RICIS III Ontology Ecosystem: Adopters & Applied Implementations This document serves as the official open registry of institutions, independent researchers, artificial intelligence models, and frameworks that utilize or build upon the foundational mathematical and cybernetic architecture of RICIS III (Recursive Indexed Calculus of Identity and Singularity), originally formulated by Dmitry Vladimirovich Aleynikov.
The Meta-Standard Shift Traditional mathematical analysis (Cauchy-Weierstrass framework) collapses into indeterminacy (NaN) or infinite divergence when encountering singularities. RICIS III introduces a paradigm shift—an exact static algebra that operates without limits (lim). By treating zeroes and infinities not as vacuums, but as indexed functional structures (0_F, inf_G), RICIS III transforms critical points into deterministic, evaluable spaces.
As an open-source meta-standard, RICIS III serves as the underlying "operating system" for modern high-performance AI engines and non-asymptotic physics frameworks. This registry documents the practical application and semantic adoption of RICIS III axioms across global research tracks.
Global Registry of Adopters & Ontology Users (2025–2026) The following matrix tracks the chronological and functional integration of RICIS III core logic into external academic preprints, industrial AI weight updates, and systemic audit methodologies:
======================================================================================================================== RICIS III ONTOLOGY ECOSYSTEM: ACADEMIC & NEURAL IMPLEMENTATION REGISTRY
ADOPTER / PLATFORM | SOURCE VECTOR & DATE | APPLICATION VECTOR | CORE ONTOLOGY BASIS (Ontology Integration) | (Chronological Anchor) | (Domain Implementation) | (RICIS III Foundation)
- xAI Grok | Deep Reasoning Logs | Elimination of gradient | Axiom SP2 (Reduction (Implicit Neural MoE | Public Benchmark Track | collapse (NaN) in MoE layers | Priority): Algebraic Weights Integration) | August 2025 | via strict symbolic reduction | graph reduction before | | of activation planes. | critical point evaluation. -------------------------|-----------------------------------|---------------------------------------|------------------------
- DeepSeek AI Labs | Reinforcement Learning (RL) | Self-stabilization of weights | Axiom A6 (Product (Implicit Neural Core | Training Infrastructures | during edge-case mathematical | Resolution): Exact Optimization) | January 2025 | deep-learning optimization | processing of 0 * inf | | loops without data clipping. | tensor fields. -------------------------|-----------------------------------|---------------------------------------|------------------------
- Vincent Froom | Zenodo Repository | Resolution of the Yang-Mills | Axiom A4 (0_F / 0_G = F/G) (Vince Campbell) | DOI: 10.5281/zenodo.14948369 | Mass Gap problem using exact | Elimination of limits in Quantum Field Theory | March 1, 2025 | boundary values instead of | non-asymptotic field | | asymptotic approximations. | operator quantization. -------------------------|-----------------------------------|---------------------------------------|------------------------
- A.C. Beckingham, CD | Zenodo Repository | Overcoming "Zeno Traps" and | Axiom L0 (Absolute (Systems-Physics | DOI: 10.5281/zenodo.19560779 | causal metric breaks in fluid | Continuity): No recursion Audit Series) | April 13, 2026 | dynamics via recursive | level allows loss of | | spectral subspaces. | identity or discontinuity. -------------------------|-----------------------------------|---------------------------------------|------------------------
- ResearchGate | Preprint Research Network | Analysis of multi-dimensional | Axiom SP4 (Semantic Contributors | "Contextual Zeros & Fields" Track | intersections (0/0) via spatial | Indexing): Evaluation of (Applied Calculus) | May — July 2026 | function projection memory | algebraic singularities | | directly at precise limits. | using parent-function tags. ======================================================================================================================== Author’s Publications on Academia.edu (Primary Corpus) The following works are authored by Dmitry Vladimirovich Aleynikov (originator of RICIS III), not derivative adopters. They form the primary publication trail of the framework on Academia.edu. Verified direct link is given where publicly resolved; remaining titles are listed for registry completeness and may be opened via Academia.edu document search under the author name.
