Sri Yantra Constraint Engine v0.1.0: Verified Base — Two Validated Engines, Four Errata to Rao (1998), and Dependency Lattice

This deposit accompanies a verified reimplementation and structural analysis of the geometric constraint system introduced by C. S. Rao (1998), Śrīyantra — A Study of Spherical and Plane Forms, Indian Journal of History of Science 33(3), 203–227. Original paper: Rao, C. S. (1998). Śrīyantra — A Study of Spherical and Plane Forms. Indian Journal of History of Science, 33(3), 203–227. Available online (INSA) Rao recast the traditional construction of the Śrīyantra as a system of simultaneous nonlinear equations — six basic variables in the spherical form, five in the plane form, with twenty geometric constraint functions F1…F20 — solved numerically for selected constraint subsets. This release provides two independent engines (spherical and plane), each validated against Rao's published solution tables, together with a complete derivation of the constraint dependency structure and an independent coordinate-geometry grounding of every constraint. Contents and principal results Two independent engines: a spherical engine validated against Rao's Table 1 and a plane engine (obtained by the r→0 reduction) validated against Table 3. All twenty constraint functions are independently grounded. Fifteen reproduce the published tables to ~10−7; the remaining five (F7, F11, F12, F17, F18), which appear in no tabulated row, are grounded by an independent reconstruction of the figure in Cartesian coordinates to ~10−16. Four transcription errata in the printed equations (eqs 2.22, 3.3, 3.4, 3.14b), together with one plane-reduction correction (eq 6.12), each established both by reproduction against Rao's own solutions and by independent geometry. These are documented in ERRATA.md and a stand-alone corrigendum note. The constraint dependency lattice: exactly two exact linear identities hold among F1…F20 (so only eighteen of the twenty constraints are mutually independent), forming a rank-4 "radial" matroid. The generically ill-posed constraint subsets are characterised analytically — one of the 816 plane systems and sixteen of the 3060 spherical systems — with no non-radial degeneracies in either form. Scope. This is a verified base. It does not include the feasibility enumeration of the well-posed constraint subsets, any optimisation or alternative-optimum search, or a pre-registration; those are intended to build on this release. All results are reproducible via the included scripts (run_all.sh). A SHA-256 manifest with detached signature and timestamp accompanies the release. Source code: https://github.com/salahealer9/sri-yantra-constraint-engine