The Meta-Ledger:
A Parameter-Free Admissibility Scaffold for Physics (v19)

Description

This paper presents a 16-stage admissibility scaffold — a "meta-ledger" — that constrains what any candidate physics must satisfy, without introducing fitted parameters. Each stage is a minimal constraint layer with explicit No-Go rules, Barriers, and Falsifiers.

The framework separates form (invariant structure: closure, symmetry, audit) from mapping (units, calibration, representation choices). Physical constants and laws emerge as derived consequences of staged admissibility, not as postulates.

Key results

• Golden rotation as forced selection: The golden ratio φ⁻¹ is derived as the unique minimax anti-resonance choice for isotropic, memoryless updates on the circle (Hurwitz extremality), not assumed as a numerological motif.
• Iteration hierarchy: A strict separation of non-termination (U⁺), aperiodicity, and equidistribution — three levels often conflated — with proof that each requires independent justification.
• Inverse-square universality: The 1/r² backbone is proven locally universal across all FRW space forms (K = 0, ±1), with curvature and expansion producing only subleading corrections.
• DSI analytical backbone: Discrete scale invariance with ratio φ produces a Mellin pole lattice at z = μ + imω_φ (ω_φ = 2π/ln φ), with strict carrier discipline: the signature lives on ln s, never on raw time.
• Golden Survival Theorem: Mean survival fraction S = 1/4 if and only if the shell ratio R_a/r_a = φ, proven specific to d = 3 dimensions. This yields a parameter-free 25/75 matter/radiation source split.
• Dynamical attractors: The 25/75 split forces a stable 9/4 radiation-to-matter attractor (w = 3/13), with logistic saturation to 50/50 (inflection at 1/4). All values are structural (ratios/fixpoints), not fitted.
• Fractal necessity: U⁺ (no terminal scale) combined with DSI algebraically forces fractal source geometry with dimension D ∈ (0,3) and log-periodic golden modulations.
• Origin ≠ Structure: The term algebra of admissible operations satisfies T(S;O) ⊆ S with ω ∉ T(S;O). No generative path from structure reaches the origin. Provenance is not derivable from law.

Methodology

The paper introduces a Barrier Calculus partitioning all claims into Existence (with proof), Barrier (with no-go proof), and Horizon (undecided). Each major result is tagged as Proof, Barrier, Conjecture, or Heuristic. A strict DSI detection protocol (8 steps, p-hack-resistant) and an All-or-Nothing test battery (4 joint tests, no parameter retuning) are provided as appendices.

Nine cross-stage Concept Boxes consolidate Time, Gravitation, Electromagnetism, Geometry & Observer, the Iteration Hierarchy, Scale Narrative (Micro→Meso→Macro), Fixpoints & Attractors, DSI→Fractality Necessity, and an optional CMB Phase-Interference Hypothesis.

Falsifiability

The framework is falsifiable at multiple levels: logical (counterexamples to form claims), structural (violation of closure/audit identities), and empirical (preregistered DSI signatures, hemisphere tests, Cauchy wave-speed ratio). A diagnostic failure-mode table maps each observable failure to the specific structural block it breaks.

Relation to companion papers

This work integrates and extends results from:

• The Simplicity Theory, Part 1 (DOI: 10.5281/zenodo.16811309): Non-collapse, golden rotation, equidistribution on S²
• The Simplicity Theory, Part 2 (DOI: 10.5281/zenodo.16837391): Dynamics, attractors, discrete scale invariance
• Supplement S to Part 2: FRW universality, Mellin analysis, Rice-type undecidability, detection protocols
• The Simplicity Theory — Math Manifest: Barrier Calculus, uncertainty barriers, one-page axiom summary
• Origin ≠ Structure (Cryptic Edition): Provenance separation, Guardian Principle

Keywords

parameter-free physics, admissibility scaffold, golden ratio, discrete scale invariance, Hurwitz extremality, inverse-square law, barrier calculus, falsifiability, equidistribution, fractal geometry

License

CC BY 4.0