Deterministic Cross-Implementation Equivalence of Structural Similarity Coefficients: A Reproducibility Contract with Pre-Specified Δ-Thresholds (Kakushin Structural Theory 2025-144)

This preprint presents the instrument-level validation of Structural Similarity
Coefficient (SSC) computation under a fully deterministic execution contract.
Two independent distance pipelines—SciPy’s condensed pdist and NumPy’s
square-distance → squareform route—are evaluated for cross-implementation
equivalence using a pre-specified Δ-specification (mean < 0.07, max < 0.10).
Under locked float64 precision, dependency pinning, OpenBLAS 0.3.30 in
single-thread mode, and fixed random seeds, cross-implementation differences
remain at machine-precision scale (≈10⁻¹⁶–10⁻¹²) across Euclidean, cosine, and
correlation distances at N=1000, D=50.

This study defines the deterministic execution contract, provides complete
reproduction instructions, and archives all outputs (ΔSSC metrics, statistical
summaries, figures, and environment snapshots). The validated instrument
constitutes the Instrument Core (I-1) of the Optics of Intelligence framework,
supporting subsequent Observation (O-series) and Theory (L-series) studies.

This archived version contains the exact code, data, and CI-generated artifacts
corresponding to the publication-ready form of Kakushin Structural Theory
preprint 2025-144.