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Small Lab, Infinite Structure. / Exploring the Hidden Structures of a Torus-Shaped Universe.

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Month: August 2026

[Paper 116] What Does the Exponent of $c$ Count? — The Exponent Formula of the Planck Reduction, $\epsilon$ as Mass Dimension, the Non-Uniqueness of $4\pi$, and the $n=d-1$ That Was Sitting in the Denominator —

2026年8月25日2026年8月25日 yuuki

What Does the Exponent of c Count? – The Exponent Formula of the Planck Reduction, epsilon as Mass Dimension, the Non-Uniqueness of 4pi, and the n = d

Papers

[Paper 115] Two Staircases — Separating Value from Generator: The Sphere-Volume Recursion, Its Parity Split, and Where This Series’ Constants Live —

2026年8月25日2026年8月25日 yuuki

Two Staircases: Separating Value from Generator – The Sphere-Volume Recursion, Its Parity Split, and Where This Series’ Constants Live.

Papers

[Paper 114] Which Objects Know They Are in Four Dimensions? — A Census of Dimension-Selective and Dimension-Agnostic Structures: Why the Tesseract Became the Face of 4D —

2026年8月25日2026年8月25日 yuuki

Which Objects Know They Are in Four Dimensions? A Census of Dimension-Selective and Dimension-Agnostic Structures: Why the Tesseract Became the Face o

Papers

[Paper 113] Modules Are Not Walls but Limits — A Distinct-Roots Census of Contraction, Deformation and Decoupling, and the Beautiful Temptation of “Stability” —

2026年8月25日2026年8月25日 yuuki

Modules Are Not Walls but Limits: A Distinct-Roots Census of Contraction, Deformation and Decoupling, and the Beautiful Temptation of “Stability”.

Papers

[Paper 112] The Allotted Region and the Freedom Within — A Census of Six Distinct Roots Sharing One Rhyme: Prohibition, Resolution, Postulate, Theorem, Exclusion, Capacity —

2026年8月25日2026年8月25日 yuuki

The Allotted Region and the Freedom Within: A Census of Six Distinct Roots Sharing One Rhyme – Prohibition, Resolution, Postulate, Theorem, Exclusion,

Papers

[Paper 111] How Far Does Light Determine Geometry? — Two Roads That Stop at Conformal Structure (Differential Geometry and Order Theory), and the Distinct Roots of the Residual “Scale” —

2026年8月25日2026年8月25日 yuuki

How Far Does Light Determine Geometry? Two Roads That Stop at Conformal Structure (Differential Geometry and Order Theory), and the Distinct Roots of

Papers

[Paper 110] Ricci Flow IS a Renormalization Group Flow

2026年8月25日2026年8月25日 yuuki

Ricci Flow IS a Renormalization Group Flow: Where Two Lineages Shake Hands over Taming the Infinite, a Census of a Royal-Road Bridge.

Papers

[Paper 109] The Geometry of Dimensional Lift

2026年8月25日2026年8月25日 yuuki

The Geometry of Dimensional Lift: Why the Power of pi Rises with Dimension, a Census of Royal-Road Topology.

Papers

[Paper 108] The Geometry Where the Invariant Lives

2026年8月25日2026年8月25日 yuuki

The Geometry Where the Invariant Lives: Minkowski’s Spacetime, and Not Conflating the “Geometries of Relativity”.

Papers

[Paper 107] The Two Noethers

2026年8月25日2026年8月25日 yuuki

The Two Noethers: Not Conflating the First Theorem (Conservation) with the Second Theorem (Identities and Constraints).

Papers

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