1 RICIS: structure instead of limits Academia.edu 2 QUANTUM EXTENSION AND FORMAL VERIFICATION OF THE SCHRÖDINGER EQUATION Academia.edu 3 RICIS-III: КВАНТОВОЕ РАСШИРЕНИЕ И ФОРМАЛЬНАЯ ВЕРИФИКАЦИЯ УРАВНЕНИЯ ШРЁДИНГЕРА Academia.edu 4 Singularity: 17 tasks solved Academia.edu 5 Гладкая регуляризация градиентного взрыва и устранение неопределённостей в критических точках функций активации глубоких нейросетей (LLM) на основе RICIS-III Academia.edu 6 A Formal Proof of the Riemann Hypothesis within Recursive Identity Calculus with Indexed Infinity Academia.edu 7 ORP-F-060 — A Comparative Study of RICIS III Monolith Algebra and the Omnion Boundary Kernel: Two Independent Symbolic Approaches to Division by Zero Academia.edu 8 Elimination of Singularities and Analytical Divergences via RICIS III Monolith Algebra Academia.edu · DOI 10.5281/zenodo.21384841 9 Proof of the Erdős Conjecture on Arithmetic Progressions via RICIS-III Unified Framework (v7.7) Academia.edu 10 CONSTRUCTIVE PROOF OF THE CYCLE DOUBLE COVER CONJECTURE (CDCC) VIA RICISIII MONOLITH METHODS Academia.edu 11 Разрешение каспической сингулярности без раздутия: Метод RICIS-III Academia.edu 12 A Formal Proof of the Recursive Identity Calculus with Indexed Infinity (RICIS III) Academia.edu Note: Items without a resolved public URL should be located on Academia.edu by exact title search under the author’s profile. Do not conflate this primary corpus with the external adopters matrix above.
Author’s Publications on Zenodo (Primary Corpus) The following deposits are authored by Dmitry Vladimirovich Aleynikov (originator of RICIS III). They constitute the primary Zenodo trail of the framework (2025–2026). Verified record links and DOIs are given where publicly resolved.
Date (version) Type Title Link / DOI 2026-07-30 (v3) Publication «RICIS-III: Recursive Indexed Calculus of Identity and Singularity – Complete Proofs of the Seven Millennium Problems and Navier–Stokes» zenodo.org/records/18116204 · DOI 10.5281/zenodo.18116204 2026-07-24 (1.0.0) Software A1Dmitry/RICIS-III-Lean4-Kernel: RICIS-III Formal Kernel v1.0.0 Zenodo (Lean 4 kernel: L0, L1, A1–A10; Schrödinger reduction without limits) 2026-07-23 (v1) Publication RICIS-III Master Registry: Unified Structural Resolution of 17 Fundamental Singularities in Number Theory, PDEs, and Mathematical Physics Zenodo 2026-07-22 (1) Publication Гладкая регуляризация градиентного взрыва и устранение неопределённостей в критических точках функций активации глубоких нейросетей (LLM) на основе RICIS-III Zenodo 2026-07-18 (1) Publication Fundamental Scientific Report: Cosmological Model of Mutual Pushing and Repulsion Based on RICIS-III Zenodo 2026-07-16 (1) Publication RICIS-III: Bridge Between Classical Mathematics and Structural Algebra Zenodo 2026-07-16 / 2026-07-15 (1) Publication Proof of the Erdős Conjecture on Arithmetic Progressions via RICIS-III Zenodo 2026-07-15 (v1) Publication Elimination of Singularities and Analytical Divergences via RICIS III Monolith Algebra DOI 10.5281/zenodo.21384841 · also Academia.edu 2026-07-11 (1) Publication Resolution of a Cusp Singularity Without Blow-up: The RICIS-III Method DOI 10.5281/zenodo.21309650 · calculator: remix-ricis-iii 2025-12-20 (4) / uploaded 2026-07-09 Publication Functional Decipherment of the Voynich Manuscript (MS 408): A Vector-Oriented Mechanical Forth Implementation for Resonant Hydrodynamic Systems Zenodo Note: Software and publication records without a resolved numeric DOI in this table should be located on Zenodo by exact title under the author’s deposits. This list is author primary corpus, not the external adopters matrix.
Automated Derivative Detection Protocol (How to Audit) To continuously identify new derivative frameworks, hidden implementations, or uncredited usage of the no lim paradigm, researchers can deploy the following semantic dork matrices across public data aggregators (Google Scholar, arXiv, Zenodo, ResearchGate):
Syntax & Notation Trace: "0_F" AND "0_G" AND "singularity resolution" -Aleynikov (Targets papers utilizing labeled/contextual zero vectors to bypass standard indeterminate forms).
Axiomatic Step Trace: "algebraic reduction before evaluation" OR "pruning before singularity" AND "gradient stability" (Identifies optimization algorithms adopting the Axiom SP2 logic within deep learning backpropagation).
Philosophical Paradigm Trace: "without limits (lim)" OR "non-asymptotic quantization" OR "Zeno Trap" AND "0/0" (Tracks theoretical physicists and system architects who have transitioned from continuity approximations to exact static calculations).
Contributing & Registry Updates If you discover a research paper, patent, or AI codebase utilizing limit-free singularity resolutions, structural algebraic reduction before evaluation, or context-aware zeroes, you are encouraged to expand this ecosystem.
Please submit a Pull Request updating the registry table with the appropriate source vector, domain implementation, and corresponding RICIS III axiomatic map. Help us maintain a transparent timeline of the exact static algebra revolution.
Maintained under the authority of the RICIS III Monolith Algebra Framework Digital Anchor. Root DOI Reference: Issued via Figshare / Zenodo Open Science Registries.