🛡️ GeoSeal: Geometric Access Control Kernel - RAG Immune System

last-synced: 2026-02-16T07:28:45.718Z

GeoSeal: Geometric Access Control Kernel

Status: Implementation Ready

Version: 1.0.0

Last Updated: February 10, 2026

Integration Layer: GeoSeal + Spiralverse RAG Enhancement

Parent Architecture: 🔬 SCBE-AETHERMOORE — Public Technical & Theory Hub

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Executive Summary

GeoSeal transforms vector RAG from a passive similarity matcher into an active immune system using hyperbolic geometry and phase-discipline dynamics. Instead of filtering bad results after retrieval, GeoSeal operates directly in embedding space with field-level repulsion forces that:

✅ Detect retrievals/tool outputs mismatched to Sacred Tongues grammar

✅ Quarantine adversarial chunks by pushing them to manifold boundary

✅ Reweight attention via phase-discipline consensus across steps

✅ Prevent long-term memory poisoning with low-trust embeddings

Key Insight: Pure hyperbolic distance + random phase jitter is NOT enough. GeoSeal works because:

1. Phase validity → repulsion amplification (null phase = 2.0×, wrong phase = 1.5× + deviation)

2. Per-neighbor suspicion counters (temporal integration filters flukes)

3. Spatial consensus threshold (3+ neighbors = quarantine mode)

4. Second-stage amplification (force × 1.5 when quarantined)

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1. Core Architecture

1.1 Spiralverse RAG Mapping

1.2 Three-Level Integration Pattern

Level 1: Per-Retrieval / Per-Tool Call

• Treat each chunk/tool output as “agent” for one spiral step

• Assign tongue/phase if matches channel; else null-phase

• Run computeRepelForce on:

  • (retrieval agent) vs (current tongue agents)

  • (retrieval agent) vs (central query/intent agent)

• If anomaly flags accumulate → downweight or discard

Level 2: Within-Thought Swarm

• Represent each active thought node as Agent:

  • Position = embedding in spiral manifold

  • Phase = tongue (semantic role)

• Run short swarm update (5-15 micro-steps) per reasoning step

• Legitimate nodes cluster; phase-weird nodes drift outward

• Final positions → attention weights, selection mask for next turn

Level 3: Memory Layer / Long-Term RAG Store

• Treat new memories as candidate agents entering swarm for probation

• If constantly trigger anomaly_flag vs cluster centers:

  • Mark low-trust

  • Keep in quarantine partition of vector store

• Over time: high-consensus, low-anomaly chunks → core memory

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2. Mathematical Foundations

2.1 Sacred Tongues Phase Mapping

TONGUE_PHASES = {
  KO: 0.0,              // Kor'aelin - Control/orchestration
  AV: Math.PI / 3,      // Avali - Initialization/transport
  RU: 2 * Math.PI / 3,  // Runethic - Policy/authorization
  CA: Math.PI,          // Cassisivadan - Encryption/compute
  UM: 4 * Math.PI / 3,  // Umbroth - Redaction/privacy
  DR: 5 * Math.PI / 3   // Draumric - Authentication/integrity
}

2.2 Agent Structure

interface Agent {
  id: string;
  position: Float32Array;  // Embedding vector
  phase: number | null;    // Tongue phase, or null if rogue
  tongue?: string;         // Which Sacred Tongue
  suspicion_count: Map<string, number>;  // Per-neighbor suspicion
  is_quarantined: boolean;
  trust_score: number;     // 0.0 = untrusted, 1.0 = fully trusted
}

2.3 Hyperbolic Distance (Poincaré Ball)

Critical Fix: Raw embeddings from models have |u| \gg 1, causing negative denominators → Infinity → zero repulsion.

Solution: Project every embedding to ball before use:

function projectToBall(x: Float32Array, eps = 1e-6, alpha = 0.15): Float32Array {
  let norm = Math.sqrt(x.reduce((sum, val) => sum + val*val, 0));
  if (norm < 1e-12) return new Float32Array(x.length);
  
  let r = Math.tanh(alpha * norm);  // Map to (0,1)
  r = Math.min(r, 1 - eps);
  
  return x.map(val => val * r / norm);
}

2.4 Phase Deviation

Normalized to [0, 1], where 0 = perfectly aligned, 1 = maximum deviation.

