Bci Colored Operad

BCI Colored Operad

Overview

Brain-Computer Interface data processing with colored operad security boundaries. Implements maximally isolated enclosure for EEG/neural signals using the same security model as Signal authentication: nested isolation layers (Network → Firewall → Container → VM → Trusted) with each layer assigned a security color that enforces data flow constraints.

┌─────────────────────────────────────────────────────────────────────────────┐
│  BCI COLORED OPERAD ISOLATION STACK                                         │
└─────────────────────────────────────────────────────────────────────────────┘

   Neural Interface (EEG Electrodes)
          │
          ▼
   ┌──────────────────────────────────────────────────────────────────────┐
   │  🔴 RED: Acquisition Boundary (trit=-1)                              │
   │      • Raw EEG signals (8 channels × 250Hz)                          │
   │      • Network isolation for wireless headsets                       │
   │      • Bluetooth/USB device boundary                                 │
   │  ┌────────────────────────────────────────────────────────────────┐  │
   │  │  🟡 YELLOW: Processing Container (trit=-1)                     │  │
   │  │      • Signal preprocessing (filtering, artifact removal)      │  │
   │  │      • Feature extraction (PSD: δ, θ, α, β, γ bands)          │  │
   │  │      • Seccomp/AppArmor isolation                             │  │
   │  │  ┌──────────────────────────────────────────────────────────┐  │  │
   │  │  │  🟢 GREEN: Compute VM (trit=0)                           │  │  │
   │  │  │      • Random walk on feature space                      │  │  │
   │  │  │      • UMAP/dimension reduction                          │  │  │
   │  │  │      • Firecracker/QEMU isolation                        │  │  │
   │  │  │  ┌────────────────────────────────────────────────────┐  │  │  │
   │  │  │  │  🔵 BLUE: Trusted Core (trit=+1)                   │  │  │  │
   │  │  │  │      • ACSet categorical structure                 │  │  │  │
   │  │  │  │      • NATS broadcast to vivarium topic            │  │  │  │
   │  │  │  │      • Agent-O-Rama pathway integration            │  │  │  │
   │  │  │  └────────────────────────────────────────────────────┘  │  │  │
   │  │  └──────────────────────────────────────────────────────────┘  │  │
   │  └────────────────────────────────────────────────────────────────┘  │
   └──────────────────────────────────────────────────────────────────────┘

GF(3) Conservation

RED(-1) ⊗ YELLOW(-1) ⊗ GREEN(0) ⊗ BLUE(+1) = -1

Balanced with signal-isolated-auth triad:
BCI(-1) + Signal(-1) + Coordinator(0) + Generator(+1) + Generator(+1) = 0 ✓

Neural Signal Pipeline

Frequency Bands (40-dimensional feature space)

GF(3) Band Conservation: δ(-1) + θ(-1) + α(0) + β(+1) + γ(+1) = 0 ✓

Brain State Profiles

;; State-dependent frequency power distributions
{:resting  {:alpha 0.8 :theta 0.3}    ; trit: 0 (ergodic)
 :focused  {:beta 0.7 :gamma 0.5}     ; trit: +1 (plus)
 :drowsy   {:theta 0.9 :delta 0.5}    ; trit: -1 (minus)
 :alert    {:gamma 0.8 :beta 0.6}}    ; trit: +1 (plus)

Security Color Rules

Color Flow Constraint (Neural → Digital)

RAW_SIGNAL → FILTERED → FEATURES → EMBEDDING → BROADCAST
    🔴           🔴         🟡         🟢          🔵
   RED         RED      YELLOW     GREEN       BLUE
   
Flow direction: INWARD ONLY (less trusted → more trusted)

ACSet Schema (Categorical Structure)

@present BCISchema(FreeSchema) begin
    # Objects
    Trial::Ob
    Channel::Ob
    FrequencyBand::Ob
    BrainState::Ob
    TrialFeature::Ob

    # Morphisms (structure)
    trial_state::Hom(Trial, BrainState)
    trial_channel::Hom(TrialFeature, Channel)
    trial_feature::Hom(TrialFeature, FrequencyBand)
    trial_trial::Hom(TrialFeature, Trial)

    # Attributes (data)
    trial_id::Attr(Trial, Symbol)
    channel_name::Attr(Channel, String)
    band_name::Attr(FrequencyBand, String)
    state_name::Attr(BrainState, String)
    feature_value::Attr(TrialFeature, Float32)
end

Usage

Julia API (with WorldColoredOperads)

using Gay.WorldColoredOperads

# Build BCI-specific enclosure
enclosure = world_color_chain(:bci_eeg, 
    [:network, :container, :vm, :trusted]; 
    seed=0x4DA02B)

