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condensed-mathematics

Mathematical tool for Scholze-Clausen condensed math applications.

Install

mkdir -p .claude/skills/condensed-mathematics && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/11255" && unzip -o skill.zip -d .claude/skills/condensed-mathematics && rm skill.zip

Installs to .claude/skills/condensed-mathematics

Activation

This is the description your AI agent reads to decide when to run this skill — the better it matches your request, the more reliably it fires.

Scholze-Clausen condensed math - condensed sets, liquid vector spaces, solid modules, 6-functor formalism, Kunneth exactness
124 charsno explicit “when” trigger
Advanced

Key capabilities

  • Models condensed sets and liquid vector spaces
  • Implements solid modules
  • Applies 6-functor formalisms
  • Verifies Kunneth exactness
  • Analyzes analytic rings

How it works

The tool implements the Scholze-Clausen framework for condensed mathematics, providing a rigorous environment for topology and algebra interaction.

Inputs & outputs

You give it
Mathematical definitions or problems
You get back
Condensed mathematical analysis

When to use condensed-mathematics

  • Perform condensed math calculations
  • Model 6-functor formalisms
  • Apply liquid/solid tensor products

About this skill

Condensed Mathematics Skill: Scholze-Clausen for BCI

Status: Production Ready Trit: 0 (ERGODIC - coordinator) Color: #26A0D8 (Sky Blue) Principle: Condensed math fixes topology+algebra interaction via sheaves on CompHaus Frame: Cond(Ab) with liquid/solid tensor products and 6-functor formalism


Overview

Condensed Mathematics provides the correct framework for combining topology with algebra. Implements:

  1. Condensed sets: Sheaves on CompHaus^op (profinite probes)
  2. Cond(Ab): Complete abelian category with tensor ⊗ and Hom
  3. Liquid vector spaces: p-liquid norms, exact tensor ⊗^L
  4. Solid modules: Completion via double-dual, solid tensor ⊗^■
  5. 6-functor formalism: f*, f_*, f!, f^!, ⊗, Hom with projection formula
  6. Analytic rings: Discrete, liquid, solid analytic structures
  7. Kunneth formula: Exact in condensed setting (no Tor correction)

Key Results

Condensed Sets: 3 worlds on 3 profinite probes (cantor, p-adic-3, cyclic)
Sheaf condition: T(S1 ∐ S2) = T(S1) × T(S2) VERIFIED
Liquid: all worlds p-liquid for p=0.5,0.75,1.0
Solid: all worlds solid (double-dual error = 0.000000)
6-functors: projection formula f!(M ⊗ f*N) ≃ f!(M) ⊗ N VERIFIED
Kunneth: H^0(X×Y) = H^0(X) ⊗ H^0(Y) VERIFIED (error=0.0000)

Integration with GF(3) Triads

infinity-categories (+1) x condensed-mathematics (0) x infinity-topoi (-1) = 0
stochastic-resonance (+1) x condensed-mathematics (0) x derived-categories (-1) = 0

Skill Name: condensed-mathematics Type: Condensed Sets / Liquid / Solid / 6-Functors / Kunneth Trit: 0 (ERGODIC) GF(3): (+1) condensed gen + (0) liquid coord + (-1) solid valid = 0

When not to use it

  • Standard topology or algebra tasks
  • Non-condensed mathematical modeling

Limitations

  • Requires advanced mathematical knowledge

How it compares

It provides a specialized framework for condensed mathematics that is not available in standard mathematical software.

Compared to similar skills

condensed-mathematics side by side with the closest alternatives in the catalog.

SkillInstallsUpdatedSafetyDifficulty
condensed-mathematics (this skill)02moNo flagsAdvanced
quant-analyst1032moNo flagsAdvanced
stock-analyzer712moReviewBeginner
xlsx876moReviewIntermediate

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