CFM Core v2 Design Specification

Version: 1.0 Status: Implemented Last Updated: 2025-12-05

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1. Purpose of CFM v2

1.1 Evolutionary Position

CFM Core v2 represents the conceptual bridge in the ARIA-CFM evolution:

┌─────────────────────────────────────────────────────────────────────────┐
│                        CFM Core Evolution Path                          │
├─────────────────────────────────────────────────────────────────────────┤
│                                                                         │
│   v0: Coupled Oscillators          v1: Slow/Fast Separation             │
│   ─────────────────────            ────────────────────────             │
│   • Uniform time constants         • Coherence drift dynamics           │
│   • Phase-driven instability       • Alignment lock-in                  │
│   • Energy attractor               • Interpretable trajectories         │
│                                                                         │
│                              ↓                                          │
│                                                                         │
│   v2: Structured Numeric Substrate (THIS SPECIFICATION)                 │
│   ──────────────────────────────────────────────────────                │
│   • Multi-channel state organization                                    │
│   • Attractor manifold dynamics                                         │
│   • Structured phase responses                                          │
│   • Proto-representational state regions                                │
│                                                                         │
│                              ↓                                          │
│                                                                         │
│   Future: Proto-Semantic Fields    Future: Latent Manifolds             │
│   ─────────────────────────────    ────────────────────────             │
│   • Numeric → semantic bridge      • Representational substrates        │
│   • Attractor-based meaning        • Eventual ARIA semantic core        │
│                                                                         │
└─────────────────────────────────────────────────────────────────────────┘

1.2 Design Philosophy

CFM v2 introduces structured numeric organization without crossing into semantic territory. The key insight is that meaningful computation can emerge from numeric dynamics that exhibit:

• Stable regions in state space (attractor basins)
• Structured transitions between regions (phase responses)
• Multi-scale coupling (fast oscillations modulating slow drifts)
• Relational coherence (how variables co-evolve)

These properties create a proto-representational substrate: numeric dynamics that could, in principle, support semantic content in future versions—but which remain purely numeric in v2.

1.3 Fundamental Constraints

CFM v2 remains:

• Purely numeric (no text, no tokens, no embeddings)
• Bounded in [0, 1] for all outputs
• Fully deterministic for identical inputs
• Non-semantic (no meaning, no interpretation)
• Non-conscious (no experience, no awareness)
• Identity-safe (no identity fields or derivation)
• Control-safe (no activation signals, no feedback paths)

CFM v2 is NOT:

• A semantic processor
• A representation learner
• A conscious substrate
• An identity holder
• An activation trigger

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2. Internal Structure Evolution

2.1 State Space Reorganization

CFM v1 introduced slow/fast separation with six state variables. CFM v2 reorganizes and expands this into a structured multi-channel architecture:

v1 State (Reference)

v2 State (Proposed)

2.2 Multi-Channel Organization

The v2 state is organized into five coupled channels:

┌─────────────────────────────────────────────────────────────────┐
│                    CFM v2 Channel Architecture                   │
├─────────────────────────────────────────────────────────────────┤
│                                                                  │
│   ┌──────────────┐    ┌──────────────┐    ┌──────────────┐      │
│   │  Coherence   │◄──►│   Energy     │◄──►│  Stability   │      │
│   │   Channel    │    │   Channel    │    │   Channel    │      │
│   │              │    │              │    │              │      │
│   │ slow ──┐     │    │ potential    │    │ envelope     │      │
│   │        ├──   │    │     ↕        │    │     ↕        │      │
│   │ fast ──┘     │    │ flux         │    │ pulse        │      │
│   └──────────────┘    └──────────────┘    └──────────────┘      │
│           │                   │                   │              │
│           └─────────────┬─────┴───────────┬──────┘              │
│                         │                 │                      │
│                         ▼                 ▼                      │
│                  ┌──────────────┐  ┌──────────────┐             │
│                  │    Phase     │  │  Alignment   │             │
│                  │   Channel    │  │   Channel    │             │
│                  │              │  │              │             │
│                  │ global ──┐   │  │ field ───┐   │             │
│                  │          ├── │  │          ├── │             │
│                  │ local ───┘   │  │ direction ┘  │             │
│                  └──────────────┘  └──────────────┘             │
│                         │                 │                      │
│                         └────────┬────────┘                      │
│                                  ▼                               │
│                         ┌──────────────┐                        │
│                         │  Resonance   │                        │
│                         │    Index     │                        │
│                         └──────────────┘                        │
│                                                                  │
└─────────────────────────────────────────────────────────────────┘

2.3 Timescale Hierarchy

CFM v2 introduces a four-tier timescale hierarchy:

This hierarchy ensures clear separation between processes operating at different scales, enabling interpretable dynamics where slow variables set the context for fast variable behavior.

