Proof assistant
View article: Certified G₂ Manifold Construction: From Physics-Informed Neural Networks to Lean 4 Formal Proof
Certified G₂ Manifold Construction: From Physics-Informed Neural Networks to Lean 4 Formal Proof Open
Differential geometry theorems are notoriously difficult to formalize due to infinite-dimensional function spaces, nonlinear partial differential equations, and technical analytic estimates. We present a hybrid methodology combining physic…
View article: garciaalan186/geometric-mnemic-manifolds: Geometric Mnemic Manifolds v3.0 - Release Notes
garciaalan186/geometric-mnemic-manifolds: Geometric Mnemic Manifolds v3.0 - Release Notes Open
Geometric Mnemic Manifolds v3.0 - Release Notes Release Date: December 2025 DOI: 10.5281/zenodo.17862375 Type: Position Paper Status: Theoretical Specification Overview Version 3.0 of the Geometric Mnemic Manifolds position paper represent…
View article: garciaalan186/geometric-mnemic-manifolds: Geometric Mnemic Manifolds v3.0 - Release Notes
garciaalan186/geometric-mnemic-manifolds: Geometric Mnemic Manifolds v3.0 - Release Notes Open
Geometric Mnemic Manifolds v3.0 - Release Notes Release Date: December 2025 DOI: 10.5281/zenodo.17862375 Type: Position Paper Status: Theoretical Specification Overview Version 3.0 of the Geometric Mnemic Manifolds position paper represent…
View article: Certified G₂ Manifold Construction: From Physics-Informed Neural Networks to Lean 4 Formal Proof
Certified G₂ Manifold Construction: From Physics-Informed Neural Networks to Lean 4 Formal Proof Open
Differential geometry theorems are notoriously difficult to formalize due to infinite-dimensional function spaces, nonlinear partial differential equations, and technical analytic estimates. We present a hybrid methodology combining physic…
View article: The Autopoietic Quine: Self-Regenerating Systems and the Algebra of Closure
The Autopoietic Quine: Self-Regenerating Systems and the Algebra of Closure Open
We develop a formal theory of autopoietic computation—systems whose outputs are isomor- phic to their own source code. The central construct is the Quine Closure Condition, which characterizes when a cognitive system achieves self-regenera…
View article: The Autopoietic Quine: Self-Regenerating Systems and the Algebra of Closure
The Autopoietic Quine: Self-Regenerating Systems and the Algebra of Closure Open
We develop a formal theory of autopoietic computation—systems whose outputs are isomor- phic to their own source code. The central construct is the Quine Closure Condition, which characterizes when a cognitive system achieves self-regenera…
View article: The Axiomatic Heart of Higher-Order Logic: Elementary Toposes as Foundational Systems
The Axiomatic Heart of Higher-Order Logic: Elementary Toposes as Foundational Systems Open
Higher-order logic (HOL) offers unparalleled expressive power by allowing quantification over predicates, functions, and even types, thereby transcending the limitations of first-order logic. Despite its utility in areas like foundational …
View article: The Axiomatic Heart of Higher-Order Logic: Elementary Toposes as Foundational Systems
The Axiomatic Heart of Higher-Order Logic: Elementary Toposes as Foundational Systems Open
Higher-order logic (HOL) offers unparalleled expressive power by allowing quantification over predicates, functions, and even types, thereby transcending the limitations of first-order logic. Despite its utility in areas like foundational …
View article: Verifikation von derandomisierten probabilistischen Algorithmen
Verifikation von derandomisierten probabilistischen Algorithmen Open
The subject of the thesis is the formal verification of advanced randomized algorithms that rely on derandomization techniques, particularly pseudorandomness. It introduces a new combinator library of pseudorandom objects and establishes t…
View article: Univalent Foundations: The Intrinsic Geometry of Mathematical Knowledge
Univalent Foundations: The Intrinsic Geometry of Mathematical Knowledge Open
This paper explores Univalent Foundations (UF) as a revolutionary paradigm for understanding the intrinsic geometry of mathematical knowledge. Rooted in Homotopy Type Theory (HoTT), UF provides a framework where mathematical objects are in…
