowledging that the topological-current phase (ₓ) must still be reconciled with observational baselines, including flat galactic rotation curves, collisionless Bullet Cluster separations, the CMB third-peak baryon-to-dark ratio, and cosmic structure growth. Near-Tautology: Noting that a global volumetric balance law on a boundaryless manifold is a mathematical consequence of momentum conservation, meaning predictive value must rely entirely on individual localized terms. The framework functions as a rigorous structural scaffold with clear predictive exposures, handing off the calculation of the dark-energy equation of state directly to Paper XVII.