README.md

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

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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