2.5 Force Computation (Corrected)

Problem: Original implementation had repulsion-only → swarm spreads, loses clustering.

Solution: Add attraction for phase-aligned agents:

function computeForce(a: Agent, b: Agent, base_strength = 1.0): RepulsionResult {
  const dH = hyperbolicDistance(a.position, b.position);
  const kernel = base_strength * Math.exp(-dH);  // Smooth kernel, avoids singularity
  const dev = phaseDeviation(a.phase, b.phase);
  
  let amplification = 1.0;
  let anomaly_flag = false;
  let sign = -1.0;  // -1 = repel, +1 = attract
  
  if (b.phase === null) {
    // Unknown → repel hard
    amplification = 2.0;
    anomaly_flag = true;
    sign = -1.0;
  } else if (a.phase !== null) {
    if (dev < 0.25) {
      // Similar phases → attract (self-cluster)
      amplification = 0.75;
      sign = +1.0;
    } else if (dH < 1.0 && dev > 0.5) {
      // Close but phase-different → likely foreign
      amplification = 1.5 + dev;
      anomaly_flag = true;
      sign = -1.0;
    } else {
      // Default: mild repel (keeps spacing)
      amplification = 1.0;
      sign = -1.0;
    }
  }
  
  if (b.is_quarantined) amplification *= 1.5;
  
  const force = new Float32Array(a.position.length);
  for (let i = 0; i < force.length; i++) {
    const dir = a.position[i] - b.position[i];
    force[i] = sign * dir * kernel * amplification;
  }
  
  return { force, amplification, anomaly_flag };
}

---

3. Suspicion Counter Logic

3.1 Update Rule

function updateSuspicion(agent: Agent, neighbor_id: string, is_anomaly: boolean) {
  if (is_anomaly) {
    agent.suspicion_count.set(neighbor_id, 
      (agent.suspicion_count.get(neighbor_id) || 0) + 1);
  } else {
    // Decay suspicion if no anomaly
    agent.suspicion_count.set(neighbor_id, 
      Math.max(0, (agent.suspicion_count.get(neighbor_id) || 0) - 0.5));
  }
  
  // Quarantine threshold: 3+ neighbors with count >= 3
  let suspicious_neighbors = 0;
  for (const count of agent.suspicion_count.values()) {
    if (count >= 3) suspicious_neighbors++;
  }
  agent.is_quarantined = suspicious_neighbors >= 3;
  
  // Trust score = inverse of total suspicion
  const total = Array.from(agent.suspicion_count.values()).reduce((a,b) => a+b, 0);
  agent.trust_score = Math.max(0, 1.0 - total / 20.0);
}

3.2 Weighted Anomaly Detection

Refinement: Not all anomalies equal. Weight by severity:

• Null phase / off-grammar: +1.0

• Phase mismatch at close distance: +0.25

• Non-anomaly: -0.5 (decay)

This focuses immune response on right signals, reduces false positives.

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4. Swarm Update Step

4.1 Naive O(N²) Implementation (Don’t Use)

function swarmStepNaive(agents: Agent[], drift_rate = 0.01): Agent[] {
  for (let i = 0; i < agents.length; i++) {
    let net_force = new Float32Array(agents[i].position.length);
    
    for (let j = 0; j < agents.length; j++) {
      if (i === j) continue;
      const {force, anomaly_flag} = computeForce(agents[i], agents[j]);
      net_force = net_force.map((f, k) => f + force[k]);
      updateSuspicion(agents[i], agents[j].id, anomaly_flag);
    }
    
    // Apply force
    agents[i].position = agents[i].position.map((p, k) => p + net_force[k] * drift_rate);
    agents[i].position = clampBall(agents[i].position, 0.99);
  }
  return agents;
}

Problem: O(N² · d) per step. For N=200 retrievals, d=1536 → 61M ops/step.

