Hilbert Steps to LRS: A One-Way Contract and Light-Bridge Test with Falsifiable Testing

This deposit documents a practical, falsifiable bridge from a normalized decision space (“Hilbert steps”) to a realized Local Reference System (LRS). The work formalizes a one-way, no-backflow contract that issues an LRS “operating system”: fixed windows, bars, flip program, seeds, and falsifiers. A Richardson G–Σ–P–L subspace serves as the ledger that binds these rules to real geometry and timing so capsules can execute identically across benches. The Truncated Wigner Approximation (TWA) provides a compact local engine at the LRS, defining stable parity and window behavior without higher-order corrections. The bridge is verified using light as the messenger with explicit, lab-bounded checks: normalization, parity (Odd/Even) flip exclusivity, distance flatness, non-dispersion, and symmetric-difference metrics. Together these elements yield engine-invariant decisions, reproducible across platforms, and auditable via commit–reveal hashes, window invariance, and versioned mappings. The result is a transportable capsule method: decide in Hilbert, execute in LRS, and report in physical units—while keeping the contract immutable and the testing falsifiable.