Framework
ATLAS: A Geometric Field Theory
of Continuous Autonomous Intelligence
Scientific Hypothesis · Architectural Theorem · Production Implementation
The dominant paradigm in artificial intelligence — gradient descent over fixed architectures — has three structural failure modes: approximation without geometry, pattern without causality, and inference without time. ATLAS is a formal response to all three simultaneously, grounded in a single architectural principle: intelligence is a physical process characterised by a Riemannian geometry that encodes causal history, a perception mechanism that maps signal trajectories into that geometry, and an action mechanism that minimises expected free energy under a self-generated model.
This is not a better approximation system. It is a categorically different architecture — one that perceives through the complete geometric invariant of signal trajectories, represents the world through a self-organising Riemannian manifold whose metric tensors evolve continuously from experience, and acts without external reward. The framework is domain-agnostic by construction: the same theorems, the same canonical equations, the same production implementation apply identically whether the signals originate from an equity order book, a drone's inertial unit, or a planetary rover's spectrometer array.
Mathematical Foundations — Eight Unified Domains
Theorem A1 · The Autonomy Theorem · Pending external review
Under hypotheses of V-geometric ergodicity and oracle-freedom, an ATLAS agent converges to the regime-optimal policy at rate O(τmix · log 1/ε), with all six constants explicitly computable from observable path data. Computationally verified. The first proved extension theorem of the framework.
I1: V-geometric ergodicity · E100: BCH Hall log-signature · E200: exact discrete OU · E300: natural gradient GNG · E600: K-step EFE lookahead · G3-k: metastable regime partition · C-family: causal DAG recovery · R-family: Q32.32 perturbation bounds
The framework has a reference implementation in production Rust — deterministic Q32.32 fixed-point arithmetic throughout, sub-microsecond decision cycles on institutional-grade hardware, streaming BCH Hall log-signatures computed over a 30-dimensional Hall basis, online Hawkes infectivity estimation via recursive maximum likelihood, and a self-evolving kernel architecture with zero heap allocation in the hot path. Theory and implementation are developed against a single canonical specification. The theoretical objects are computable, not merely formally stated.
Sealed Spine
V-geometric ergodicity, projection operators, minorization, Q32.32 invariants
Module A
Oracle-free regime convergence — proved, constants derived, computationally verified
G-family
Geometric regime detection with spectral gap guarantees and GNG convergence
R-family
Quantization robustness — invariant-law perturbation bounds under Q32.32
C-family
Causal DAG recovery — consistency and convergence rate under causal rates model
M-family
Metacognitive closure — self-knowledge index and second-order perception
The framework generates five falsifiable predictions with explicit falsification criteria: power-law prediction error decay consistent with self-organised criticality, causal skeleton recovery convergence from online infectivity estimation, somatic stability under exact Ornstein-Uhlenbeck dynamics, causal DAG recovery at rate O(n−1/2), and swarm coherence emerging from mutual perception alone — without communication protocol, coordinator, or explicit state sharing. These are not design goals. They are necessary consequences of the theory.
Contact
k.petrov@synoragroup.euEnquiries regarding the ATLAS framework, research collaboration, peer review, and certification methodology are welcome.