Archived research
This section constitutes the formal archival record of the Structural Coherence Mathematics (SCM) research programme.
While the Research page describes ongoing development and open lines of inquiry, the documents listed here represent fixed, versioned, and citable outputs. These texts define the specific statements, principles, and derivations for which the programme accepts structural accountability at the time of publication.
The Publications page is archival in nature. It does not summarize, promote, or interpret the content of these works. Its purpose is to make the research record explicit, stable, and independently examinable.
Where revisions occur, they are versioned. Earlier versions remain accessible in order to preserve the integrity of citation and the transparency of development.
Prospectus
Prospectus of the Coherence Algebra Programme
Status: Published
Version: v1.0
Date: December 2025
This document provides a concise axiomatic and structural overview of the monograph The Coherence Algebra. It states the foundational principles (FP1 and FP2), clarifies the scope and limits of the framework, and outlines how the subsequent formal development is organized.
The prospectus does not present full derivations or technical proofs. Its role is to fix the structural commitments of the work and to make explicit the assumptions under which the formal development proceeds.
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Foundations of Coherence Algebra
Status: Paper (Preprint)
Version: v1.0
Date: January 2026
This paper establishes the foundational structure of the SCM programme. Starting from minimal assumptions about persistence and self-verification, it derives the mathematical arena required for coherent existence.
The work introduces two foundational principles (FP1 and FP2) and shows that their joint requirements force a specific algebraic and geometric structure. In particular, the paper derives Hilbert space as the minimal representational arena capable of supporting recursive self-verification, without assuming quantum mechanics, probability, or dynamical laws.
The scope of the paper is deliberately foundational. It does not propose new dynamics or physical models, but fixes the structural conditions under which such models can meaningfully exist.
This document serves as the primary reference for the structural commitments of the SCM framework.
Download: Foundations of Coherence Algebra
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Physical Law from Structural Coherence
Status: Monograph (Preprint)
Version: v1.0
Date: March 2026
This monograph presents the full structural development of the Structural Coherence Mathematics (SCM) programme.
Starting from two minimal postulates — coherent return and triadic closure — the work investigates which mathematical structures are admissible for any system capable of coherent persistence under finite resolution. Within explicitly stated domain restrictions, the analysis derives the minimal representational and relational frameworks required to sustain such persistence.
The monograph develops these consequences sequentially. It derives complex Hilbert space structure and quadratic weighting as the minimal representation compatible with composable return, establishes relational geometry as the external response required to accommodate distributed coherence cost, and shows how irreversible pruning under finite resolution induces temporal ordering and thermodynamic monotonicity. Localization of internal representational redundancy leads to gauge connection and curvature structure, while triadic equilibrium applied to quadratic mass amplitudes yields the Koide relation as a conditional numerical constraint.
The work does not introduce new dynamical laws or phenomenological models. Its aim is structural: to identify why the mathematical forms of quantum theory, gauge theory, general relativity, and thermodynamics are admissible at all within a framework of coherent persistence. Empirical theories operate within this admissible space, selecting particular solutions and parameter values.
This document constitutes the most complete formal statement of the SCM framework to date and integrates the results presented in earlier programme papers into a single structural development.
Download: Physical Law from Structural Coherence (via Zenodo)