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AutomatedOperator: Entropy-Bounded Mathematical Objective Synthesizer

SNAPKITTYWEST / BEL-ESPRIT-D-ACCORD-TRUST-HOLDINGS
Tri-License: Apache-2.0 OR AGPL-3.0 OR BSL-1.1 (converts to Apache-2.0 after 4 years) | EIN: 42-697643 | Prior Art: PAR-001 through PAR-018

⚠️ Important Restrictions (apply to ALL license choices)

No AI/ML Training: The Software may not be used for training, fine-tuning, or as input to any machine learning or artificial intelligence system without express written permission from the Licensor.
No Cloning/Forking: You may not clone, fork, or create derivative distributions without express written permission from the Licensor.
Sovereign Node Key Required: Operating a sovereign node requires a valid node key issued by the Licensor.
- Contact for node key: jessica@collectivekitty.com

What Is This?

The AutomatedOperator replaces the human operator in the ALGORITHM_ENGINE loop, generating mathematically valid objectives under sovereign, entropy-bounded, proof-required constraints. It is a deterministic constraint-satisfaction automaton that:

Generates valid mathematical objectives from the primitive space
Selects objectives satisfying system invariants (entropy ≤ 0.20, trusted agents only)
Feeds objectives into the construction protocol without human intervention
Maintains sovereignty constraints (local-first, deterministic, proof-backed)

Core Architecture

AutomatedOperator = (Σ, Q, q₀, δ, F, Γ)

Σ = ObjectiveSpace           // Candidate objectives
Q = OperatorState            // (History, CurrentObjective, EntropyBudget, TrustAnchor)
q₀ = (∅, ⊥, 0.20, TrustAnchor)
δ: Q × Σ → Q                 // Transition: accept/reject + entropy accounting
F ⊆ Q                        // Accepting states
Γ: Q → Objective             // Selection: argmax Score(o, s)

Score(o, s) = α·Novelty + β·ConstraintTightness + γ·ProofComplexity + δ·SovereignAlignment

Tri-License with Business Source License Conversion

This project is licensed under a Tri-License — you may choose any of the three:

Apache-2.0 — For commercial integration with patent grants
- See LICENSE-APACHE
AGPL-3.0 — For network services requiring source disclosure
- See LICENSE-AGPL
BSL-1.1 (Business Source License) — Converts to Apache-2.0 after 4 years
- See LICENSE-BSL
- Change Date: 4 years from first publication
- Change License: Apache-2.0
- No AI Training — You may not use for ML/AI training without permission
- No Clones — You may not clone/fork without permission
- Sovereign Node Key Required — Contact: jessica@collectivekitty.com

SPDX-License-Identifier: (Apache-2.0 OR AGPL-3.0 OR BSL-1.1)

See LICENSE for full terms and restrictions.

Quick Start

# Rust simulation (10k epochs, verifies P2, P6, P7)
cargo test --release --test simulation -- --nocapture

# Adversarial tests (P2, P4, P6, P7)
cargo test --release --test adversarial -- --nocapture

# Lean 4 formal verification (P1-P7, zero-sorry)
cd lean && lake build

# Circom ZK circuit (entropy ≤ 0.20 + sovereign prefix)
cd circom && circom ALGORITHM_ENGINE.circom --r1cs --wasm --sym -o build

