Proxy Coupling Structure Tests (PCST) - Dataset

Description This dataset contains the full experimental package for the Proxy Coupling Structure Tests (PCST) used to provide constraint-level empirical grounding for the geometry construction in: Distinguishability Geometry on Admissible Recursion Manifolds (Baggs, 2026) The dataset records proxy response under controlled coupling variation on IBM quantum hardware. The purpose is to test ordering, continuity, and structural response of a retained-fraction proxy under discrete and continuous coupling configurations. Contents The package includes: Raw and processed datasets for: PCST (separation test) PCST-BL (discrete coupling ladder) PCST-CAS (continuous coupling-angle sweep) Replication datasets across multiple backends: ibm_fez ibm_kingston Hardware calibration state for each run: T1, T2 gate error readout error Analysis outputs including: ordering metrics (Spearman correlation) curve fitting results derived proxy summaries Key Observations Across all experiments: Discrete coupling ladders exhibit strict monotone ordering Continuous coupling sweeps exhibit monotone and nonlinear response Results are stable under repetition Results are preserved across backend variation These observations are consistent with structured, non-flat proxy response within the tested quantum measurement process class. Interpretation Limits This dataset: does not measure curvature does not determine the coupling function α(x) does not determine curvature-to-stiffness mapping does not determine coefficient c does not provide a dynamical model The dataset supports constraint-level empirical grounding only. Methodology All experiments use a retained-fraction proxy defined as: retained_fraction = 1 − (H_measured / H_max) Coupling variation is introduced through controlled circuit parameterization, including discrete ladder configurations and continuous angle sweeps. Full protocol details are provided in the included documentation. Relationship to URT Framework This dataset supports the geometry layer (Priority 4) of Unified Recursion Theory by providing empirical tests of proxy structure under admissibility-constrained configurations. It does not modify canonical operators or admissibility conditions. Reproducibility The dataset includes: full raw outputs backend calibration states analysis summaries to enable independent verification and replication.