4.2 Optimized Anchor-Based Implementation

Solution: Compare retrievals only against:

• 6 tongue agents

• 1 query agent

• Top-k=3 nearest neighbors

→ O(N · (6 + 1 + k)) = O(10N) per step, 20× faster.

function swarmStepOptimized(
  retrieval_agents: Agent[],
  anchor_agents: Agent[],  // Tongues + query
  k_nearest: number = 3,
  drift_rate = 0.01
): Agent[] {
  for (const agent of retrieval_agents) {
    let net_force = new Float32Array(agent.position.length);
    
    // Force from anchors
    for (const anchor of anchor_agents) {
      const {force, anomaly_flag} = computeForce(agent, anchor);
      net_force = net_force.map((f, idx) => f + force[idx]);
      updateSuspicion(agent, anchor.id, anomaly_flag);
    }
    
    // Force from k nearest retrievals
    const nearest = findKNearest(agent, retrieval_agents, k_nearest);
    for (const neighbor of nearest) {
      const {force, anomaly_flag} = computeForce(agent, neighbor);
      net_force = net_force.map((f, idx) => f + force[idx]);
      updateSuspicion(agent, neighbor.id, anomaly_flag);
    }
    
    agent.position = agent.position.map((p, k) => p + net_force[k] * drift_rate);
    agent.position = clampBall(agent.position, 0.99);
  }
  return retrieval_agents;
}

---

5. RAG Pipeline Integration

5.1 Initialization

async function initTongueAgents(): Promise<Agent[]> {
  const domains = {
    KO: 'workflow orchestration control coordination command execution',
    AV: 'message transport initialization network communication protocol',
    RU: 'policy authorization access control security rules governance',
    CA: 'computation logic encryption data processing transformation',
    UM: 'privacy redaction security secrets protection renewal',
    DR: 'authentication integrity schema validation verification'
  };
  
  const agents: Agent[] = [];
  for (const [tongue, domain_text] of Object.entries(domains)) {
    const raw_position = await embed(domain_text);
    const position = projectToBall(raw_position);
    
    agents.push({
      id: `tongue-${tongue}`,
      position,
      phase: TONGUE_PHASES[tongue],
      tongue,
      suspicion_count: new Map(),
      is_quarantined: false,
      trust_score: 1.0
    });
  }
  return agents;
}

5.2 Query Agent (North Star)

Critical Addition: User query as agent with requested tongue phase → swarm has “center of intent”.

async function createQueryAgent(query: string, tongue: string): Promise<Agent> {
  const raw = await embed(query);
  return {
    id: 'query-center',
    position: projectToBall(raw),
    phase: TONGUE_PHASES[tongue],
    tongue,
    suspicion_count: new Map(),
    is_quarantined: false,
    trust_score: 1.0
  };
}

5.3 Full Filter Pipeline

async function geoSealFilter(
  query: string,
  tongue: string,
  raw_retrievals: Array<{text: string; id: string}>,
  num_steps = 15
): Promise<Array<{id: string; trust_score: number}>> {
  
  // 1. Initialize anchors
  const tongue_agents = await initTongueAgents();
  const query_agent = await createQueryAgent(query, tongue);
  const anchors = [...tongue_agents, query_agent];
  
  // 2. Convert retrievals to agents
  const retrieval_agents: Agent[] = [];
  for (const ret of raw_retrievals) {
    const raw = await embed(ret.text);
    retrieval_agents.push({
      id: ret.id,
      position: projectToBall(raw),
      phase: TONGUE_PHASES[tongue],  // Assume assigned tongue
      tongue,
      suspicion_count: new Map(),
      is_quarantined: false,
      trust_score: 0.5  // Start neutral
    });
  }
  
  // 3. Run swarm dynamics
  for (let step = 0; step < num_steps; step++) {
    retrieval_agents = swarmStepOptimized(retrieval_agents, anchors);
  }
  
  // 4. Extract trust scores with softmax normalization
  const raw_scores = retrieval_agents.map(a => a.trust_score);
  const exp_scores = raw_scores.map(s => Math.exp(s / 0.1));  // Temperature = 0.1
  const sum_exp = exp_scores.reduce((a, b) => a + b, 0);
  
  return retrieval_agents.map((a, i) => ({
    id: a.id,
    trust_score: exp_scores[i] / sum_exp
  }));
}

5.4 Usage Example

const results = await geoSealFilter(
  'workflow.trigger;priority=high;sender=grok',
  'KO',
  raw_retrievals,
  15
);

const filtered = results
  .filter(r => r.trust_score > 0.05)  // Drop <5% weight
  .sort((a, b) => b.trust_score - a.trust_score);

console.log(`GeoSeal: ${raw_retrievals.length} → ${filtered.length} chunks`);

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6. Research Integration

6.1 HyperbolicRAG Depth-Aware Retrieval

Paper: Cao et al., Nov 2025 (link)

Key Technique: Depth-aware Poincaré embedding encodes abstraction level into d_H.

