What question did this study set out to answer?

The goal is to derive the hierarchical filter factor $k$ within the context of the Projective Dynamic Logo framework.

April 23, 2026Open Access

Closure of OP-B: Derivation of the Hierarchical Filter Factor k from the PDL Axioms

Key Points

The goal is to derive the hierarchical filter factor $k$ within the context of the Projective Dynamic Logo framework.
Utilized finite signed graphs based on four axioms
Analytically derived key parameters such as gravitational constant without free parameters
Connected $k$ to various elements in a causal chain including $eta_{ ext{geom}}$ and coherence filters.
Successfully derived $k = 0.921716$ with a minimal residual of 0.4 ppm compared to the CODATA 2022 value
Established a complete causal chain from PDL axioms leading to significant physical constants
Ensured the derivation does not rely on external parameters apart from the mass difference $eta_m$

Abstract

The Projective Dynamic Logo (PDL) programme derives the structure of physical reality from four axioms on finite signed graphs, without presupposing spacetime, particles, or fields. This document resolves OP-B, the last remaining structural gap in the gravitational branch of the PDL causal chain. The hierarchical filter factor k = 0. 921716, which connects the geometric leakage parameter ₆₄₎₌ = 329/10087 to Newton's gravitational constant G via 18 coherence filters, is derived analytically from axioms C1–C4 without any free parameter. The key result is k = (1-₆₄₎₌) (rₕ₀₋/Rₓ₎ₓ) ^1/18, yielding k = 0. 92172 with a residual of 0. 4 ppm relative to the CODATA 2022 experimental value. With OP-B resolved, the complete causal chain C1–C4 → K₄ → proton quintuplet → ₆₄₎₌ → G → G is established as a sequence of unconditional theorems, with m₈ₒ₎ = md - mᵤ as the sole external input. Document D44 of the PDL Framework.

Closure of OP-B: Derivation of the Hierarchical Filter Factor k from the PDL Axioms

Key Points

Abstract

Cite This Study