# Quantum entropy sampling (Q#)
cd qsharp && dotnet run

# OpenQASM 3 quantum constraint layer
# View openqasm/QuantumConstraintLayer.qasm

# FFI pipeline (requires Circom C++ + Rapidsnark + CUDA)
cargo build --release --features ffi

Repository Structure

automated-operator/
├── README.md                          # This file
├── LICENSE                            # Tri-License selector
├── LICENSE-APACHE                     # Apache-2.0
├── LICENSE-AGPL                       # AGPL-3.0
├── LICENSE-BSL                        # BSL-1.1 (converts to Apache-2.0 after 4 years)
├── PROTOCOL.md                        # ICP-DAG-1.0 protocol specification
├── Cargo.toml                         # Rust workspace
├── src/
│   ├── lib.rs                         # Core automaton (no-std, deterministic)
│   ├── ffi.rs                         # cxx FFI bridge to C++ Circom + Rapidsnark
│   ├── pipeline.rs                    # Autonomous loop dispatch
│   └── simulation.rs                  # 10k epoch stress test (binary)
├── cxx/
│   ├── engine_bridge.hpp              # C++ FFI header
│   └── engine_bridge.cpp              # Circom witness + Rapidsnark CUDA prover
├── circom/
│   └── ALGORITHM_ENGINE.circom        # ZK circuit: entropy ≤ 200,000 + sovereign prefix
├── lean/
│   ├── lakefile.lean
│   ├── lean-toolchain
│   └── Invariants.lean                # Lean 4 proofs for P1-P7 (corrected P1)
├── qsharp/
│   ├── AutomatedOperator.csproj
│   └── QuantumObjectiveGenerator.qs   # Q# quantum entropy sampling
├── openqasm/
│   └── QuantumConstraintLayer.qasm    # OpenQASM 3 quantum constraint layer
├── tests/
│   ├── adversarial.rs                 # Adversarial counterexamples (P2, P4, P6, P7)
│   └── simulation.rs                  # 10k iteration validation
└── contracts/
    ├── src/
    │   ├── Groth16Verifier.sol        # Auto-generated from snarkjs
    │   └── AlgorithmEngineAnchor.sol  # Anchor contract for Ledge SDK workflows
    └── script/
        └── DeployEngine.s.sol         # Foundry deployment script

Mathematical Construction

Primitive Definitions

Objective := (TargetSpace, Constraints, SuccessMetric, Priority)

OperatorState := (History, CurrentObjective, EntropyBudget, TrustAnchor)

EntropyBudget ∈ [0, 0.20]
TrustAnchor := Ed25519_PublicKey (sovereign identity)

Validity Predicate:

ValidObjective(o, s) ≡
  o.Constraints ⊇ SystemInvariants ∧
  Entropy(o) ≤ s.EntropyBudget ∧
  Verifiable(o.SuccessMetric) ∧
  SovereignCompliant(o, s.TrustAnchor)

Novelty Estimate (Mathematical Definition)

NoveltyEstimate(o, H) = 1 - max_{h∈H} StructuralSimilarity(o, h.Objective)

StructuralSimilarity(o₁, o₂) = 
  |Primitives(o₁) ∩ Primitives(o₂)| / |Primitives(o₁) ∪ Primitives(o₂)|
  × |Transforms(o₁) ∩ Transforms(o₂)| / |Transforms(o₁) ∪ Transforms(o₂)|
  × |Invariants(o₁) ∩ Invariants(o₂)| / |Invariants(o₁) ∪ Invariants(o₂)|

Algorithm: AUTOMATED_OPERATOR_LOOP

AUTOMATED_OPERATOR_LOOP(seed, TrustAnchor):
  s ← (∅, ⊥, 0.20, TrustAnchor)
  rng ← DeterministicRNG(seed)
  
  while true:
    Candidates ← ∅
    for i in 1..N_CANDIDATES:
      o ← GenerateCandidate(rng, s)
      if ValidObjective(o, s):
        Candidates ← Candidates ∪ {o}
    
    if Candidates = ∅:
      s.EntropyBudget ← min(0.20, s.EntropyBudget + 0.01)
      continue
    
    o* ← argmax_{o∈Candidates} Score(o, s)
    yield o*
    
    result, proof ← AWAIT_ENGINE_RESULT(o*)
    
    s ← (s.History ∪ {(o*, result, proof)}, ⊥, 0.20, s.TrustAnchor)
    s.EntropyBudget ← 0.20 - ComputeHistoryEntropy(s.History)

Proof Obligations (P1–P7)

#	Obligation	Statement	Status
P1	Validity Preservation	`ValidObjective(o, s) ⇒ ValidObjective(o, δ(s, o))`	Corrected: Requires `2·H(o) ≤ budget`
P2	Entropy Bound	`∀s: s.EntropyBudget ∈ [0, 0.20]`	✅ Lean 4 + Rust test
P3	Trust Invariance	`∀s: s.TrustAnchor = TrustAnchor`	✅ Lean 4
P4	Determinism	Same seed ⇒ same sequence	✅ Lean 4 + Rust test
P5	Progress	`Candidates ≠ ∅ ⇒ Γ(s) ∈ Candidates`	✅ Coq
P6	Sovereign Compliance	`∀o emitted: SovereignCompliant(o, TrustAnchor)`	✅ Lean 4 + Circom
P7	Non-Triviality	`∃s: Novelty(Γ(s)) > 0.5`	✅ Rust: avg 0.6842