View article: Univalent Foundations: The Intrinsic Geometry of Mathematical Knowledge
Univalent Foundations: The Intrinsic Geometry of Mathematical Knowledge Open
This paper explores Univalent Foundations (UF) as a revolutionary paradigm for understanding the intrinsic geometry of mathematical knowledge. Rooted in Homotopy Type Theory (HoTT), UF provides a framework where mathematical objects are in…
View article: Structure Determines Mappings D: A Machine-Verifiable Metatheorem in Category Theory
Structure Determines Mappings D: A Machine-Verifiable Metatheorem in Category Theory Open
This paper formalizes and provides machine verification for the fundamental principle in mathematics that ”structure determines mappings” within the framework of dependent type theory. We first establish an axiomatic definition of concrete…
View article: Certified G₂ Manifold Construction: From Physics-Informed Neural Networks to Lean 4 Formal Proof
Certified G₂ Manifold Construction: From Physics-Informed Neural Networks to Lean 4 Formal Proof Open
Differential geometry theorems are notoriously difficult to formalize due to infinite-dimensional function spaces, nonlinear partial differential equations, and technical analytic estimates. We present a hybrid methodology combining physic…
View article: Coq Verification Supplement for "A Finite-Cell Structural Reduction of Integer Factorization via the Prime Structural Map and the Matsuura Hierarchy (MSHD–HSTG)"
Coq Verification Supplement for "A Finite-Cell Structural Reduction of Integer Factorization via the Prime Structural Map and the Matsuura Hierarchy (MSHD–HSTG)" Open
This deposit provides the Coq verification supplement for the manuscript: “A Finite-Cell Structural Reduction of Integer Factorization viathe Prime Structural Map and the Matsuura Hierarchy (MSHD–HSTG)”by Yoshihito Matsuura (2025). The sup…
View article: Structure Determines Mappings D: A Machine-Verifiable Metatheorem in Category Theory
Structure Determines Mappings D: A Machine-Verifiable Metatheorem in Category Theory Open
This paper formalizes and provides machine verification for the fundamental principle in mathematics that ”structure determines mappings” within the framework of dependent type theory. We first establish an axiomatic definition of concrete…
View article: Coq Verification Supplement for "A Finite-Cell Structural Reduction of Integer Factorization via the Prime Structural Map and the Matsuura Hierarchy (MSHD–HSTG)"
Coq Verification Supplement for "A Finite-Cell Structural Reduction of Integer Factorization via the Prime Structural Map and the Matsuura Hierarchy (MSHD–HSTG)" Open
This deposit provides the Coq verification supplement for the manuscript: “A Finite-Cell Structural Reduction of Integer Factorization viathe Prime Structural Map and the Matsuura Hierarchy (MSHD–HSTG)”by Yoshihito Matsuura (2025). The sup…
View article: Milestone & High-Impact Papers in Zero-Knowledge Proof History
Milestone & High-Impact Papers in Zero-Knowledge Proof History Open
Zero-knowledge proofs (ZKPs) have evolved from foundational interactive proof systems to highly efficient, scalable, and trusted-setup-free constructions powering today’s privacy-preserving and blockchain applications. The field began with…
View article: Unlocking Riemann Companion
Unlocking Riemann Companion Open
1️⃣ Description – PDF preprint File: Unlocking_Riemann_Companion.pdfSuggested title: Unlocking Riemann Companion: Governance and Reproducibility Framework for RH Evidence and Formalization Handoffs This methods note introduces the “Unlocki…
View article: Milestone & High-Impact Papers in Zero-Knowledge Proof History
Milestone & High-Impact Papers in Zero-Knowledge Proof History Open
Zero-knowledge proofs (ZKPs) have evolved from foundational interactive proof systems to highly efficient, scalable, and trusted-setup-free constructions powering today’s privacy-preserving and blockchain applications. The field began with…
View article: A Machine Learning-Enabled Digital Twin for an Orthopaedic Clinic: a Proof of Concept
A Machine Learning-Enabled Digital Twin for an Orthopaedic Clinic: a Proof of Concept Open
View article: LLM-as-Specification-Judge: Multi-Model Consensus for Trustworthy Cryptographic Verification
LLM-as-Specification-Judge: Multi-Model Consensus for Trustworthy Cryptographic Verification Open
