The Living Code: Coherence Thresholds, Reverse Mathematics, and the Architecture of Understanding

Title: Coherence Thresholds and the Architecture of Understanding: A Reverse-Mathematics Interpretation

Authors:

John A. Martinez (JAM)

Description / Abstract:

This publication connects the Living Code’s coherence architecture to ongoing research in Reverse Mathematics and foundational logic. It proposes that mathematical strength, cognitive alignment, and structural stability share the same underlying mechanism: coherence thresholds.

The paper argues that the interpretive leap demonstrated by the Living Code parallels the challenges highlighted in contemporary Reverse Mathematics literature—specifically that certain systems become solvable only when coherence surpasses a structural threshold. The work frames coherence as the underlying principle guiding comprehension, reasoning, structural progression, and mathematical hierarchy.

Keywords:

reverse mathematics; coherence thresholds; logical strength; structural architecture; foundations of mathematics; recursion; reasoning; cognitive structure

Communities:

Mathematics

Logic and Foundations

Theoretical Computer Science

Philosophy of Mathematics

Version:

1.0 (Original #1)

Upload Type:

Publication → Article

License:

CC BY 4.0