The Moduli Degeneracy: The Real Post-Quantum Cryptography Standard
Skip to main
You are using an outdated browser. Please upgrade your browser to improve your experience.
Published June 10, 2026
| Version v1
Standard
Open
The Moduli Degeneracy: The Real Post-Quantum Cryptography Standard
Authors/Creators
Tibedo, Charles
Description
Abstract
This manuscript develops a unified algebraic, computational, and physical framework for rep-<br>resenting, certifying, and exploiting structured partitions of high- dimensional spaces.
Serving as the operational initialization for the categorical classification of non-associative gauge vacua, this work translates determinantal sheaf theory and functorial doubling into exact, machine-verifiable algorithms.
The text begins with fully certified octonion (k = 3) and sedenion (k = 4) case studies,<br>followed by applied treatments of determinantal geometry, canonicalization via Luna slices, spectral<br>mass gap diagnostics, and exact topological transport.
It concludes with the formal specification of a minimal reproducible artifact bundle, establishing the exact computational standards required for independent verification.
"The Moduli Degeneracy: The Real Post-Quantum Cryptography .arr Standard":
Table of Contents<br>Introduction<br>Part I: The Initialization Stages<br>Chapter 1: Octonions as Initialization Stage: Functorial Origin, Determinantal Sheaf, and Certified Structure<br>* 1.1 Introduction and overview<br>* 1.2 Functorial origin of O<br>* 1.3 Left multiplication family and determinantal loci<br>* 1.4 Determinantal sheaf W<br>* 1.5 Orbit reduction and canonicalization via Luna slices<br>* 1.6 Certification mandate: Positivstellensatz and Thom encodings<br>* 1.7 Main structural theorem (octonion determinantal classification)<br>* 1.8 Worked canonical example (sheaf language and full certificates)<br>* 1.9 Stabilizer computation and gauge projection<br>* 1.10 Spectral gap, mass gap certification, and Davenport-Mahler<br>* 1.11 Concluding remarks
Chapter 2: Sedenions: Doubling, Zero Divisors, Determinantal Pathologies, and Certified Examples<br>* 2.1 Introduction and overview<br>* 2.2 Functorial doubling: S = D_beta(O)<br>* 2.3 Algebraic pathologies: zero divisors, alternator, and cohomology<br>* 2.4 Left multiplication, determinantal loci, and the sheaf W<br>* 2.5 Primary decomposition and embedded components<br>* 2.6 Main structural statements for S<br>* 2.7 Automorphisms, derivations, and the induced G_2 action<br>* 2.8 Stabilizer computation under the induced action<br>* 2.9 Certification mandate for sedenion examples<br>* 2.10 Canonical seeds and worked sedenion examples<br>* 2.11 Topological and spectral pathologies<br>* 2.12 Algorithmic complexity and practical heuristics<br>* 2.13 Figures, incidence tables, and data artifacts<br>* 2.14 Concluding remarks
Part II: Operational Geometry and Canonicalization<br>Chapter 3: Degeneracy Planes and Determinantal Geometry (Applied)<br>* 3.1 Overview and objectives<br>* 3.2 Determinantal ideals and schemes<br>* 3.3 The determinantal sheaf W<br>* 3.4 Local normal forms near transversal points<br>* 3.5 Degeneracy planes and hyperplane arrangements<br>* 3.6 Algorithmic detection and certification<br>* 3.7 Local normal forms: computational extraction of slice equations<br>* 3.8 Examples revisited: octonion and sedenion loci<br>* 3.9 Incidence data, Hasse diagrams, and repository manifest<br>* 3.10 Concluding remarks
Chapter 4: Canonicalization and Stabilizers (Operational)<br>* 4.1 Overview and objectives<br>* 4.2 Preliminaries and notation<br>* 4.3 Stabilizer extraction and representation computation<br>* 4.4 Deterministic canonicalization with field extension handling<br>* 4.5 Certificate invariants and mandatory verification checklist<br>* 4.6 Numeric witness to exact reconstruction refined<br>* 4.7 Complexity, heuristics, and mitigations<br>* 4.8 Worked operational sketch with representation data<br>* 4.9 Concluding remarks
Part III: Physical Translation and Stability<br>**Chapter 5: Algebraic Charge and Spectral Readings (Applied Technical)<br>* 5.1 Overview and objectives<br>* 5.2 Algebraic charge and the physical vacuum dictionary<br>* 5.3 Transverse spectral extraction: isolating the physical mass gap<br>* 5.4 Signature diagnostics, Sturm counts, and multiplicity handling<br>* 5.5 Topological responses: holonomy, Chern evaluations, and loop safety<br>* 5.6 Compatibility checks: representation vs spectral projectors<br>* 5.7 Exact certificate format and verification checklist (revised)<br>* 5.8 Complexity, heuristics, and practical safeguards<br>* 5.9 Concluding remarks
Chapter 6: Perturbations, Topology, and Minimal Artifact Bundle<br>* 6.1 Overview and objectives<br>* 6.2 Notation and standing hypotheses<br>* 6.3 Algebraic stability of determinantal fibers<br>* 6.4 Transverse spectral continuity and certified mass gaps<br>* 6.5 Certified projector transport and holonomy<br>* 6.6 Lyapunov-Schmidt reduction adapted to the determinantal sheaf<br>* 6.7 Minimal artifact bundle (final specification)<br>* 6.8 Verification recipes and automation notes<br>* 6.9 Concluding remarks
Part IV: Appendices: The...