Indiscrete Scalar Ontology: A Universal Framework for Scale-Relative Combination and Emergence

Indiscrete Scalar Ontology (ISO) proposes that scale is a fundamental dimension of reality. Four primitives — scale position (θ), coupling (κ), cross-scale resonance (ℛ) and a conserved combination potential (Ω) — generate testable structure across particle physics, cosmology, quantum foundations, atomic and chemical physics, fluid dynamics, and beyond. This second edition extends the original framework across fifteen application domains, adds a plain-language overview and per-section summary panels, states the honest negative results alongside the successes, and ties every numerical claim to an archived verification script (143 checks). Seven companion papers provide the detailed derivations, including the proposed geometric invariant 1/α = 4π³ + π² + π (2.2 ppm), the derived dark-energy oscillation frequency ω_Λ = πH_∞, and a pre-registered, parameter-free 21cm prediction in the cosmic dark ages (z = 19.5, 69.4 MHz). What's New in v2: Expanded thermodynamics (5.3): second law from Ω-dispersal; temperature as θ-gradient. Arrow of time (6.6): unifies thermodynamic, cosmological and psychological arrows via monotonic tick count n. Hierarchy problem (6.7): ℛ-suppression mechanism for the 10^36 force ratio. Atomic physics (6.8–6.10): helium ground state −79 eV; chemical bonding ΔΩ > 0 criterion, H₂ = 4.5 eV; periodic table 2n² shell capacity. Turbulence (6.11): Kolmogorov −5/3 spectrum from the θ-cascade; C_K ≈ 1.5, intermittency μ ≈ 0.2. Fundamental constants, updated (6.12–6.13): fine structure as the proposed geometric invariant 1/α = 4π³ + π² + π (2.2 ppm), epoch-independent, with z ≈ 19 reinterpreted as a resonance crossing; dark energy with derived oscillation frequency ω_Λ = πc/R_E = πH_∞ (period ≈ 35 Gyr), reproducing the reconstructed w(z) shape. Speculative applications (6.14–6.15): musical harmony C(p:q) = 1/(pq)^(3/2); Riemann hypothesis in Mellin space. Summary table (6.16): all applications organised by confidence level. Falsifiability (9.3, updated): α exactly constant at all epochs; a parameter-free 21cm coordinate at z = 19.5 (69.4 MHz) with computed depth −475 mK. Synthesis (NEW 9.4): three-tier assessment (translation / structural unification / selective failure); unengineered convergences; four programme initiatives, with the dark-ages programme executed in two companion papers. Accessibility: plain-language overview ("ISO in Plain Terms") and non-technical panels opening every application section. Appendix B: companion list expanded to include the geometric-invariant, dark-ages programme and crossing-coupling papers. This version (2.1) corrects the typesetting of all mathematics in the PDF.