Topological Protection Through Validated Memory: A Mathematical Framework for Identity Persistence in Adaptive Systems
Year: 2025
Type: article
Abstract: We introduce the Coherence-Rupture-Regeneration (CRR) framework, a mathematicaltheory for adaptive systems that maintain identity through discontinuous transformations.The framework’s core innovation is a topological arrow of time that protects system iden-tity via distributed memory encoding whilst permitting local plasticity through rupture-regeneration cycles.Three operators define the dynamics: coherence integration C(t) = R L(x, τ )dτ , rupturedetection via degradation signatures, and validated memory regeneration R[χ] = R ϕ(τ ) exp(C(τ )/Ω)dτ .Critically, the scalar coherence C(t) can reset locally at ruptures whilst the field configura-tion {C(τ )}τ
Author: Cohere.org.uk
Language: English
Topic: Complex Systems and Dynamics
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7088017570
FWCI:
Cites:
Cited by:
Related to: