topos-unified

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Topos Unified Skill

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Sourceplurigrid/asi
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NPX Install

npx skill4agent add plurigrid/asi topos-unified

Tags

Translated version includes tags in frontmatter
topos-theoryai-agentunified-resource-accessmathematical-researchclojure-scripting

SKILL.md Content

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Topos Unified Skill

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.

GF(3) Triads

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]

Resource Index

Core Projects

PathDescription
~/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

Gayzip Manifests (~/ies/rio/gayzip/*.topos)

FilePurpose
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

Pretopos Forest Trees (~/ies/hatchery_repos/bmorphism__pretopos/trees/)

  • topos-0001.tree
    → Berkeley Seminar Notes index
  • topos-0002.tree
    through 
    topos-000J.tree
    → Seminar sessions
  • efr-*.tree
    → Effective topos constructions
  • double-operad.tree
    → Double operad structures

PDFs (~/ies/)

FileContent
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

.topos Directories (World Markers)

~/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

Installed Skills (topos-related)

From 
~/.claude/plugins/cache/local-topos-skills/topos-skills/1.0.0/skills/
:
  • acsets/
    - Attributed C-Sets algebraic databases
  • glass-bead-game/
    - Hesse interdisciplinary synthesis
  • world-hopping/
    - Badiou possible world navigation
  • unworld/
    - Color chain derivations
  • bisimulation-game/
    - Resilient skill dispersal

Quick Access Commands

bash
# 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/

Clojure Integration

clojure
(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"))))

Categorical Structure

                    ∞-Topos
                       │
           ┌──────────┼──────────┐
           ▼          ▼          ▼
      Pretopos    Topos     Effective
           │          │          │
     ┌─────┴────┐  ┌──┴──┐    ┌──┴──┐
     ▼          ▼  ▼     ▼    ▼     ▼
   Trees    Arrows Music  CT  zkVM  Witness

Workflow

  1. Explore: Use 
    find-topos-files
    to locate resources
  2. Load: Read 
    .topos
    manifests for interactome graphs
  3. Navigate: Follow pretopos tree links for seminar notes
  4. Compose: Combine music-topos with gayzip coloring
  5. Verify: Use infinity-topos zkVM for proofs

Ilya Extension: Self-Modeling + Compression

From Ilya Sutskever's Berkeley 2023 talk "An Observation on Generalization":
"Compression is prediction and vice versa."

Extended Scaling Law

julia
# 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

Key Insight

VariableMeaningLimit Behavior
ρgzipability (world complexity)ρ → 0: world fully compressed
σself-modeling capacityσ → 1: agent predicts itself
Lloss/reconciliation errorL → E: irreducible minimum
When both limits are approached: Agent ≈ World Simulator ≈ Self
See ILYA_EXTENSION.md and ilya_self_modeling.jl.

Dependencies

  • babashka (bb) for fast Clojure scripting
  • DuckDB for topos artifact storage
  • Gay.jl / gay-rs for deterministic coloring