Geometric Bridge in RICIS-III: A Local Determinant Invariant for Typed 0_F × ∞_G Nodes

This technical-note preprint specifies a local geometric reduction contract within the author-defined Recursive Indexed Calculus of Identity and Singularity (RICIS-III). For a source node designated by the model as 0_F × ∞_G, where finite orthogonal components A and B are supplied under an explicit representation contract, the note encodes the components as u = (A, 0) and v = (0, B) and defines the local bridge value by det(u, v). The exact local algebraic statement is det((A, 0), (0, B)) = A·B.The package contains the LaTeX source, a preprint-ready manuscript, a portable Lean 4 computable prototype, the verbatim author-supplied Lean source, metadata, a reproducibility README, and SHA-256 checksums. The package distinguishes the determinant identity from the RICIS-III representation contract that retains semantic identities and provenance. It does not claim a general replacement for limits, a scalar arithmetic product with physical infinity, a proof of external applications, or a complete formal verification beyond the exact stated scope.Reproducibility boundary: the Lean source is an executable prototype for the supplied local examples. A full formal proof of the bridge acceptance relation and reducer soundness requires a dedicated pinned Lean project, theorem source, CI run, and separately auditable proof artefacts.