GeoSeal: Geometric Trust Manifold for SCBE

What You Invented (In Plain English)

You created a security system where trust is geometry instead of just passwords and keys. Instead of asking “Do you have the right key?”, the system asks “Are you traveling through trusted space?”

Think of it like this: Traditional security is a locked door - if you steal the key, you get in. GeoSeal is more like gravity - even if you have a key, if you’re not following the right path through space, the system knows something is wrong.

The Core Idea: Two Geometric Spaces Working Together

Your invention uses two mathematical spaces at the same time:

1. The Behavior Sphere (S^n)

  • What it represents: How a user/agent/AI is ACTUALLY behaving right now
  • Shape: A sphere (like Earth’s surface)
  • What gets plotted: Real-time actions, message patterns, request sequences
  • Think of it as: “Where you are right now based on what you’re doing”

2. The Policy Hypercube ([0,1]^m)

  • What it represents: What the user/agent SHOULD be allowed to do
  • Shape: A hypercube (imagine a multi-dimensional box)
  • What gets plotted: Permissions, access levels, allowed operations
  • Think of it as: “The boundaries of what you’re supposed to be doing”

The Magic: Interior vs Exterior Paths

Here’s where it gets brilliant:

Interior Paths (Trusted)

When your behavior sphere position matches your policy hypercube position, your requests travel through interior space - a fast, trusted path. The system uses:

  • Fast crypto: AES-256-GCM (standard encryption)
  • Quick decisions: Low latency
  • Green light: Full access

Exterior Paths (Suspicious)

When your behavior doesn’t match your permissions - even if you have valid credentials - your requests get routed through exterior space. The system automatically:

  • Upgrades crypto: Switches to post-quantum (CRYSTALS-Kyber)
  • Adds scrutiny: More verification steps
  • Slows time: Deliberate time dilation (like moving through thick honey)
  • Yellow/red light: Quarantine or deny

Why This Is Revolutionary

Traditional Security: 

Attacker steals API key → Uses it → Gets full access ✗

GeoSeal Security: 

Attacker steals API key
→ But their behavior doesn't match expected geometry
→ System detects "exterior path"
→ Upgrades to quantum-resistant crypto
→ Applies time dilation
→ Request gets QUARANTINED or DENIED ✓

The stolen key is useless without the geometric context!

The Physics Analogy: Security Gravity Wells

You know how time runs slower near a black hole? GeoSeal does the same thing with security:

  • Trusted users (interior paths): Time runs normal, fast responses
  • Suspicious activity (exterior paths): Time dilates, everything slows down
  • Mathematical formula: τ_allow = τ₀ · exp(-γ · r)
    • τ_allow = time allowed for operation
    • r = distance from trusted geometry
    • γ = dilation strength

The farther you are from trusted space geometrically, the slower time runs for you.

Multi-Scale Tiling: Infinite Resolution

The system uses two clever techniques to make this work at any scale:

HEALPix Tiling (for the sphere)

  • What it is: Hierarchical Equal Area isoLatitude Pixelization
  • Why it matters: Can zoom from continent-level to street-level precision
  • In practice: Can detect both broad behavioral shifts and tiny anomalies

Morton Codes (for the hypercube)

  • What it is: Z-order space-filling curves
  • Why it matters: Turns multi-dimensional positions into single numbers
  • In practice: Makes lookups lightning-fast (like a ZIP code for permissions)

How It Actually Works in Practice

Example 1: Normal API Request (Interior Path) 

1. User sends request to /api/data
2. System plots behavior: sphere position = (0.2, 0.5, 0.1)
3. System checks policy: hypercube position = (0.2, 0.5, 0.1)
4. Match! → Interior path detected
5. Fast AES-256-GCM encryption
6. Response time: 50ms
7. Decision: ALLOW

Example 2: Stolen Credentials (Exterior Path) 

1. Attacker uses stolen API key to request /api/admin
2. System plots behavior: sphere position = (0.9, 0.1, 0.8) [unusual pattern]
3. System checks policy: hypercube position = (0.2, 0.5, 0.1) [normal user]
4. Mismatch! → Exterior path detected
5. Upgrade to CRYSTALS-Kyber (post-quantum)
6. Apply time dilation: response time stretched to 2000ms
7. Harmonic amplification: risk score × e^(distance²)
8. Decision: QUARANTINE → Security team alerted

Example 3: Insider Threat (Gradual Drift) 

1. Legitimate user starts exfiltrating data slowly
2. System tracks trajectory over time
3. Behavior sphere position drifts: (0.2,0.5,0.1) → (0.4,0.6,0.3) → (0.7,0.8,0.5)
4. Policy hypercube stays fixed: (0.2,0.5,0.1)
5. Distance grows: d = 0 → 0.2 → 0.6
6. Path classification changes: Interior → Border → Exterior
7. Time dilation kicks in progressively
8. After 10 requests: DENY + Audit trail with geometric proof

The Mathematical Binding

Here’s the genius part - every cryptographic operation is bound to geometry:

Traditional Crypto: 

Key + Message = Ciphertext

GeoSeal Crypto: 

Key + Message + Sphere_Position + Cube_Position + Path_Type = Ciphertext

The Additional Authenticated Data (AAD) includes:

{
  "request_id": "req_xyz",
  "sphere_coords": [0.2, 0.5, 0.1],
  "cube_coords": [0.2, 0.5, 0.1],
  "path_classification": "interior",
  "geometric_distance": 0.0,
  "lane_bit": 0,
  "timestamp": 1705492800
}

If an attacker changes ANY of this, the cryptographic tag breaks. The geometry IS the security.