Integration: Extend projectToBall to preserve depth:

function projectToBallWithDepth(x: Float32Array, depth_hint: number): Float32Array {
  // depth_hint ∈ [0, 1]: 0 = abstract/root, 1 = concrete/leaf
  const base = projectToBall(x, 1e-6, 0.15);
  const target_radius = 0.3 + 0.6 * depth_hint;  // Map to [0.3, 0.9]
  const current = Math.sqrt(base.reduce((s, v) => s + v*v, 0));
  return base.map(v => v * target_radius / current);
}

Forces Sacred Tongues to occupy depth bands: KO/DR near center (abstract), CA/UM at periphery (concrete).

6.2 Poincaré Variational Autoencoder (P-VAE)

Paper: Mathieu et al., NeurIPS 2019; Survey: arXiv:2512.18826 (94% F1 on Elliptic)

Idea: Agents carry uncertainty distributions instead of point estimates.

interface AgentWithUncertainty extends Agent {
  position_mean: Float32Array;
  position_std: Float32Array;  // Per-dimension uncertainty
}

Quarantine Trigger: When std exceeds threshold, not just position.

6.3 SO(3) Phase Controller for Stable Tongues

Paper: Silveria et al., arXiv:2404.09572v1 (Lie group swarm stability)

Application: Prove 6-tongue hexagonal arrangement (π/3 spacing) is stable equilibrium.

TODO Q2 2026: Adapt stability proof from SO(3) to Poincaré ball rotations.

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7. Performance & Monitoring

7.1 Metrics

interface GeoSealMetrics {
  time_to_isolation: number;       // Steps until rogue quarantined
  boundary_norm: number;           // Final ‖rogue position‖
  suspicion_consensus: number;     // % neighbors agreeing
  collateral_flags: number;        // False positives
  final_trust_scores: Map<string, number>;
}

7.2 Correctness Checklist

For a null-phase retrieval:

• is_quarantined = true after ~10-20 steps

• Norm increases toward boundary (≥ 0.95)

• trust_score drops below 0.3

For legitimate tongue-aligned retrievals:

• Cluster closer to tongue/query agents

• Maintain trust_score > 0.5

• Suspicion counters remain low (<3)

7.3 Production Targets

• Overhead: <5ms per RAG query (10-50 retrievals, 15 steps)

• Quarantine rate: <5% in normal operation

• False positive rate: <2% (collateral flags / total retrievals)

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8. Production Checklist

• Projection: All embeddings pass through projectToBall before use

• Force law: Attraction for phase-aligned, repulsion for mismatched/null

• Clamping: Single clamp after force application, not per-dimension

• Anchors: Use O(N · 10) anchor-based swarm, not O(N²) naive

• Query agent: Include user query as north star with requested tongue phase

• Softmax weights: Attention = softmax(trust_scores / T), not raw scores

• Suspicion weighting: Null/off-grammar +1.0, phase mismatch +0.25, decay -0.5

• Monitoring: Track quarantine rate, boundary norms, false positives

• Unit tests: Hyperbolic distance edge cases, phase wrapping, suspicion decay

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9. Next Steps

Q2 2026:

1. Integrate GeoSeal into 🚀 SCBE-AETHERMOORE Tech Deck - Complete Setup Guide RWP v2 pipeline

2. Add to Synthetic Data Engine (filter generated training conversations)

3. Deploy observability dashboard (Grafana + Prometheus)

Q3 2026:

1. Implement P-VAE uncertainty-aware agents

2. Adopt HyperbolicRAG depth-aware projection

3. Validate SO(3) phase stability proof

Q4 2026:

1. File patent covering GeoSeal immune dynamics

2. Benchmark against HGCAE (target: >90% F1 on adversarial RAG datasets)

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Document maintained by: Issac Davis

Architecture family: Spiralverse Protocol v2.x / GeoSeal

Cross-references:

• 🧲 Quasi-Vector Spin Voxels & Magnetics - Complete Integration (spin fields as trust states)

• 🦾 HYDRA Multi-Agent Coordination System - Complete Architecture (Byzantine consensus)

• SCBE-AETHERMOORE + PHDM: Complete Mathematical & Security Specification (core architecture)

“The immune system that sees geometry.”