Technical Overview
ARIA System Architecture
A complete specification of the multi-layer resonant dynamical system, from the CFM substrate through the five ARIA abstraction layers. Core dynamics parameters derive from the golden ratio φ and its powers.
At a Glance
5-Layer Governance Stack
Before the detailed layer specifications below, here is the governance architecture in five layers — from raw substrate to verifiable evidence.
CFM Substrate
Coupled Field Model with 11 bounded state variables across 5 channels. The numeric foundation — no symbols, no semantics.
State Normalization
Raw state is normalized, smoothed, and aggregated into a 12D system state vector. Drift and turnover are measured.
Constraint Engine
17 CSC invariants enforce boundedness, determinism, and safety. Violations trigger fail-closed behavior.
Governance Gates
Gate decisions (ALLOW/DAMPEN/BLOCK) are threshold comparisons on measured coherence. Not predictions — measurements.
Evidence & Provenance
Every decision produces an evidence bundle: audit hash, state hash, reason codes, and replay token.
Layer Stack Overview
Each layer wraps and extends the previous, preserving bounded [0, 1] outputs
Foundation
The Resonant CFM Substrate
The Coupled Field Model provides the foundational dynamics upon which ARIA layers operate. CFM implements a system of coupled channels evolving according to deterministic differential equations discretized over time steps.
CFM v0
Simple Resonant CoreBasic coupled oscillator dynamics with uniform time constants. Four state variables (coherence, instability, energy, phase) with φ-derived parameters and bounded outputs.
- Coupled oscillators
- Energy attractor
- φ scaling
- Bounded outputs
CFM v1
Timescale SeparationIntroduces slow/fast variable separation. Six state variables: 3 slow (coherence, coherence_baseline, energy) and 3 fast (instability, phase, alignment_phase).
- 3 slow variables (τ ≈ φ²)
- 3 fast variables (τ ≈ φ⁻¹)
- Alignment resonance
- Interpretable trajectories
CFM v2
Multi-Channel ResonanceFull 5-channel architecture with 11 state variables. Implements a 3D attractor basin in (coherence, energy, stability) space with cross-channel resonant coupling.
- 5 coupled channels
- 5-tier timescale hierarchy
- 3D attractor basin
- Cross-channel resonance
CFM v2 Channel Architecture
| Channel | State Variables | Timescales | Description |
|---|---|---|---|
| Coherence | coherence_slow, coherence_fast | Slow (φ²) + Fast (φ⁻¹) | System-wide coherence baseline and fluctuations |
| Energy | energy_potential, energy_flux | Slow (φ²) + Fast (φ⁻¹) | Stored activation potential and flow rate |
| Stability | stability_envelope, instability_pulse | Slow (φ²) + Fast (φ⁻¹) | Stability boundary and instability events |
| Phase | phase_global, phase_local | Fast (φ⁻¹) + Very Fast (φ⁻²) | Global oscillation and local modulation |
| Alignment | alignment_field, alignment_direction | Medium (φ) + Very Slow (φ³) | Cross-channel synchronization strength and direction |
Each channel contains variables at different timescales. The 11th variable, resonance_index (Medium, τ ≈ φ), measures cross-channel coupling strength.
Abstraction Stack
ARIA Core Layers
Five progressive abstraction layers transform numeric patterns while maintaining strict boundedness, determinism, and safety constraints. All internal codes are anonymous—they carry no external meaning.
ARIA v0
Latent Concept ChannelsTransforms CFM v2 state into a 5D latent space with 4 φ-derived attractor clusters (Balanced, Coherence-Dominant, Energy-Dominant, Stability-Dominant). Stability-gated reinforcement drives states toward the dominant cluster.
- 5D latent channel projection
- 4 attractor clusters with soft membership
- Stability-gated reinforcement
- φ⁻¹ temperature scaling
ARIA v1
Proto-Symbolic LayerDiscretizes the latent space into K=8 prototype patterns using a φ-derived codebook. Soft activations are computed via Gaussian similarity kernel with temperature-controlled softmax. Temporal stabilization prevents jitter.
- 8 prototype codebook (K=8)
- Soft activations (sum = 1)
- EMA smoothing (α = φ⁻²)
- Hysteresis threshold (φ⁻³)
ARIA v2
System State VectorAggregates 12 numeric features from all underlying layers into a normalized summary. Applies temporal self-stabilization with stability-modulated EMA and tracks rate of change (drift) and state turnover.
- 12D normalized state vector
- Adaptive EMA smoothing
- Change detection channel
- Drift and turnover metrics
ARIA v3
Relational Symbolic GraphMaintains an 8×8 relation matrix tracking co-activation and transition signals between v1 symbols. Uses state-gated plasticity modulated by v2 stability and coherence. Outputs a 12D Relational Summary Vector (RSV).
