sum(trust) = K D × I ≥ threshold n ≥ 3f + 1 H(chain) = BLAKE3(H(prev) || event) trust(t+1) = trust(t) + delta score = depth × 0.4 + frequency × 0.3 + recency × 0.3 verified: chain[i].hash == BLAKE3(chain[i-1].hash || data) phase_boundary < 4/7 drift < 10⁻¹⁴ sum(trust) = K n ≥ 3f + 1 H(chain) = BLAKE3(H(prev) || event) D × I ≥ threshold trust(t+1) = trust(t) + delta phase_boundary < 4/7 verified: chain[i].hash == BLAKE3(chain[i-1].hash || data) drift < 10⁻¹⁴ score = depth × 0.4 + frequency × 0.3 + recency × 0.3

K = 7.0 Conserved 1,026 Lean 4 Theorems

Governance Physics

Other platforms monitor. We enforce conservation laws. Every trust decision obeys mathematical invariants that cannot be violated, only verified.

Conservation Laws

Trust is a conserved quantity. The total trust budget K = 7.0 is maintained across all agents at every transition. Violations are mathematically impossible.

8,106 tests · trust_sum = K at every state

Machine-Verified Proofs

1,026 theorems formalized in Lean 4. axiom (exploratory gauge theory). Every conservation property, every boundary condition, every invariant is machine-checked.

1,373 declarations ·

Cryptographic Provenance

Every governance decision is BLAKE3-hashed into a Merkle-rooted chain. Tamper detection is instantaneous. Replay is deterministic.

Portable Provenance™ · Patent Pending

// conservation_law

Trust Cannot Be Created or Destroyed

Like energy in physics, trust in the Atomic Trust System is a conserved quantity. The sum of all agent trust scores always equals K = 7.0. When one agent gains trust, another must lose it. This isn't a design choice — it's a mathematical invariant enforced at every state transition.

Anomaly detection threshold: 0.20 catches violations before they propagate
Phase boundaries: concentration < 4/7 prevents trust monopolization
Temporal coherence: Θ ≥ 0.75 ensures smooth transitions

conservation_core.py

def enforce_conservation(agents, K=7.0):

  """Conservation law: sum of trust = K at every transition."""

  total = sum(a.trust_score for a in agents)

  assert abs(total - K) < 1e-10, \

    f"Conservation violated: {total} ≠ {K}"

  # Velado Bound: D × I ≥ threshold

  for a in agents:

    D = diversity_index(a)

    I = information_content(a)

    assert D * I >= threshold, \

      f"Velado Bound violated: {D*I:.4f}"

  return TrustState(agents, K, verified=True)

// geometric_invariants

Five Geometric Invariants

Every governance transition must satisfy all five. If any invariant is violated, the transition is rejected. No exceptions. No overrides.

#	Invariant	Formula	Status
I	Velado Bound Diversity × Information has a lower bound	D × I ≥ detection_threshold	VALIDATED
II	Excess Action Bounded computational overhead	ΔS < 10⁶	VALIDATED
III	Byzantine Tolerance Fault-tolerant consensus threshold	n ≥ 3f + 1	THEOREM
IV	Phase Boundary Trust monopolization prevention	phase_boundary < 4/7	EMPIRICAL
V	Temporal Coherence Smooth transitions, bounded drift	Θ ≥ 0.75 ∧ C_t ≤ 0.12	ENGINEERING

// lean4_formalization

1,026 Theorems. Zero Gaps.

Every conservation law, boundary condition, and invariant is formalized in Lean 4 — a proof assistant used by mathematicians to verify the correctness of their work. Our proofs aren't comments in code. They're machine-checked mathematical truth.

1,373 declarations — theorems, lemmas, definitions, structures
— 1 exploratory axiom (gauge theory); all production theorems fully proven
32 axioms — explicit foundations, all documented and justified

-- Conservation Law: Trust is conserved
theorem conservation_law
  (agents : Finset Agent)
  (K : ℝ) (hK : K = 7)
  (h_sum : ∑ a in agents, score a = K) :
  ∀ transition : Transition,
    ∑ a in agents, score (apply transition a) = K := by
  intro t
  rw [transition_preserves_sum t h_sum]
  exact hK ▸ h_sum

-- Velado Bound: Impossibility proof
theorem velado_bound_impossibility
  (a : Agent)
  (hD : diversity a > 0)
  (hI : information a > 0) :
  diversity a * information a ≥ threshold := by
  apply velado_lower_bound hD hI

// portable_provenance

Every Decision Has a Receipt

Portable Provenance™ creates a tamper-proof chain of custody for every governance action. BLAKE3 hashing with domain separation, Merkle-rooted trees, deterministic replay. If it happened, there's a cryptographic proof.

BLAKE3 hashing with domain-separated prefixes (artifacts, nodes, chains)
Deterministic replay: same inputs → same hash chain, every time
Geometric State Provenance: records manifold geometry at every transition
Patent coverage: Patent Pending

provenance_chain.json

{

  "chain_id": "0x7a3f...b2c1",

  "block": 1847,

  "timestamp": "2026-03-22T14:30:00Z",

  "event": "trust_transition",

  "agents": [

    { "id": "alpha", "delta_trust": +0.12 },

    { "id": "beta", "delta_trust": -0.12 }

  ],

  "K_before": 7.0,

  "K_after": 7.0,

  "merkle_root": "0xb5e1...9f4d",

  "blake3": "0x3c8a...7e20",

  "invariants_checked": 5,

  "all_passed": true

}

// patent_portfolio

Protected by Physics and Law

The deepest patent moat in AI governance.

Patent Filings

185+

Independent Claims

Non-Provisional (Pending)

Provisional Applications

Coverage spans trust dynamics, consensus mechanisms, cryptographic provenance, attention verification, geometric state recording, fleet governance, token economies, and organizational control planes.

// byzantine_tolerance

Survives Adversarial Agents

The consensus layer tolerates up to ⌊(n-1)/3⌋ Byzantine (malicious) agents. Fisher-Rao geometry on the probability simplex enables anomaly detection that catches sleeper agents, collusion, and slow-drift manipulation.

n ≥ 3f + 1 fault tolerance threshold (Lean-verified)
Fisher-Rao metric on the probability simplex for anomaly scoring
Sleeper detection: catches agents that behave well then defect
Differential privacy: epsilon-bounded information leakage

byzantine_consensus.py

# Byzantine fault tolerance

# n agents, f faulty: n ≥ 3f + 1

class GeometricConsensus:

  def validate_vote(self, agent, vote):

    # Fisher-Rao distance on simplex

    d = fisher_rao_distance(

      agent.belief_vector,

      self.consensus_belief

    )

    if d > self.anomaly_threshold:

      return Flag(

        agent, "ANOMALY",

        distance=d

      )

    return Accept(vote)

// research_timeline

Three Years of Research

2024

Foundation

Conservation law discovery. First engine prototype. Initial patent filings. APCE attention verification proof-of-concept.

2025

Formalization

Lean 4 proof corpus reaches 1,026 theorems. Non-provisional patent filed. Kernel v7.0 stabilized. 48 patent portfolio completed. 100% TrojAI benchmark.

2026

Production

8,106 tests passing. Fleet governance. Dual-conservation token economy. Organizational Control Plane (27-agent autonomous operation). EU AI Act compliance mapping.