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	---
	license: other
	license_name: snapkitty-tri-license
	license_link: https://huggingface.co/Snapkitty/automated-operator/blob/main/LICENSE
	tags:
	- snapkitty
	- agents
	- python
	---

	<!--
	Copyright 2026 Bel Esprit D'Accord Irrevocable Trust (EIN: 42-697643)

	Licensed under the Apache License, Version 2.0 (the "License");
	you may not use this file except in compliance with the License.
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	Licensed under the Business Source License 1.1 (BSL-1.1);
	converts to Apache-2.0 after 4 years. See LICENSE-BSL for terms.
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	# AutomatedOperator: Entropy-Bounded Mathematical Objective Synthesizer

	[![License](https://img.shields.io/badge/License-Apache%202.0%20OR%20AGPL%203.0%20OR%20BSL%201.1-blue.svg)](LICENSE)
	[![Rust](https://img.shields.io/badge/Rust-1.75%2B-orange.svg)](src/)
	[![Lean 4](https://img.shields.io/badge/Lean-4.19.0-purple.svg)](lean/)
	[![Circom](https://img.shields.io/badge/Circom-2.1.6-teal.svg)](circom/)
	[![Q#](https://img.shields.io/badge/Q%23-0.28-violet.svg)](qsharp/)
	[![OpenQASM](https://img.shields.io/badge/OpenQASM-3.0-red.svg)](openqasm/)
	[![Protocol](https://img.shields.io/badge/Protocol-ICP--DAG--1.0-gold.svg)](PROTOCOL.md)

	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:

	1. Apache-2.0 — For commercial integration with patent grants
	- See [LICENSE-APACHE](LICENSE-APACHE)

	2. AGPL-3.0 — For network services requiring source disclosure
	- See [LICENSE-AGPL](LICENSE-AGPL)

	3. BSL-1.1 (Business Source License) — Converts to Apache-2.0 after 4 years
	- See [LICENSE-BSL](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](LICENSE) for full terms and restrictions.

	---

	## Quick Start

	```bash
	# 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](PROTOCOL.md) for full specification including ASP encoding and MUMPS reference implementation.

	---

	## Citation

	```bibtex
	@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

	---

	## License

	Licensed under SnapKitty Tri-License ([LICENSE](LICENSE)), with these additional license files:

	- [LICENSE-BSL](LICENSE-BSL): Business Source License 1.1
	- [LICENSE-AGPL](LICENSE-AGPL): AGPL-3.0
	- [LICENSE-APACHE](LICENSE-APACHE): Apache-2.0

	### 💼 Commercial License

	Snapkitty code is free and open under AGPL-3.0 for open-source use. Building a commercial product or service? A proprietary commercial license from Snapkitty Collective LLC lets you ship this code without the AGPL's source-sharing and network-use obligations.

	[→ Get a commercial license](mailto:A.parr@belespritdaccord.uk?subject=Commercial%20license:%20automated-operator) · A.parr@belespritdaccord.uk