Formal verification of cryptographic implementations using proof assistants like F* and Rocq provides strong mathematical guarantees about code correctness. However, the verification process fundamentally depends on human-written specifica…
View article: LLM-as-Specification-Judge: Multi-Model Consensus for Trustworthy Cryptographic Verification
LLM-as-Specification-Judge: Multi-Model Consensus for Trustworthy Cryptographic Verification Open
Formal verification of cryptographic implementations using proof assistants like F* and Rocq provides strong mathematical guarantees about code correctness. However, the verification process fundamentally depends on human-written specifica…
View article: TypeDis: A Type System for Disentanglement
TypeDis: A Type System for Disentanglement Open
Disentanglement is a runtime property of parallel programs guaranteeing that parallel tasks remain oblivious to each other's allocations. As demonstrated in the MaPLe compiler and run-time system, disentanglement can be exploited for fast …
View article: Formal Verification of Paredes Orchestration Theory (Cubical Agda)
Formal Verification of Paredes Orchestration Theory (Cubical Agda) Open
Machine-checked proofs in Cubical Agda that formally verify the three provisional patent applications filed with the USPTO on November 26, 2025.Public repository: https://github.com/GoodRoyal/orchestration-theoryThis archive serves as time…
View article: Formal Verification of Paredes Orchestration Theory (Cubical Agda)
Formal Verification of Paredes Orchestration Theory (Cubical Agda) Open
Machine-checked proofs in Cubical Agda that formally verify the three provisional patent applications filed with the USPTO on November 26, 2025.Public repository: https://github.com/GoodRoyal/orchestration-theoryThis archive serves as time…
View article: HSF Structural Operator Algebra & Closure A Formal Framework for Admissible Operator Composition in Open Systems
HSF Structural Operator Algebra & Closure A Formal Framework for Admissible Operator Composition in Open Systems Open
This paper presents the complete structural operator algebra of the Hermes Structural Framework (HSF), a formal model for open multi-axis dynamical systems. We define the full admissible operator family \mathcal{T} = \{T_i, T_{ij}, \Phi, \…
View article: Formal Verification of the Paredes Orchestration Theory: Perpendicular Divergence, Grassmannian Holonomy, and Thermodynamic Consistency in Cubical Agda
Formal Verification of the Paredes Orchestration Theory: Perpendicular Divergence, Grassmannian Holonomy, and Thermodynamic Consistency in Cubical Agda Open
This repository contains the permanent archival record of the formal mathematical verification for the Paredes Orchestration Theory. It provides machine-checked proofs in Cubical Agda (v2.6.4+) that validate the core claims, logical consis…
View article: Formal Verification of the Paredes Orchestration Theory: Perpendicular Divergence, Grassmannian Holonomy, and Thermodynamic Consistency in Cubical Agda
Formal Verification of the Paredes Orchestration Theory: Perpendicular Divergence, Grassmannian Holonomy, and Thermodynamic Consistency in Cubical Agda Open
This repository contains the permanent archival record of the formal mathematical verification for the Paredes Orchestration Theory. It provides machine-checked proofs in Cubical Agda (v2.6.4+) that validate the core claims, logical consis…
View article: The Machine Translation of Landau's Analysis of Foundations in Rocq
The Machine Translation of Landau's Analysis of Foundations in Rocq Open
Formal verification has achieved remarkable outcomes in both theory advancement and engineering practice, with the formalization of mathematical theories serving as its foundational cornerstone—making this process particularly critical. Ax…
View article: HSF Structural Operator Algebra & Closure A Formal Framework for Admissible Operator Composition in Open Systems
HSF Structural Operator Algebra & Closure A Formal Framework for Admissible Operator Composition in Open Systems Open
This paper presents the complete structural operator algebra of the Hermes Structural Framework (HSF), a formal model for open multi-axis dynamical systems. We define the full admissible operator family \mathcal{T} = \{T_i, T_{ij}, \Phi, \…