The Braided Memory Register: A Consilient Model of Memory Across Mathematics, Computation, and Social Propagation
Year: 2026
Type: article
Abstract: Memory — whether biological, computational, or social — has been described using incompatible formalisms: ultrametric trees for hierarchical clustering, braid groups for associative binding, Merkle DAGs for content-addressable versioning, and graph theory for social propagation. This paper proposes that these are not competing models but facets of a single abstract structure: the Braided Ultrametric Register. We present evidence from five converging domains — spin-glass physics, Andean quipu record-keeping, blockchain/git version control, social media propagation, and modern hierarchical neural networks — that a unified mathematical object exists at their intersection. The central conjecture (ultrametric distance = braid word length, up to scaling) was falsified across all five metric variants (R^2 < 0.5) using 60 synthetic topologies, but the five-pillar structural consilience survives independently. The QNFO living-paper corpus was enriched with individual author metadata (100 papers) but confirmed as a single-author corpus, blocking co-authorship-based validation. The paper recommends a pivot from metric to structural/entropy measures (Jones polynomial, braid index, Vassiliev invariants) and documents the infrastructure (2 live Cloudflare Workers, Python library v0.1.0, R2 archive) built to support the research.
Author: Quni-Gudzinas, Rowan Brad
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7167252205