Split-Zero Geometry and Common Deformation Registers: Project Atlas, Exact Results, Formalization, and Visualizations

This is the human-readable public home for a continuing mathematics project connecting explicit Erdos--Strauss arithmetic registers, split-zero and tagged-sedenion models, finite moonshine and Sigma(2,3,5) calculations, exact formal checks, and selected geometric experiments. The main Project Atlas explains the current mathematical state, gives direct reading routes, and separates exact theorems, checked calculations, generated constructions, obstructions, diagnostics, and genuinely open interfaces. The full payload contains the complete current result packets rather than summaries alone: a bookmarked results compendium; Lean and Python sources; proof-status and axiom audits; machine-readable ledgers and text; editable visual sources; exact scene data; and replay/QA material. Central results include the exact 48-state arithmetic register, the Gamma_107 block decomposition, the no-go theorem for an unnormalised sector-289 intertwiner, a diagnostic showing why a kernel-collapse interface is too weak, and an exact generated exponential order-six repair. The Sigma(2,3,5) sequence includes finite module and trace results, explicit obstructions, W1/Habiro source-label correction, prefactor recovery, regularised totals, and an openly marked physical Wilson-identification boundary. The newest result identifies the regularised indefinite-theta cone support as the XOR character of a Klein-four sign register. For -Sigma(2,3,5), the second cone vector c2=(3,10) is checked as a primitive negative boundary datum whose combined contribution to the displayed shadow vanishes. This gives an exact support-active, shadow-invisible mechanism and a precise open problem: construct a natural predatum/associator morphism that canonically selects the ray [c2], rather than recognizing it after it is supplied. The record also corrects a conflation between the holomorphic coordinate-half-turn K4 and the classical zeta-zero reflection K4. Ownership and status. No JT-authored corpus dump is published here. Jacolm Tobley is credited as a researcher/project relationship; direct JT source remains under its own ownership and provenance. The public files contain repository-maintainer work, generated project mathematics, rights-screened derivatives, and exact checks. Conversational hunches are not promoted to conjectures, and known-failing maps are recorded as obstructions rather than conditional theorems. The formal archive reports the exact Lean axiom footprint; no public theorem depends on a native code-generation axiom. This is a working research record, not a claim of a completed universal framework or a refereed proof of any famous open problem.