Donald G. Palmer

SS-PIVOT: From Scale Geometry to Gravitational Dynamics: What the Configuration Manifold Determines—and What It Does Not

Promoting physical logarithmic scale to a coordinate produces a well-defined Riemannian Scale Space configuration manifold. The companion geometry paper derives its normalized hyperbolic metric, invariant measure, scalar Green function and finite-profile projection theorem. Those...

SS-GEO: Logarithmic Scale as a Geometric Coordinate: Exact-Distance Projection and Radial Scale Response

Physical scale is represented by the dimensionless logarithmic coordinate u = ln(ℓ/ℓ₀). Under the explicit postulate that ordinary spatial intervals scale as eᵘ and that the scale direction has constant metric coefficient, the configuration metric is dΣ² = e^(2u)dx² + a²du². It i...

CNRS-Pr4: Partial Operational Completeness of a Positional Number System for Complex Numbers

We study operational completeness of the canonical number system (CNS) for the base z0 =−2 + i in Z[i], extended to a positional system for the complex numbers, together with a differential extension. The system comprises: Layer 1 (CNRS-A), the CNS itself with digit alphabet {0,1...

CNRS-Pr3-1: Arithmetic Closure for the Complex Numeric Representational System: Working Paper — Problem 3 of the CNRS Programme

Problem 3 of the Complex Numeric Representational System (CNRS) programme asks whether addition and multiplication of CNRS digit strings — that is, digit strings in base−2 + i with digit alphabet {0, 1, 2, 3, 4}— are computable by finite automata. This is the difference between h...

CNRS-Pr2: Complex Numbers as Single Values: A Three-Layer Architecture for the Complex Numeric Representational System

We present a three-layer architecture for Problem 2 of the Complex Numeric Representational System (CNRS) programme: the construction of a positional numeral system in which a single sequence of real integer digits encodes a single complex number, with no ordered-pair structure,...

CNRS-Pr2(1-3): A Single-Value Complex Numeral System via Canonical Number Systems and the Riemann Surface of the Logarithm

We construct a positional numeral system in which a single sequence of real integer digits encodes a single complex number — with no ordered-pair structure and no separator symbol between real and imaginary parts — and on which the logarithm and exponentiation are single-valued....