PhaseBridge: A Strict Lossless Mapping Between Discrete Alphabets and Phase Space for Cognitive Systems

PhaseBridge is an experimental open-source framework that defines a strict, lossless mapping between discrete alphabets (uintM) and continuous phase space (θ ∈ [0, 2π)). It provides a minimal and verifiable interchange format (PIF) that enables reversible round-trip conversion across data modalities such as time series and images.

Unlike compression-oriented containers (Parquet, CBOR) or learned embeddings, PhaseBridge emphasizes reversibility, integrity, and a uniform diagnostic signal. Each mapping is guaranteed bit-exact under the declared alphabet when meta.note = "no_processing". Integrity is enforced via SHA-256 hashes, while κ-coherence (|⟨e^{iθ}⟩|) provides a simple, read-only measure of structural coherence.

The framework includes:
- A Python SDK and CLI tools (pb-encode, pb-decode, pb-validate, pb-kappa).
- A formal JSON Schema for PIF v1, with optional MessagePack serialization.
- Conformance tests, including property-based tests for round-trip correctness.

Demonstrations include strict round-trip for synthetic time series and grayscale images, with hash and κ validation. The approach complements existing formats by providing a minimal representational substrate that can be embedded into wider analytic or multimodal pipelines.

PhaseBridge is intended as a foundational layer for cognitive systems where strict invertibility, integrity checks, and cross-modality consistency are essential.