Z-Bit: Lambda-Proof Bitcoin Standalone Module

Z-Bit is a comprehensive, standalone suite for Bitcoin integration within the Lambda-Proof ecosystem, focusing on the Multiplicity stack. It bridges production-grade anchoring, prime-indexed dynamical search research (ZRSD+PWEH), and formally verified stability.

Overview

Z-Bit provides the technical bindings required to anchor the Lambda-Proof "Conscious Sovereignty Layer" (CSL) to the Bitcoin blockchain. It ensures that every cryptographic proof generated by the stack is tied to the thermodynamic security of Bitcoin PoW through a transparent, verifiable, and governed pipeline based on Multiplicity principles.

Core Components

1. Taproot Anchor System (Production)

A descriptor-based anchoring engine for Bitcoin Core v26+.

• Miniscript-Compatible: Utilizes Taproot descriptors for seamless integration with modern Bitcoin infrastructure.
• Soft Reveal: Proves commitment to a batch of receipts without requiring an on-chain spend.
• Two-Leaf Tree: Implements a commitment leaf for proofs and an admin leaf for timelocked recovery.
• JSON Schemas: Standardized formats for Receipt, BatchHeader, and AnchorProof.

2. ZRSD + PWEH (Research Simulation)

The "Zeta-Recursive Semantic Dynamics" engine for search acceleration.

• Attestation (PWEH): Generates tamper-evident, hash-chained execution trajectories for every search step.
• Oracle Feedback: Promotes SHA-256 closeness to an explicit dynamical driver in Fock space.
• Resonance Search: Explores the prime-weighted search space to accelerate the discovery of valid Bitcoin nonces.

3. PIRTM & CCRE Learning Loop

The machine learning and refinement core of the Phase Mirror architecture.

• PIRTM Core: Mathematical foundation for Prime-Indexed Recursive Tensor Mathematics, providing stability certification.
• CCRE (Contraction-Constrained Resonance Engine): The parametric refinement loop that ensures all parameter updates satisfy contraction, drift, and resonance invariants.
• Stability Enforcement: Uses the StabilityGate to ensure contractive bounds during recursive operations.

4. Formal Verification (Lean 4)

Mathematically rigorous proofs for the underlying foundations of Z-Bit.

• AffineCore: Formalization of spectral theory, stability gates, and contractivity.
• Existence & Uniqueness: Proofs for the existence of stable fixed points in recursive dynamics.
• BIBO Stability: Bounded-Input Bounded-Output stability guarantees for the core operators.

Project Structure

agi-os/packages/z-bit/
├── lean4/                  # Lean 4 formal proofs (AffineCore)
├── python/                 # Integrated Python dependencies
│   ├── ccre/               # CCRE learning loop & parametric refinement
│   ├── pirtm/              # PIRTM mathematical core & stability certs
│   └── zrsd/               # ZRSD + PWEH research engine
├── scripts/                # Automation (Regtest, Sim, Benchmarks)
├── schemas/                # JSON Schema definitions (Draft 2020-12)
├── docs/                   # Technical specifications & ADRs
├── pyproject.toml          # Python build config (z-bit)
└── package.json            # Node.js build config (@lambda-proof/z-bit)

Quick Start

Python Research & Simulation

cd agi-os/packages/z-bit
pip install -e .
python scripts/run_bitcoin_sim.py
python scripts/benchmark_resonance.py

Node.js Anchoring

npm install
npm run test-schemas
# See scripts/anchor_regtest.sh for usage

Formal Verification

cd lean4
lake build

Governance & Integrity

Z-Bit is governed by the Phase Mirror Epistemic Framework. Every architectural choice is documented as an explicit set of assumptions and contradictions.

• Certified Benchmarking: All performance claims must be backed by PWEH logs.
• Assumptions Register: See docs/PROJECT_INTEGRITY.md.

License

UNLICENSED - See repository root LICENSE.txt