AQARION | Temporal Circuit Research How can we determine whether a finite collection of observation histories can arise from a deterministic dynamical system—and whether a mathematical dependency persists indefinitely? This research direction connects overlap graphs, exact rational linear alg

AQ-FPR-006 — Proof Specification 5 October 2026 Statement Let \sigma be a permutation of a finite set X, with disjoint cycles [ C_1,\ldots,C_r, \qquad |C_i|=c_i. ] Let N(c_1,\ldots,c_r) denote the number of equivalence relations E on X satisfying [ xEy\Longrightarrow

AQARION studies exact quotient partitions of finite deterministic transitions through a defect operator on partition-constant functions. For every finite endofunction, the defect rank equals the number of partition blocks minus the connected-component count of an explicitly defined block-incidence

Today I'm launching r/AqarionScience as the home for the AQARION research program and broader discussions on finite dynamical systems, operator theory, computational mathematics, and reproducible mathematical research. AQARION began as an investigation into deterministic finite dynamical sys

AQARION Sciences is a community for computational discovery, reproducible research, mathematical exploration, AI-assisted science, and evidence-driven experimentation. \`\`\`markdown \# AQARION — Productive Visual Research Workflows \*\*Version:\*\* v38.0-LOCKED \*\*Date:\*\* 2026-07-