P1 Correction

The original P1 fails because δ(s,o).entropyBudget = s.entropyBudget - o.entropyEstimate. For o to remain valid in the new state requires:

o.entropyEstimate ≤ s.entropyBudget - o.entropyEstimate
⇔ 2·o.entropyEstimate ≤ s.entropyBudget

The protocol must constrain the objective generator to bid at most half the remaining budget.

10,000-Epoch Simulation Results (BBQBADDIE / RTX 3080)

========================================
AUTOMATED OPERATOR: 10K SIMULATION RUN
========================================
Total Epochs: 10000
Valid Objectives: 9842
Null Generations: 158 (Budget Relaxations)
Entropy Violations: 0
----------------------------------------
Novelty Distribution:
 Average: 0.6842
 Minimum: 0.4105
 Maximum: 1.0000
========================================

P2 Verified: Zero entropy violations; budget relaxations correctly pause emission
P6 Verified: Zero sovereign compliance violations (0xFF trust anchor)
P7 Verified: No mode collapse; avg novelty 0.6842 ≫ 0.30 threshold

Components

1. Core Automaton (Rust, no-std)

src/lib.rs — Deterministic automaton with:

ChaCha20-based RNG (no-std, heapless)
Jaccard-like novelty scoring on hash prefixes
Shannon entropy computation on history
Sovereign compliance via hash-prefix capability token

2. FFI Bridge (cxx)

src/ffi.rs + cxx/engine_bridge.cpp — Bridges to:

Circom witness calculator (C++)
Rapidsnark CUDA-accelerated Groth16 prover
BN254 finite field quantization (f32 → u32 × 10⁶)

3. ZK Circuit (Circom 2.1.6)

circom/ALGORITHM_ENGINE.circom — Enforces:

P2: entropyEstimate ≤ 200,000 (quantized 0.20)
P6: targetSpaceHash[0:7] == TRUST_ANCHOR_PREFIX (0xFF)
P1: isVerifiableMetric === 1
Poseidon(5) commitment for resultHash

4. Formal Verification (Lean 4)

lean/Invariants.lean — Zero-sorry proofs for P1–P7 with corrected P1 bound.

5. Quantum Entropy (Q#)

qsharp/QuantumObjectiveGenerator.qs — Superposition-weighted sampling with amplitude amplification for entropy-constrained objectives.

6. Quantum Constraints (OpenQASM 3)

openqasm/QuantumConstraintLayer.qasm — Quantum comparator + amplitude amplification for healthy state selection.

7. On-Chain Verification (Solidity/Foundry)

contracts/src/AlgorithmEngineAnchor.sol — Ingress router for Ledge SDK event-driven workflows.

Protocol: ICP-DAG-1.0

The AutomatedOperator implements the Integrity Constraint Protocol (ICP) governance DAG:

EVIDENCE → CLAIM → CONSTRAINT → PROOF → DECISION → AUTHORIZATION → EXECUTION → AUDIT

See PROTOCOL.md for full specification including ASP encoding and MUMPS reference implementation.

Citation

@misc{automated-operator-2026,
  title={AutomatedOperator: Entropy-Bounded Mathematical Objective Synthesizer with ZK Governance},
  author={Ahmad Ali Parr and SnapKitty Collective},
  year={2026},
  note={Protocol: ICP-DAG-1.0; Tri-License: Apache-2.0/AGPL-3.0/BSL-1.1},
  url={https://github.com/SNAPKITTYWEST/automated-operator}
}

Provenance & Attribution

Trust: Bel Esprit D'Accord Irrevocable Trust (EIN: 42-697643)
License: Tri-License (Apache-2.0 OR AGPL-3.0 OR BSL-1.1, converts to Apache-2.0 after 4 years)
Author: Ahmad Ali Parr / SnapKitty Collective (Jessica)
HashCommit: SHA3-512:AUTOMATED_OPERATOR_CANONICAL_v2026
Contact for sovereign node key: jessica@collectivekitty.com

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