Validator-Grade Grothendieck Resolution: Spectral Descent, Homotopy Convergence, and Universal Cohomology
| Title: | Validator-Grade Grothendieck Resolution: Spectral Descent, Homotopy Convergence, and Universal Cohomology |
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| Authors: | Forrest M. Anderson, Forrest |
| Publisher Information: | Zenodo, 2025. |
| Publication Year: | 2025 |
| Subject Terms: | Grothendieck Standard Conjectures Homological vs Numerical Equivalence Weil Cohomology Theory Spectral Motif Encoding Motivic Filtration Homotopy Limit Convergence Derived Category of Sheaves Algebraic Cycles Primitive Decomposition Intersection Pairing Positivity Cycle Class Map Spectral Descent Validator-Grade Proof Architecture Universal Cohomology Construction Motivic Realization Étale Cohomology Triangulated Categories Derived Functors Six-Functor Formalism Spectral Sequence Stabilization Validator-grade mathematical reproducibility Formal verification in algebraic geometry Spectral descent architecture Cohomological containment and convergence Peer-to-peer replication frameworks Motivic sheaf descent Cycle equivalence resolution Derived inverse system stabilization Universal cohomology axioms Symbolic traceability in motivic theory Replicable proof systems in algebraic geometry Homotopy coherence in derived categories Positivity enforcement on primitive cycles Reproducible spectral filtration Validator-grade LaTeX formalization MSC 14C25 — Algebraic cycles MSC 14F20 — Étale and other Grothendieck topologies and cohomologies MSC 14F42 — Motivic sheaves MSC 18G80 — Derived categories, triangulated categories MSC 18E30 — Derived functors and triangulated categories MSC 14D07 — Special sheaves and cohomology theories MSC 14F10 — Differentials and de Rham cohomology MSC 13D07 — Homological methods, resolutions, complexes MSC 55T99 — Spectral sequences (general topology, algebraic topology) MSC 14A15 — Algebraic geometry foundations (Grothendieck-style) |
| Description: | The Validator-Grade Grothendieck Resolution: A Unified Architecture for Algebraic Cycle Equivalence, Derived Descent, and Weil Cohomology Abstract:This trilogy presents a complete validator-grade resolution of Grothendieck’s Standard Conjectures and cohomological axioms through three interlocking packages: spectral motif encoding (Package A), homotopy limit verification (Package B), and Weil cohomology construction (Package C). Together, they form a reproducible, numerically stable, and symbolically traceable framework that settles longstanding obstacles in algebraic geometry and motivic theory. Package A resolves Conjecture D by encoding algebraic cycles into spectral motifs and recursively filtering homologically trivial classes. Package B verifies the convergence of derived inverse systems of motivic sheaves, ensuring that spectral descent yields stable cohomological realizations. Package C constructs a complete Weil cohomology theory satisfying all axioms, including positivity on primitive cycles, and integrates it with motivic and spectral architectures. Each package is presented with formal proofs, precise operator definitions, numerical error analyses, foundational citations, and LaTeX-formatted replication frameworks. The VGGR Framework sets a new standard for validator-grade reproducibility in both mathematical and symbolic domains, and is designed for peer-to-peer transmission, journal publication, and formal verification. |
| Document Type: | Other literature type |
| Language: | English |
| DOI: | 10.5281/zenodo.16991877 |
| DOI: | 10.5281/zenodo.17060805 |
| Rights: | CC BY |
| Accession Number: | edsair.doi.dedup.....075b54d1eed73e327603e5e1354a3bc4 |
| Database: | OpenAIRE |
| DOI: | 10.5281/zenodo.16991877 |
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