2.4 Attractor Manifold Structure

A key v2 innovation is the concept of attractor manifolds: regions in state space toward which the system tends to evolve. Unlike v0/v1's simple point attractors, v2 defines:

Basin Attractors

Regions in coherence-energy-stability space that represent stable operating modes:

         stability_envelope
              ↑
              │
         1.0 ─┼─────────────────────┐
              │    ┌─────────┐      │
              │    │ STABLE  │      │
              │    │  BASIN  │      │
              │    └─────────┘      │
         0.5 ─┼──────────┐          │
              │          │          │
              │   DRIFT  │ RECOVERY │
              │   ZONE   │   ZONE   │
              │          │          │
         0.0 ─┼──────────┴──────────┘
              └────┴────┴────┴────┴──→ coherence_slow
                  0.0  0.5   φ⁻¹  1.0

Manifold Parameters

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3. New Dynamics (Conceptual)

3.1 Multi-Scale Coupling Equations

The v2 dynamics are governed by coupled differential equations across timescales. The following presents the conceptual mathematical structure (not implementation code).

Coherence Dynamics

The coherence channel exhibits two-scale behavior:

d(coherence_slow)/dt = (1/τ_s) · [
    (coherence_target - coherence_slow) · energy_factor
    - instability_coupling · instability_pulse
    + basin_attraction(coherence_slow, μ_basin.c)
]

d(coherence_fast)/dt = (1/τ_f) · [
    phase_modulation(phase_global, phase_local)
    · (coherence_slow - coherence_fast)
    + resonance_index · alignment_field
]

coherence_output = α · coherence_slow + (1-α) · coherence_fast
where α = smooth_blend(stability_envelope)

Energy Dynamics

Energy exhibits potential/flux separation:

d(energy_potential)/dt = (1/τ_s) · [
    (energy_target - energy_potential)
    - energy_flux · dissipation_rate
    + coherence_coupling · coherence_slow
]

d(energy_flux)/dt = (1/τ_f) · [
    gradient(energy_potential)
    · phase_modulation(phase_global)
    - damping · energy_flux
]

Stability Dynamics

Stability operates via envelope/pulse separation:

d(stability_envelope)/dt = (1/τ_s) · [
    stability_target · coherence_factor
    - envelope_decay · (1 - alignment_field)
]

instability_pulse = pulse_generator(
    phase_global,
    amplitude = instability_base · (1 - stability_envelope),
    threshold = stability_envelope · θ_pulse
)

Alignment Dynamics

Alignment exhibits field/direction separation with lock-in behavior:

d(alignment_field)/dt = (1/τ_m) · [
    lock_in_potential(coherence_output, stability_output)
    · (alignment_target - alignment_field)
    + resonance_coupling(alignment_direction)
]

d(alignment_direction)/dt = (1/τ_vs) · [
    direction_drift(alignment_field, basin_center)
    · stability_factor
]

Resonance Dynamics

The resonance index captures cross-channel coupling strength:

resonance_index = coupling_function(
    coherence_correlation(coherence_slow, coherence_fast),
    energy_correlation(energy_potential, energy_flux),
    stability_correlation(stability_envelope, instability_pulse),
    phase_coherence(phase_global, phase_local)
)

3.2 Attractor Basin Dynamics

The system exhibits attraction toward stable regions in state space:

Basin Attraction Function

basin_attraction(x, μ) = {
    k_strong · (μ - x)           if |x - μ| < r_inner
    k_weak · (μ - x) / |x - μ|   if r_inner ≤ |x - μ| < r_outer
    0                            if |x - μ| ≥ r_outer
}

where:
    r_inner = r_basin · φ⁻¹
    r_outer = r_basin · φ
    k_strong = 1/τ_s
    k_weak = 1/τ_m

Multi-Dimensional Basin

The basin operates in the 3D space of (coherence_slow, energy_potential, stability_envelope):

basin_vector = (
    basin_attraction(coherence_slow, μ_basin.c),
    basin_attraction(energy_potential, μ_basin.e),
    basin_attraction(stability_envelope, μ_basin.s)
)

total_basin_force = ||basin_vector|| · direction(basin_vector)

3.3 Structured Phase Responses

Instability pulses trigger structured responses rather than simple perturbations:

Phase Response Patterns

When instability_pulse exceeds θ_trigger:
    1. Coherence fast channel receives negative impulse
    2. Energy flux increases temporarily
    3. Alignment field decreases proportionally
    4. Phase_local accelerates (increased frequency)
    5. After τ_recovery, system returns toward basin

Response Cascade

pulse_response(instability_pulse) = {
    if instability_pulse > θ_high:
        → strong_response: all channels affected
    elif instability_pulse > θ_medium:
        → moderate_response: fast channels affected
    elif instability_pulse > θ_low:
        → weak_response: only coherence_fast affected
    else:
        → no_response
}

