What question did this study set out to answer?

The aim is to integrate various mathematical concepts, including explicit arithmetic registers and geometric models.

July 20, 2026Open Access

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

Key Points

The aim is to integrate various mathematical concepts, including explicit arithmetic registers and geometric models.
Utilized explicit Erdős–Strauss arithmetic and split-zero models.
Conducted geometric experiments and encoded checks using scripts.
Maintained a comprehensive digital record via machine-readable ledgers.
Fixed terminology and dependency direction in the N17 script without introducing new theorems.
Preserved substantial computational outputs including a fresh UTF-8 rerun and various comprehensive checks.
Identified unresolved external computations related to topology and Gauss-linking.

Abstract

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 Project Atlas separates exact theorems, checked calculations, generated constructions, obstructions, diagnostics, and genuinely open interfaces. The retained payload includes the Project Atlas, bookmarked result-packet compendium, Lean and Python sources, proof-status and axiom audits, machine-readable ledgers, editable working texts, visual sources, scene data, replay material, and the Part 8-C2B residual-Niemeier audit. New bounded supplement: 07PredatumK4HopfWorkingNotesₐndChecks₂0260718. zip preserves the N16--N18 sequence on the K4 sphere, the terminology/typing charter, and the Hopf-fibration section-sheaf candidate, together with the cumulative lane ledger, executable scripts, recorded outputs, a fresh UTF-8 rerun, manifest, and hashes. The four script groups reran at 12/12, 17/17, 10/10, and 12/12 encoded checks. N17 explicitly contributes no new theorem; it fixes terminology and dependency direction. Status. This is a working research record, not peer review, not a completed universal framework, and not a proof of a famous open problem. The script reruns certify only their encoded finite symbolic checks. Topos-level statements, bundle classification, cited topology, and the referee-recorded Gauss-linking computation remain identified external or non-machine-checked steps. The Project Atlas PDF remains the recommended entry point.

Ask AI

Helpful

Bookmark

View Full Paper