GitHub topics: constructive-mathematics

Repositories

Mk9207/-6n-1-Enhanced-Prime-Generation-Rule-6n-1-Theory

この理論は、6n±1 によって表現可能な数のうち、合成数を除去して残る純粋な素数列（A型素数）を構成的に導出する補強モデルです。暗号や数論の応用に適したA型素数を効率的に生成する新たな数論的アプローチを提供します。 This theory proposes a constructive refinement of the 6n±1 prime form by systematically eliminating composites to extract pure A-type primes, enabling efficient generation for cryptographic and theoretical applications.

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Mk9207/-Constructive-Collatz-Conjecture

このリポジトリは、コラッツ予想に対する構成的完全証明を示します。あらゆる自然数が、特定の再帰的変換を経て最終的に1へと収束することを、合同類の構造論理とループ排除の形式によって証明します。 This repository presents a constructive complete proof of the Collatz Conjecture. It shows that any natural number ultimately converges to 1 via recursive transformation, using congruence class structure and loop elimination.

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Mk9207/Constructive-Goldbach-Conjecture-

A formal constructive proof of the Goldbach Conjecture using A-type primes. The theory guarantees every even number ≥4 can be expressed as a sum of two primes, offering a reproducible and extendable number-theoretical foundation. A型素数を用いた構成的手法により、すべての偶数（4以上）が2つの素数の和で表現可能であることを証明。再現性と拡張性を兼ね備えた数論的基盤を提供します。

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Mk9207/Constructive-Unified-Proof-Principle-

A compositional theory that unifies the proof of unsolved problems, AI structure, medical control, and physical modeling using a single constructive function C(x). 単一の構成関数C(x)により、未解決問題、AI構造、医療制御、物理モデルを統一的に証明・構成する理論です。

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martinescardo/TypeTopology

Logical manifestations of topological concepts, and other things, via the univalent point of view.

Language: Agda - Size: 17.7 MB - Last synced at: 3 days ago - Pushed at: 3 days ago - Stars: 257 - Forks: 47

iblech/constructive-maximal-ideals

Reifying dynamical algebra: maximal ideals in countable rings, constructively

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Mk9207/Constructive-Existential-Quantization-Hypothesis-

A foundational theory redefining "existence" as quantizable via constructive logic. Applicable to AI cognition, encryption, quantum memory, and beyond. 構成的論理により「存在」を量子化可能な単位として再定義。AI認知・暗号・量子記憶など幅広い応用を想定した基礎理論です。

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Mk9207/catalan-conjecture-constructive-proof

onstructive proof of the Catalan Conjecture (Mihăilescu's Theorem)

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Mk9207/beal-conjecture-constructive-proof

Constructive proof of the Beal Conjecture using ABC-model extension and coprime domain elimination

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Mk9207/littlewood-conjecture-constructive-proof

A constructive and complete proof of the Littlewood Conjecture using structured prime density, convergence restrictions, and constructive fluctuation bounds.

Language: TeX - Size: 6.84 KB - Last synced at: 9 days ago - Pushed at: 9 days ago - Stars: 0 - Forks: 0

newca12/awesome-rust-formalized-reasoning

An exhaustive list of all Rust resources regarding automated or semi-automated formalization efforts in any area, constructive mathematics, formal algorithms, and program verification.

Size: 316 KB - Last synced at: 5 days ago - Pushed at: 24 days ago - Stars: 342 - Forks: 11

Petko0321/GeoConstructAndVerify

A tool for verifying constructive geometry problems. This repository focuses on the systematic verification of step-by-step solutions to ensure correctness and adherence to geometric principles.

Language: Python - Size: 312 KB - Last synced at: 2 months ago - Pushed at: 2 months ago - Stars: 0 - Forks: 0