A Thales-Sphere Three-Zone Screening Operator with Directionality and Rapidity Layers Construction, Exact Identities, and a Four-Domain Calibration Audit

This release contains Version 0.1 of a Thales-sphere screening diagnostic and its initial Python reference implementation. The operator lifts conserved binary partitions (a+b=1) into a Thales-sphere coordinate system with three screening zones: exponential/logarithmic response ((Z_E)), projected-geometric landmark screening ((Z_G)), and spherical triloop-closure testing ((Z_T)). It also includes two auxiliary diagnostic layers: a directionality/tilt channel and a rapidity channel (\xi=\operatorname{arctanh}\chi). The purpose of the operator is not to propose a new physical law or universal constant. It is a reproducible screening framework designed to distinguish exact algebraic identities, useful coordinate witnesses, controlled empirical signals, and failed or circular matches. The release emphasizes “zone first, number second”: the observable type, coordinate face, normalization, controls, and null tests must be fixed before interpreting numerical proximity to any landmark. The accompanying working paper documents the Tier-1 identities of the construction and a four-domain calibration audit. Two calibrations pass: a flat-(\Lambda)CDM rapidity calibration, where the bounded matter–dark-energy asymmetry evolves nonlinearly but rapidity is exactly linear with (d\xi/d\ln a=3/2); and a Kozai–Lidov test-particle quadrupole altitude calibration, where (K=\sqrt{1-e^2}\cos i=2h(e)\cos i) is conserved to numerical precision. One calibration returns a controlled null: a scalar binary-black-hole mass–energy–spin coupling-circle test on SXS catalog metadata verifies the exact partition algebra but adds no predictive value beyond standard numerical-relativity variables and fails permutation-null closure. A fourth precessing-spin vector-closure test is reported as feasible but pending real horizon time-series analysis. This release should be understood as an exploratory, versioned research instrument. The Python implementation is an initial reference implementation intended for reproducible screening and future extension. Future versions will improve the operator API, automate gate checks and report generation, add data loaders, archive generated calibration outputs, and run the pending precessing-spin vector-closure test on real SXS Horizons data. Negative and null results are intentionally retained as part of the audit trail.