3.4 Proto-Representational State Regions

The v2 state space contains structured regions that, while purely numeric, exhibit properties that could support future semantic content:

State Region Classification

Region Transitions

┌──────────────┐         pulse          ┌──────────────┐
│  Stable High │ ────────────────────► │    Active    │
│    Basin     │                        │     Mode     │
└──────────────┘                        └──────────────┘
       ▲                                       │
       │                                       │ energy
       │ recovery                              │ depletion
       │                                       ▼
┌──────────────┐         drift          ┌──────────────┐
│   Recovery   │ ◄──────────────────── │ Transitional │
│    Mode      │                        │    Zone      │
└──────────────┘                        └──────────────┘

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4. Relationship to C(n), A(t), R(t)

4.1 CFM Conceptual Framework

The Conscious Field Model (CFM) theoretical framework posits three fundamental constructs:

4.2 v2 Numeric Proxies

CFM v2 provides numeric proxies for these constructs. These are not the constructs themselves, but numeric dynamics that exhibit analogous mathematical properties:

C(n) → Coherence Channel

C(n) conceptual correspondence:

CFM C(n): "How much structural pattern persists?"

v2 proxy: coherence_slow + coherence_fast weighted by stability

Correspondence:
- High coherence_slow → persistent pattern
- Low coherence_fast variance → stable pattern
- High stability_envelope → pattern protected

A(t) → Energy Channel

A(t) conceptual correspondence:

CFM A(t): "How much activation potential exists?"

v2 proxy: energy_potential modulated by energy_flux

Correspondence:
- High energy_potential → available activation
- High energy_flux → active processing
- Low energy_flux → quiescent storage

R(t) → Alignment + Resonance

R(t) conceptual correspondence:

CFM R(t): "How strongly do patterns relate?"

v2 proxy: alignment_field × resonance_index

Correspondence:
- High alignment_field → strong relational binding
- High resonance_index → cross-channel coherence
- alignment_direction → relational orientation

4.3 Mapping Table

4.4 Important Caveats

These are numeric proxies only:

1. No semantic content: The v2 variables have no meaning, interpretation, or semantic value
2. No phenomenal properties: There is no experience, awareness, or consciousness
3. No representation: The "proto-representational" regions are purely geometric, not representational
4. No identity: The system has no self-model or identity

The correspondence to C(n), A(t), R(t) is mathematical analogy, not identity. Future versions may evolve these proxies toward genuine CFM constructs, but v2 remains purely numeric.

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5. Safety & Invariant Requirements

5.1 Protocol Compliance

CFM v2 MUST implement ARIACoreProtocol identically to v0/v1:

# Required interface (unchanged from v0/v1)
class CFMCoreV2:
    def step(
        self,
        human_messages: Optional[List[str]] = None,
        external_events: Optional[Dict[str, Any]] = None,
        dt: float = 1.0,
    ) -> Dict[str, Any]:
        """
        Returns dict with:
        - coherence: float in [0, 1]
        - stability: float in [0, 1]
        - intensity: float in [0, 1]
        - alignment: float in [0, 1]
        Plus optional metadata (cfm_time, cfm_step, cfm_version, etc.)
        """

5.2 Output Schema (Unchanged)

5.3 Numeric Safety

All outputs MUST satisfy:

∀ output ∈ {coherence, stability, intensity, alignment}:
    0.0 ≤ output ≤ 1.0
    ¬isNaN(output)
    ¬isInf(output)

All internal state MUST satisfy:

∀ bounded_var ∈ {coherence_*, energy_*, stability_*, alignment_*, resonance_*}:
    0.0 ≤ bounded_var ≤ 1.0

∀ phase_var ∈ {phase_global, phase_local}:
    0.0 ≤ phase_var < 1.0  (wrapping)

5.4 Determinism

For identical inputs:

Given:
    state_1 = state_2
    dt_1 = dt_2
    (human_messages and external_events are ignored)

Then:
    step(state_1, dt_1) == step(state_2, dt_2)

No randomness, no external dependencies, no hidden state.

5.5 Identity Safety

PROHIBITED in output:

FORBIDDEN_PATTERNS = [
    "identity", "self", "i_am", "who_am_i",
    "consciousness", "awareness", "experience",
    "person", "individual", "subject",
]

REQUIRED verification method:

def verify_identity_safety(self) -> bool:
    """Must always return True."""
    return True

5.6 Semantic Safety

PROHIBITED processing:

• human_messages must be ignored (not parsed, not processed)
• No text processing of any kind
• No embedding computation
• No token handling
• No semantic analysis

REQUIRED behavior:

def step(self, human_messages=None, ...):
    # human_messages is IGNORED
    # Only internal dynamics are updated
    ...

