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 mixed-support sequence identifies the regularised indefinite-theta cone support as the XOR character of a Klein-four sign register. Its source-enriched theorem retains the ordered datum A=diag(-2p pbar,x), d2=(1,pbar): the unique positive primitive generator of d2-perp is (x/g,2p/g), where g=gcd(x,2p). For the ordered Sigma(2,3,5) data this selects the projective ray c2=(3,10) and an exact coordinate-natural odd projector. Packet 202 independently reconstructs the displayed no-defect L=8, j=2 shadow aggregate and proves exact noncancellation: the unique coefficient at q^(1/120) qbar^(1/24) is 2*exp(2*pi*i/12). Pointwise support and the source-enriched selector remain exact; all-Wilson-sector and full-shadow classification remain open. No algebra-valued predatum/Jordan intertwiner or physical half-index theorem is claimed. Packet 201 adds an exact finite Cayley-Dickson audit: multiplication by e3+e10 is skew with rank 12 and a displayed four-dimensional kernel, while the full 16-vector multiplication-frame identity fails. The packet sharply separates those generated calculations from cited Poincare-Hopf, Bott--Milnor--Kervaire, and Adams topology. The release also includes a rights-safe, hash-pinned K-ladder charter integration that preserves the project definitions without promoting its mixed working source to theorem authority. The D3 Descartes depth-reveal visualization was re-rendered with larger, high-contrast annotation and explicit 960-by-540 readability checks. A release-level reference-closure gate ensures that every generated result named in the atlas has its proof, checker, ledger, or replay artifact in this same public payload; private GitHub is not a proof dependency. 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.