# Verify security properties
result = verify_enclosure(enclosure)
println("Security score: ", result.security_score)
println("GF(3) balanced: ", result.gf3_balanced)

# Output as s-expression
println(to_sexp(enclosure))

Babashka (Simple Broadcaster)

# Start BCI random walk broadcaster (20 steps, 3s interval)
bb /path/to/bci_nats_broadcaster_simple.clj

Python API (Agent-O-Rama Pathway)

from agentorama_pathway_dispatch import AgentOramaDispatcher, PathwayType
from signal_isolation_manager import SecurityColor

# Register BCI pathway with dispatcher
dispatcher = AgentOramaDispatcher(enforce_gf3=True)

dispatcher.register_pathway(
    name="bci-neural",
    pathway_type=PathwayType.CUSTOM,
    color_chain=[
        SecurityColor.RED,    # Raw acquisition
        SecurityColor.YELLOW, # Feature extraction
        SecurityColor.GREEN,  # Random walk
        SecurityColor.BLUE,   # ACSet broadcast
    ],
    capabilities={"eeg_stream", "feature_extract", "random_walk", "nats_publish"},
)

NATS Integration

Topic: vivarium

{
  "timestamp": 1761977242359,
  "step": 5,
  "position": [0.05010, 0.03181, 0.07015, ...],
  "dimension": 40,
  "history_length": 5
}

Connection

Host: nonlocal.info
Port: 4222
Protocol: NATS (TCP pub/sub)
Seed: 1069 (deterministic)

S-Expression Output

(bci-enclosure
  :target "bci_eeg"
  :seed 5086251
  :fingerprint "4da02b8e7f3a"
  :gf3-sum 0
  :valid t
  :security-score 100
  :color-chain (:red :yellow :green :blue)
  :layers (
    (layer :name "acquisition" :color :red :tech :network :trit -1)
    (layer :name "processing" :color :yellow :tech :container :trit -1)
    (layer :name "compute" :color :green :tech :vm :trit 0)
    (layer :name "trusted" :color :blue :tech :enclave :trit 1)
  )
  :frequency-bands (
    (band :name "delta" :range (0.5 4) :trit -1)
    (band :name "theta" :range (4 8) :trit -1)
    (band :name "alpha" :range (8 12) :trit 0)
    (band :name "beta" :range (12 30) :trit 1)
    (band :name "gamma" :range (30 100) :trit 1)
  ))

Hardware Integration

Supported Devices

Firecracker microVM Config

vm:
  type: firecracker
  vcpus: 2
  memory_mb: 1024
  kernel: vmlinux-bci
  rootfs: bci-rootfs.ext4
  boot_args: "console=ttyS0 reboot=k panic=1 pci=off"

Pathway Architecture

graph TB
    subgraph BrainSignals[🔴 RED: Acquisition]
        Raw[Raw EEG]
        Filtered[Filtered]
        Raw -->|Preprocessing| Filtered
    end

    subgraph Processing[🟡 YELLOW: Container]
        Features[PSD Features]
        Filtered -->|FFT| Features
    end

    subgraph Compute[🟢 GREEN: VM]
        Walk[Random Walk]
        Features -->|Init| Walk
    end

    subgraph Trusted[🔵 BLUE: Core]
        ACSet[ACSet]
        NATS[NATS Pub]
        Walk -->|Encode| ACSet
        ACSet -->|Broadcast| NATS
    end

    classDef red fill:#E12A4E,color:#fff;
    classDef yellow fill:#F5A623,color:#000;
    classDef green fill:#4DA02B,color:#fff;
    classDef blue fill:#3D91C9,color:#fff;

    class Raw,Filtered red;
    class Features yellow;
    class Walk green;
    class ACSet,NATS blue;

Required Skills (Dependency Triad)

Files

Security Considerations

1. Raw Signal Isolation: EEG data never leaves RED boundary unprocessed
2. Feature Space Only: Only PSD features (not raw signals) cross to YELLOW
3. Encrypted Transport: NATS TLS for vivarium topic
4. No PII: Position vectors are abstract feature space, not identifiable
5. Seed Determinism: Reproducible with seed 1069 for auditing

Related Skills

• signal-isolated-auth - Signal client isolation (same operad model)
• hyperbolic-bulk - On-chain entropy with EEG component
• gay-mcp - Deterministic color generation
• livekit-omnimodal - Real-time coaching with neural feedback
• qri-valence - Phenomenal state mapping via XY model

Autopoietic Marginalia

The interaction IS the skill improving itself.

Every use of this skill is an opportunity for worlding:

• MEMORY (-1): Record what was learned
• REMEMBERING (0): Connect patterns to other skills
• WORLDING (+1): Evolve the skill based on use

Add Interaction Exemplars here as the skill is used.

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