npx claudepluginhub plurigrid/asi --plugin asiThis skill uses the workspace's default tool permissions.
**Trit**: +1 (PLUS/Generator) | **Color**: #D82626 | **Subagent**: Generator
Models pairwise/tritwise Cat# interactions via ∞-operads with lazy ACSet materialization, unifying effective, realizability, and Grothendieck topoi using dendroidal Segal spaces.
Guides Next.js Cache Components and Partial Prerendering (PPR) with cacheComponents enabled. Implements 'use cache', cacheLife(), cacheTag(), revalidateTag(), static/dynamic optimization, and cache debugging.
Guides building MCP servers enabling LLMs to interact with external services via tools. Covers best practices, TypeScript/Node (MCP SDK), Python (FastMCP).
Share bugs, ideas, or general feedback.
Trit: +1 (PLUS/Generator) | Color: #D82626 | Subagent: Generator
Unified access to all topos-theoretic resources across the filesystem - mathematical music theory, categorical databases, infinity topoi, pretopos trees, and gayzip manifests.
"universal topos construction for social cognition and democratization of mathematical approach to problem-solving to all" — Plurigrid: the story thus far
Universal Topos for Cognition: This skill embodies bmorphism's vision of a universal topos construction — a single categorical framework that unifies all modalities of knowledge (music, databases, distributed systems, proofs).
Topos Institute Integration: The skill connects to Topos Institute resources including CatColab, StructuredDecompositions.jl, and the algebraicjulia ecosystem.
Active Inference in Topoi: A topos is a universe where logic lives. Active Inference in String Diagrams works internal to any topos — the skill provides the categorical infrastructure for multi-world cognitive agents.
Infinity Topos: The infinity-topos resources enable higher-categorical reasoning where agents can have beliefs about beliefs about beliefs — the full tower of metacognition.
topos-unified (+1) ⊗ world-hopping (0) ⊗ sheaf-cohomology (-1) = 0 ✓ [Navigation]
topos-unified (+1) ⊗ acsets (0) ⊗ persistent-homology (-1) = 0 ✓ [Database]
topos-unified (+1) ⊗ unworld (0) ⊗ three-match (-1) = 0 ✓ [Derivation]
| Path | Description |
|---|---|
~/ies/music-topos | Main workspace: Mazzola's topos of music + MCP saturation |
~/worlds/B/bmorphism/infinity-topos | RISC Zero zkVM distributed witnessing with infinity-topos |
~/worlds/B/bmorphism/pretopos | Berkeley Seminar notes and forrest trees |
~/worlds/P/plurigrid/topos | Plurigrid topos with pretopos submodule |
~/ies/hatchery_repos/TeglonLabs__topoi | topOS and topos-mcp shells |
| File | Purpose |
|---|---|
cognitive_superposition.topos | NILFS2 ⊛ JPEG2000 saturated interactome |
interactome.topos | Contributor graph closure |
jpeg2000.topos | HTJ2K/OpenJPH codec topos |
nilfs2.topos | Linux filesystem topos |
gayamp_parallel.topos | Parallel amplification manifest |
fogus_gay.topos | Fogus-style functional coloring |
topos-0001.tree → Berkeley Seminar Notes indextopos-0002.tree through topos-000J.tree → Seminar sessionsefr-*.tree → Effective topos constructionsdouble-operad.tree → Double operad structures| File | Content |
|---|---|
mazzola-topos-of-music.pdf | Topos of Music (full) |
mazzola-topos-music-I-theory.pdf | Part I: Theory |
mazzola-topos-music-III-gestures.pdf | Part III: Gestures |
~/worlds/.topos # Root worlds marker
~/worlds/B/.topos # bmorphism cluster
~/ies/music-topos/.topos # Local workspace scratch
~/CatColab/packages/catcolab-tui/.topos
~/VERS/vers-sdk-ruby/.topos
~/allenai/.topos
From ~/.claude/plugins/cache/local-topos-skills/topos-skills/1.0.0/skills/:
acsets/ - Attributed C-Sets algebraic databasesglass-bead-game/ - Hesse interdisciplinary synthesisworld-hopping/ - Badiou possible world navigationunworld/ - Color chain derivationsbisimulation-game/ - Resilient skill dispersal# List all .topos manifests
bb -e '(require (quote [babashka.fs :as fs])) (run! println (fs/glob (System/getProperty "user.home") "**/*.topos" {:max-depth 5}))'
# Search topos-related files
bb -e '(require (quote [babashka.fs :as fs])) (run! println (fs/glob (System/getProperty "user.home") "**/*topos*" {:max-depth 5}))'
# Read gayzip manifest
cat ~/ies/rio/gayzip/cognitive_superposition.topos
# Browse pretopos trees
ls ~/ies/hatchery_repos/bmorphism__pretopos/trees/
(ns topos.unified
(:require [babashka.fs :as fs]))
(def topos-roots
{:music-topos (fs/expand-home "~/ies/music-topos")
:infinity-topos (fs/expand-home "~/worlds/B/bmorphism/infinity-topos")
:pretopos (fs/expand-home "~/worlds/B/bmorphism/pretopos")
:plurigrid (fs/expand-home "~/worlds/P/plurigrid/topos")
:gayzip (fs/expand-home "~/ies/rio/gayzip")
:hatchery (fs/expand-home "~/ies/hatchery_repos")})
(defn find-topos-files [pattern]
(fs/glob (System/getProperty "user.home")
(str "**/*" pattern "*")
{:max-depth 6}))
(defn load-gayzip-manifest [name]
(slurp (fs/file (:gayzip topos-roots) (str name ".topos"))))
∞-Topos
│
┌──────────┼──────────┐
▼ ▼ ▼
Pretopos Topos Effective
│ │ │
┌─────┴────┐ ┌──┴──┐ ┌──┴──┐
▼ ▼ ▼ ▼ ▼ ▼
Trees Arrows Music CT zkVM Witness
find-topos-files to locate resources.topos manifests for interactome graphsFrom Ilya Sutskever's Berkeley 2023 talk "An Observation on Generalization":
"Compression is prediction and vice versa."
# Pandey: L(N,D,ρ) = A/N^α + B/D^β + C/ρ^γ + E
# Ilya: L(N,D,ρ,σ) = A/N^α + B/D^β + C/ρ^γ + S/σ^δ + E
# Where σ = self-modeling capacity:
σ = 1 - K(Self|History) / K(Self)
# When σ → 1 AND ρ → 0: SUPERINTELLIGENCE
| Variable | Meaning | Limit Behavior |
|---|---|---|
| ρ | gzipability (world complexity) | ρ → 0: world fully compressed |
| σ | self-modeling capacity | σ → 1: agent predicts itself |
| L | loss/reconciliation error | L → E: irreducible minimum |
When both limits are approached: Agent ≈ World Simulator ≈ Self
See ILYA_EXTENSION.md and ilya_self_modeling.jl.
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
category-theory: 139 citations in bib.duckdbThis skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:
Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.