INU: A Structural Framework for Compressed Arithmetic and Discrete Transformation
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2025
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| author | STUDENT, By |
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| contents | <p>This archive presents INU (Intuitive Numerical Unification), a proposed framework for compressing arithmetic operations through structural classification and periodic transformations. INU includes a notation system for INU operations, an n-radix extension, and a dimensional generalization applicable to problems such as the Collatz Conjecture and the Four Color Theorem.</p> <p>The file contains LaTeX source documents, preliminary classification tables, and symbol definitions. INU treats numerical entities as convertible types and provides discrete analogs for topological transformations.</p> <p>This research aims to inspire new approaches to number theory, combinatorics, and structural proofs.</p> <p> </p> <p>This framework does not seek final correctness, but rather the richness of inquiry. It is offered not as a conclusion, but as a beginning—an invitation to transform arithmetic through structure.</p> <p>This work may contain errors. But if its structure holds, others will correct the rest. It is shared not for perfection, but for possibility.</p> <p> </p> <p><strong>Note on Naming</strong><br>The name <em>INU</em> (Intuitive Numerical Unification) carries a personal and symbolic meaning. In Japanese, the word <em>inu</em> (dog) is sometimes used as a prefix to denote something humble or inferior. The framework embraces this nuance, reflecting the idea that even from a modest or overlooked origin, intuitive thinking can lead to meaningful mathematical structures. <em>INU</em> thus represents a system born from simplicity and insight, aiming to unify and compress arithmetic through structural transformation.</p> <p> </p> <p><strong>Note on Fool Algebra</strong><br>In addition to its structural framework, INU embraces a philosophical stance known as <em>fool algebra</em>.<br>Unlike traditional algebraic systems that seek rigor through abstraction, fool algebra begins with intuition, visual structure, and the courage to appear foolish. It reflects the idea that wisdom often wears the mask of simplicity, and that breakthroughs may arise not from complexity, but from clarity.</p> <p>Fool algebra treats numerical entities not merely as values, but as types—visual, compressible, and transformable. It invites the mathematician to step outside formalism, to see patterns where others see noise, and to compress arithmetic into structure.</p> <p>This is not a rejection of rigor, but a reordering of priorities: structure first, proof second.<br>Fool algebra is not a conclusion—it is a stance. A way of thinking. A way of seeing.</p> <p> </p> <p><strong>Words to be engraved on a gravestone (inscription style)</strong></p> <p>Here lies the mind behind INU(x) := ρ(ϕτ(x)(x)),<br>A transformation of arithmetic into structure.</p> <p>If x ∈ {INU}, then perhaps P != NP.<br>Let future mathematicians decide.</p> <p>By STUDENT</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17067051 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
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| spellingShingle | INU: A Structural Framework for Compressed Arithmetic and Discrete Transformation STUDENT, By <p>This archive presents INU (Intuitive Numerical Unification), a proposed framework for compressing arithmetic operations through structural classification and periodic transformations. INU includes a notation system for INU operations, an n-radix extension, and a dimensional generalization applicable to problems such as the Collatz Conjecture and the Four Color Theorem.</p> <p>The file contains LaTeX source documents, preliminary classification tables, and symbol definitions. INU treats numerical entities as convertible types and provides discrete analogs for topological transformations.</p> <p>This research aims to inspire new approaches to number theory, combinatorics, and structural proofs.</p> <p> </p> <p>This framework does not seek final correctness, but rather the richness of inquiry. It is offered not as a conclusion, but as a beginning—an invitation to transform arithmetic through structure.</p> <p>This work may contain errors. But if its structure holds, others will correct the rest. It is shared not for perfection, but for possibility.</p> <p> </p> <p><strong>Note on Naming</strong><br>The name <em>INU</em> (Intuitive Numerical Unification) carries a personal and symbolic meaning. In Japanese, the word <em>inu</em> (dog) is sometimes used as a prefix to denote something humble or inferior. The framework embraces this nuance, reflecting the idea that even from a modest or overlooked origin, intuitive thinking can lead to meaningful mathematical structures. <em>INU</em> thus represents a system born from simplicity and insight, aiming to unify and compress arithmetic through structural transformation.</p> <p> </p> <p><strong>Note on Fool Algebra</strong><br>In addition to its structural framework, INU embraces a philosophical stance known as <em>fool algebra</em>.<br>Unlike traditional algebraic systems that seek rigor through abstraction, fool algebra begins with intuition, visual structure, and the courage to appear foolish. It reflects the idea that wisdom often wears the mask of simplicity, and that breakthroughs may arise not from complexity, but from clarity.</p> <p>Fool algebra treats numerical entities not merely as values, but as types—visual, compressible, and transformable. It invites the mathematician to step outside formalism, to see patterns where others see noise, and to compress arithmetic into structure.</p> <p>This is not a rejection of rigor, but a reordering of priorities: structure first, proof second.<br>Fool algebra is not a conclusion—it is a stance. A way of thinking. A way of seeing.</p> <p> </p> <p><strong>Words to be engraved on a gravestone (inscription style)</strong></p> <p>Here lies the mind behind INU(x) := ρ(ϕτ(x)(x)),<br>A transformation of arithmetic into structure.</p> <p>If x ∈ {INU}, then perhaps P != NP.<br>Let future mathematicians decide.</p> <p>By STUDENT</p> |
| title | INU: A Structural Framework for Compressed Arithmetic and Discrete Transformation |
| url | https://doi.org/10.5281/zenodo.17067051 |