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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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安装命令

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

复制此命令并粘贴到 Claude Code 中以安装该技能

来源

zhiping0913/physics_skills

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更新时间2026年5月28日 23:45

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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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同仓库

electrodynamics

zhiping0913/physics_skills

Electrodynamics reasoning and knowledge graph — extends landau-graph with boundary-value methods, waveguides, antennas, scattering, crystal optics, coherence theory, and nonlinear/strong-field electrodynamics from 6 standard textbooks.

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optics

zhiping0913/physics_skills

Optics engineering skill — extends landau-graph, electrodynamics, and plasma with Fourier optics, laser engineering, ultrashort pulse generation/measurement, acousto/electro-optics, stimulated scattering, and wave propagation in real media from 11 specialized textbooks.

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plasma

zhiping0913/physics_skills

Plasma physics reasoning and knowledge graph — extends landau-graph and electrodynamics with magnetized plasma waves, MHD stability, transport, laser-plasma interaction, and surface plasmonics from 10 standard textbooks.

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landau-graph

zhiping0913/physics_skills

LandauGraph — reasoning-constrained skill graph distilled from Landau-Lifshitz 10-volume Course of Theoretical Physics. 97 nodes, 196 edges. 4 edge types: prerequisite, reasoning-instance, abstraction, analogy. Production graph for agent physics reasoning.

2026-06-030

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).

2026-06-030

discipline-distillation

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).

2026-05-290

来源

zhiping0913

zhiping0913/physics_skills

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适用职业SOC

物理学家生命、物理与社会科学类职业19-2012L4

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.