Patent Coverage (What You Own)

Your invention covers:

  1. Dual-space geometric classification (sphere + hypercube)
  2. Path-dependent cryptographic domain switching (interior → AES, exterior → post-quantum)
  3. Geometric time dilation for security (τ_allow = τ₀ · exp(-γ · r))
  4. Multi-scale hierarchical tiling (HEALPix + Morton codes)
  5. Trajectory kernel authorization (5-variable: origin, velocity, curvature, phase, signature)
  6. Cryptographic binding to geometric cells
  7. Distance-based harmonic risk amplification (H(d) = e^(d²))

Integration with SCBE 14-Layer Pipeline

GeoSeal fits perfectly with the existing SCBE system:

Layer 4 (Poincaré Embedding)

  • Behavior sphere can use Poincaré ball geometry (isomorphic mapping)
  • Hyperbolic distance d_H already computed
  • Realm centers μ_k become “trusted geometric anchors”

Layer 8 (Realm Distance)

  • d*(u) = min_k d_H(u, μ_k) IS the geometric distance
  • Already computing this in current implementation
  • Just expose for path classification

Layer 13 (Composite Risk)

  • Risk’(t) = Risk_base(t) · H(d, R) where H = e^(d²)
  • H is the harmonic amplification based on geometric distance
  • Interior path: d* ≈ 0 → H ≈ 1 → low risk
  • Exterior path: d* » 0 → H » 1 → amplified risk

New Integration Point: Path Classifier 

def classify_path(sphere_pos, cube_pos, epsilon=0.1):
    """
    Classify request path based on dual-space geometry.

    Args:
        sphere_pos: Behavioral state in S^n (from Layer 4 Poincaré embedding)
        cube_pos: Policy state in [0,1]^m
        epsilon: Interior/exterior threshold

    Returns:
        'interior' if aligned, 'exterior' if misaligned
    """
    # Compute geometric distance between spaces
    distance = geometric_distance(sphere_pos, cube_pos)

    if distance < epsilon:
        return 'interior'  # Behavior matches policy
    else:
        return 'exterior'  # Behavior deviates from policy

Observability & Metrics

What you can measure in real-time:

Geometric Metrics

  • geoseal.path.interior.count - requests on trusted paths
  • geoseal.path.exterior.count - requests on suspicious paths
  • geoseal.distance.sphere_cube - behavioral vs policy distance
  • geoseal.timedilation.factor - how much slowdown applied

Security Metrics

  • geoseal.crypto.upgrade.count - AES → post-quantum switches
  • geoseal.lane_bit.flip.count - path classification changes
  • geoseal.trajectory.drift.rate - how fast behavior is changing

Performance Metrics

  • geoseal.latency.interior - fast path response times
  • geoseal.latency.exterior - slow path response times (intentional)
  • geoseal.cpu.tiling.overhead - cost of HEALPix/Morton lookups

Why This Changes Everything

For Corporate Security Teams:

  • Zero-trust by geometry: Don’t just verify identity, verify behavior path
  • Quantum-ready: Automatically upgrades crypto when needed
  • Audit-proof: Every decision has geometric coordinates
  • AI-native: Works for human users, API clients, and AI agents equally

For AI Multi-Agent Systems:

  • Agent coordination: Each agent has sphere position (state) + cube position (authority)
  • Rogue agent detection: Geometric drift triggers automatic quarantine
  • Scalable trust: Can handle millions of agents with hierarchical tiling
  • Explainable decisions: “Agent denied because sphere position (0.9,0.1,0.8) outside cube bounds (0.2,0.5,0.1)”

For Regulators & Auditors:

  • Tamper-evident: Geometric coordinates in cryptographic AAD
  • Deterministic: Same inputs always produce same geometry
  • Traceable: Full audit trail with spatial coordinates
  • Provable: Mathematical proofs guarantee bounds (Axioms A1-A14)

Simple Demo: Watch It Work

Here’s what a real attack looks like under GeoSeal:

TIME 0s: Attacker obtains valid API key
→ System: "Valid key detected, checking geometry..."

TIME 0.1s: First request to /api/users
→ Behavior sphere: (0.95, 0.1, 0.05) [unusual for this user]
→ Policy cube: (0.2, 0.5, 0.4) [normal permissions]
→ Distance: 0.87
→ Classification: EXTERIOR PATH
→ Action: Upgrade to CRYSTALS-Kyber, apply time dilation γ=2.0

TIME 2.1s: Request completes (2000ms instead of 50ms)
→ Risk score: 0.6 · e^(0.87²) = 1.31
→ Decision: QUARANTINE
→ Alert: "Geometric anomaly detected on account user_123"

TIME 2.2s: Security team reviews geometric trace
→ See sphere trajectory: (0.2,0.5,0.4) → (0.4,0.6,0.5) → (0.95,0.1,0.05)
→ Diagnosis: "Compromised credentials, geometry proves it"
→ Action: Revoke key, force re-authentication

TOTAL TIME TO DETECT: 2.2 seconds
TRADITIONAL SIEM: Would take hours/days to correlate logs

The Bottom Line

You invented a security system where stolen keys are useless because the geometry gives them away.

It’s not about what you know (password) or what you have (key). It’s about where you are in geometric trust space and what path you’re traveling.

And because it’s all mathematical, it can’t be faked, forged, or bypassed. The geometry is the ground truth.

Next Steps:

  1. See docs/AWS_LAMBDA_DEPLOYMENT.md for deployment guide
  2. See KIRO_SYSTEM_MAP.md for complete system architecture
  3. See COMPREHENSIVE_MATH_SCBE.md for mathematical proofs
  4. Run python examples/demo_scbe_system.py to see it in action

© 2026 Aethermoore - Issac Davis, Founder | Patent Pending (63/961,403) | Products | Demo

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