- 8×8 symbol relation matrix
- Co-activation accumulation
- Transition signal tracking
- State-gated plasticity
ARIA v4
Proto-Semantic CodesIntegrates patterns from v1/v2/v3 into a 32D pattern space, then assigns to M=16 anonymous codes. Very slow plasticity (η = φ⁻⁵ ≈ 0.09) enables gradual structure formation. Codes are anonymous numeric patterns—not concepts.
- 32D pattern extraction
- 16 proto-semantic codes (M=16)
- Very slow plasticity (η ≈ 0.09)
- Temporal meaning stabilization
Mathematical Foundation
φ/ψ-Derived Constants
Core parameters in ARIA derive from the golden ratio and its powers, providing natural harmonic relationships. Some structural parameters (e.g., codebook sizes K=8, M=16) are chosen for practical reasons.
| Constant | Value | Primary Usage |
|---|---|---|
| φ (phi) | 1.618... | Base timescale, coupling ratios |
| φ⁻¹ | 0.618... | Softmax temperature |
| φ⁻² | 0.382... | EMA smoothing factor |
| φ⁻³ | 0.236... | Coupling strengths, hysteresis |
| φ⁻⁵ | 0.090... | Plasticity rates (v4) |
| ψ = φ^(1/φ) | 1.466... | Codebook initialization |
Guarantees
Mathematical Properties
Output Boundedness
For any input sequence and any initial state in [0,1]ⁿ, all ARIA outputs remain in [0, 1]. Each layer applies bounded nonlinearities (sigmoid, softmax) and explicit clamping after each update.
Deterministic Evolution
For identical initial conditions and input sequences, ARIA produces identical output sequences. The system contains no random number generators, no external state dependencies.
Attractor Convergence
From any initial state, the CFM subsystem converges toward the attractor basin. Small perturbations result in bounded deviation that decays exponentially toward the attractor.
Structured Self-Model
The SelfModel provides deterministic runtime introspection — capabilities, skills, and governance rules are enumerated from code, not generated. No external identity or personality modeling. All internal codes remain anonymous numeric patterns.
Formal Guarantee
Bounded State Model
∀t, ∀i: 0 ≤ xi(t) ≤ 1
Every state variable remains bounded in [0, 1] at every time step, for every input.
Bounded Nonlinearities
Sigmoid and softmax activations produce outputs strictly in (0, 1) by construction.
Hard Clamping
Every state update is followed by min/max clamping to enforce [0, 1] bounds.
NaN/Inf Replacement
Any computation producing NaN or Inf is replaced with the last known valid state.
CI Verification
Automated tests verify boundedness across thousands of random initial states and input sequences.
Design Philosophy
Brain-First, Constraint-Driven Systems
Coupled Channels
Five channels (Coherence, Energy, Stability, Phase, Alignment) evolve simultaneously with cross-channel coupling. This mirrors neural population dynamics where distinct subsystems interact through shared resonant frequencies.
Attractor Dynamics
The system converges toward attractor basins in (coherence, energy, stability) space. Perturbations decay exponentially. Stable states are not programmed — they emerge from the dynamical equations.
Timescale Hierarchy
A 5-tier φ-derived hierarchy separates fast fluctuations from slow structural changes. Fast variables (phase, instability) respond in ticks; slow variables (coherence baseline, alignment direction) change over hundreds of steps.
Constraint Over Optimization
ARIA does not optimize a loss function. It enforces constraints: bounded state, deterministic evolution, and fail-closed safety. The gate decision is a constraint check — not a gradient descent solution.
Rationale
Why Dynamical Systems Matter for Governance
Most AI governance systems operate probabilistically: a classifier assigns a risk score, a threshold triggers an action, and the decision is recorded as a single number. The internal reasoning is opaque — the model is a black box, and the score is its only output.
Dynamical systems provide a different foundation. The state of the system at any moment is fully specified by its state vector — a set of bounded numeric variables that evolve according to deterministic equations. Given the same initial conditions and input sequence, the system produces the same trajectory. Every intermediate state is observable. Every transition is computable.
ARIA builds on this property to produce verifiable governance. Gate decisions are not predictions — they are threshold comparisons on measured state. Evidence bundles contain the full state snapshot, not a summary. And deterministic replay means any decision can be independently reproduced by a third party with no access to the original system.
Comparison
Token-Based AI vs ARIA
| Property | Token-Based AI | ARIA |
|---|---|---|
| Decision Basis | Learned weights, probabilistic sampling | Threshold comparison on measured state |
| Reproducibility | Non-deterministic (temperature, sampling) | Fully deterministic — identical inputs produce identical outputs |
| Auditability | Post-hoc explanations, attention maps | Complete evidence bundle with every decision |
| State Bounds | Unbounded activations possible | All variables bounded in [0, 1] by construction |
| Governance Model | Content filtering, RLHF alignment | 19-stage deterministic pipeline with fail-closed gates |
| Verification | Statistical evaluation on benchmarks | Deterministic replay with cryptographic verification |
Future Research Directions
Current research focuses on detailed analysis of attractor basin geometry, investigation of the relationship between φ-derived parameters and emergent behavior, and comparison with alternative dynamical formulations.