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mathematics-theorems

Repository of mathematical theorems referenced by LandauGraph reasoning nodes. Stores complete proofs for results that are asserted but not derived in templates: Bertrand's theorem, Liouville-Arnold theorem, distribution identities, Airy asymptotics, and other mathematical infrastructure required for full derivations.

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Commande d'installation

npx skills add https://github.com/zhiping0913/physics_skills --skill mathematics-theorems

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zhiping0913/physics_skills

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Mis à jour28 mai 2026 à 23:45

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3 fichiers

SKILL.md

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name	mathematics-theorems
description	Repository of mathematical theorems referenced by LandauGraph reasoning nodes. Stores complete proofs for results that are asserted but not derived in templates: Bertrand's theorem, Liouville-Arnold theorem, distribution identities, Airy asymptotics, and other mathematical infrastructure required for full derivations.

Mathematics Theorems Repository

Complete proofs for mathematical theorems that LandauGraph reasoning nodes assert but do not derive. Agents load these when encountering "this is a theorem" statements in reasoning templates.

How to Use

When a reasoning node says "this is a theorem — the proof requires...", load the corresponding reference file. Proofs are mathematical, not physical.

Index

Theorem	Used in	File
Bertrand's theorem	`conservation_to_effective_reduction` (V1)	`bertrand-theorem.md`
Liouville-Arnold theorem	`separation_of_variables` (V1)	`liouville-arnold.md`
Distribution limit sin²(αt)/α²→δ(α)	`quantum_perturbation_theory` (V3)	`distribution-limits.md`
Airy function asymptotics	`wkb_quasiclassical` (V3)	`airy-asymptotics.md`
4D δ-function with Jacobian	`retarded_green_function` (V2)	`delta-function-4d.md`

Maintenance

Add new entries when a reasoning node asserts a non-trivial mathematical result or when agents consistently get stuck on a mathematical step.

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zhiping0913/physics_skills

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si-gaussian-conversion

zhiping0913/physics_skills

Complete SI ↔ Gaussian unit conversion for electrodynamics. Replace ε₀, μ₀, c factors when translating between Jackson (SI), Landau (Gaussian), and other sources. Essential when using landau-graph (Gaussian) alongside electrodynamics skill (SI).

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zhiping0913/physics_skills

Universal methodology for distilling any mathematically rigorous discipline into a reasoning-constrained skill graph consumable by AI agents. Three-track extraction (reasoning mining, knowledge grounding, dependency mining), systematic rumination with blind-derivation validation, and cross-volume bridge construction. Complete worked example: Landau-Lifshitz 10-volume Course of Theoretical Physics (96 nodes, 188 edges).

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Source

zhiping0913

zhiping0913/physics_skills

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PhysiciensSciences de la vie, physiques et sociales19-2012L4

name	mathematics-theorems
description	Repository of mathematical theorems referenced by LandauGraph reasoning nodes. Stores complete proofs for results that are asserted but not derived in templates: Bertrand's theorem, Liouville-Arnold theorem, distribution identities, Airy asymptotics, and other mathematical infrastructure required for full derivations.

Mathematics Theorems Repository

Complete proofs for mathematical theorems that LandauGraph reasoning nodes assert but do not derive. Agents load these when encountering "this is a theorem" statements in reasoning templates.

How to Use

When a reasoning node says "this is a theorem — the proof requires...", load the corresponding reference file. Proofs are mathematical, not physical.

Index

Theorem	Used in	File
Bertrand's theorem	`conservation_to_effective_reduction` (V1)	`bertrand-theorem.md`
Liouville-Arnold theorem	`separation_of_variables` (V1)	`liouville-arnold.md`
Distribution limit sin²(αt)/α²→δ(α)	`quantum_perturbation_theory` (V3)	`distribution-limits.md`
Airy function asymptotics	`wkb_quasiclassical` (V3)	`airy-asymptotics.md`
4D δ-function with Jacobian	`retarded_green_function` (V2)	`delta-function-4d.md`

Maintenance

Add new entries when a reasoning node asserts a non-trivial mathematical result or when agents consistently get stuck on a mathematical step.