math.CT · math-ph · seven-part modular series

A Math→Physics Representation Library

Six mathematical faculties (motives, algebraic geometry, algebraic topology, category theory & homotopy type theory, and sheaves/stacks/gauge), each formalized as a physical-representation module. The modules compose hierarchically, Part I through Part VI, into a single modular synthesis.

Papers

Faculties

Synthesis

The Papers

Part I

Foundations: The Representation Stack and the Realization Pipeline

We open a seven-part modular program that formalizes each mathematical domain as a physical-representation module. This first part supplies the common…

math.CT · 25 pages · code

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Part II

Motives, Periods, and Amplitudes: The Coalgebraic Anatomy of Physical Representation

Part II of the modular series A Math→Physics Representation Library. An explicit pipeline realizes physical quantities from structured mathematical in…

math-ph · 26 pages · code

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Part III

Algebraic Geometry: Spaces of Physical Possibility

Part III of the modular series. We supply the geometric stage on which motives and periods live and vary: schemes, moduli spaces and stacks, variation…

math.AG · 27 pages · code

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Part IV

Algebraic Topology: Conserved Global Information

Part IV of the modular series. Algebraic topology encodes conserved global information: (co)homology as deformation-stable observables, characteristic…

math.AT · 24 pages · code

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Part V

Category Theory and Homotopy Type Theory: Composition and Identity

Part V of the modular series. Category theory formalizes composition and identity; homotopy type theory supplies identity proper. Univalence turns the…

math.CT · 24 pages · code

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Part VI

Sheaves, Stacks, Gauge Redundancy, and Quantum High-Availability

Part VI, the capstone module. Sheaves, stacks, gauge redundancy, and quantum high-availability are one construction viewed through four lenses: many l…

math.CT · 23 pages · code

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Synthesis

A Modular Representation Synthesis: Composing Six Mathematical Faculties into Physical Representation

The capstone synthesis recomposes the six modular papers into one coherent account of physical representation and proves the Closure Theorem: the repr…

math.CT/hep-th · 24 pages

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