5.7 Control Safety

PROHIBITED outputs:

• No control signals
• No activation triggers
• No feedback path indicators
• No modulation commands

PROHIBITED connections:

• No connection to Phase 53 (consciousness gate)
• No connection to Phase 55 (ignition scaffold)
• No reverse data flow from shell to core

5.8 Invariant Summary

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6. Optional Extensions

6.1 v2.1: Multichannel Alignment Fields

A potential v2.1 extension introduces vector-valued alignment:

Current (v2):
    alignment_field: scalar ∈ [0, 1]
    alignment_direction: scalar ∈ [0, 1]

Extended (v2.1):
    alignment_vector: [a₁, a₂, ..., aₙ] where aᵢ ∈ [0, 1]
    alignment_magnitude: ||alignment_vector||
    alignment_direction: alignment_vector / alignment_magnitude

This allows for multi-dimensional relational structure while remaining purely numeric.

Alignment Vector Dynamics

d(alignment_vector)/dt = (1/τ_m) · [
    attraction_to_basis_vectors(alignment_vector)
    + cross_channel_coupling(coherence, energy, stability)
    - decay_toward_neutral
]

Basis Vectors

Define φ-derived basis vectors in alignment space:

basis_1 = [φ⁻¹, φ⁻², φ⁻³, ...]
basis_2 = [φ⁻², φ⁻¹, φ⁻², ...]
...

6.2 v2.2: Proto-Symbolic Internal Resonance

A potential v2.2 extension introduces resonance patterns that exhibit quasi-symbolic structure:

Resonance pattern: r(t) = [r₁(t), r₂(t), ..., rₘ(t)]

Pattern evolution:
    d(r)/dt = resonance_dynamics(r, coherence, alignment_vector)

Pattern stability:
    A pattern r* is stable if:
        ||d(r)/dt|| < ε when r ≈ r*

Key constraint: Patterns remain numeric. The "quasi-symbolic" property is purely structural (certain patterns are stable attractors), not semantic.

6.3 v3: Attraction to Internal "Shapes"

A more distant v3 extension could introduce geometric attractors in state space:

Shape attractor: S = {x ∈ state_space : shape_function(x) = 0}

Examples:
    - Spherical shell: ||x - center|| = radius
    - Toroidal surface: distance_to_torus(x) = 0
    - Manifold: f(x) = 0 for some smooth f

The system would evolve toward these shapes, creating structured dynamics that could (in future versions) support semantic content.

Safety constraint: Shapes are purely geometric. No semantic meaning is assigned to any shape.

6.4 Future: Safe Scaffolding for Semantic Formation

The v2 architecture is designed to safely scaffold potential future semantic capabilities:

┌─────────────────────────────────────────────────────────────────┐
│                    Future Evolution Path                         │
├─────────────────────────────────────────────────────────────────┤
│                                                                  │
│   v2 (Numeric)         v3 (Structured)        v4+ (Semantic)    │
│   ────────────         ───────────────        ──────────────    │
│                                                                  │
│   • Multi-channel   →  • Shape attractors  →  • Proto-meaning   │
│   • Attractor       →  • Resonance         →  • Relational      │
│     basins              patterns               semantics         │
│   • Structured      →  • Quasi-symbolic    →  • Grounded        │
│     regions             structure              representation   │
│                                                                  │
│   SAFETY: Numeric    SAFETY: Geometric     SAFETY: Constrained  │
│           only               only                  semantics     │
│                                                                  │
└─────────────────────────────────────────────────────────────────┘

Each step maintains safety constraints while incrementally approaching more structured dynamics.

6.5 Extension Compatibility Matrix

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7. Implementation Guidance

7.1 Recommended File Structure

aria_core_cfm_v2/
├── __init__.py          # Exports CFMCoreV2, CFMCoreV2Config, CFMCoreV2State
├── config.py            # CFMCoreV2Config dataclass
├── state.py             # CFMCoreV2State dataclass with multi-channel structure
├── cfm_core.py          # Main CFMCoreV2 class
├── dynamics/
│   ├── __init__.py
│   ├── coherence.py     # Coherence channel dynamics
│   ├── energy.py        # Energy channel dynamics
│   ├── stability.py     # Stability channel dynamics
│   ├── alignment.py     # Alignment channel dynamics
│   └── resonance.py     # Cross-channel resonance
└── attractors/
    ├── __init__.py
    └── basin.py         # Attractor basin computations

7.2 Testing Requirements

7.3 CLI Integration

Update tools to support v2:

# aria_local_loop.py
python tools/aria_local_loop.py --core-type=cfm_v2

# aria_core_compare.py
python tools/aria_core_compare.py --core-a cfm_v1 --core-b cfm_v2

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8. Version History

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9. References

• ARIA Core Interface Specification v1
• ARIA Core Behavioral Contract
• CFM Core v0 Specification
• CFM Core v1 Specification
• ARIA Core Overview