Monogenic Exponential Decompositions of Punctured Three-Space: Explicit Constructions, Normal Forms, and Rigidity – Towards a Classification

This record contains version 1 of a research monograph that introduces and develops monogenic exponential decompositions: tilings of punctured space ℝ³∖{c*} by the integer orbit of a single compact convex prototype under one expanding similarity, with exactly one cell at each exponential scale. Main results – Universal structure. Covering and disjoint interiors alone force the prototype to be a convex polytope and the generator to be a genuine rotoreflection. No facet count or face-to-face condition is assumed. In every dimension, an orthogonal factor is admissible exactly when its complex spectrum is simple and excludes +1, and every admissible factor is realised.– Cap branch. Convex cumulative stages are exactly the equivariant half-space Caps, in every dimension. In three dimensions the Cap branch is completely parametrised by (x, θ, η).– Complete null support. Complete actual null support is characterised by a finite cyclic cone-frustum normal form with three, four or five null facets. A spherical corner count with T-junctions determines the order-four case.– Finite descriptions. Canonical finite transfers, finite acceptance criteria and moment rigidity describe and test complete prototypes.– Classification. At the quarter turn, every prototype belongs to exactly one of three explicit families, with no restriction on inner or null facets. Further classifications cover specified rational rotors and facet regimes.– Constructions. An extensive catalogue of explicit constructions, including Cap, non-Cap and parity-half-space families, with exact parameter domains and certificates. The global classification remains open, in particular in the centre-transversal and mixed-support branches. Open problems are stated precisely. Files – Monogenic_Exponential_Decompositions_260923_v1_results.pdf – short edition (8 pages): abstract, introduction and a six-page overview of all results– Monogenic_Exponential_Decompositions_260923_v1.pdf – main paper (156 pages)– Monogenic_Exponential_Decompositions_260923_v1_Appendix.pdf – supplementary proofs and certificates (483 pages)– Monogenic_Exponential_Decompositions_260923_v1_sources.zip – LaTeX sources, figures and verification scripts Keep the PDFs in one folder with their original names; they link to each other. Use of AI. AI tools, including ChatGPT/Codex (OpenAI) and Claude (Anthropic), supported proof development and drafting, verification code and editing. The author is responsible for all mathematical claims. Contact: mail@manuelschubbe.de · ORCID 0009-0005-5353-9944. Feedback and corrections are welcome.