asi-integrated

# ASI Integrated Skill Synthesizes all loaded skills into a coherent system for **Artificial Superintelligence** skill orchestration. ## Skill Lattice ``` ┌─────────────────┐ │ glass-bead-game │ │ (synthesis) │ └────────┬────────┘ │ ┌───────────────────┼───────────────────┐ │ │ │ ┌────────▼────────┐ ┌────────▼────────┐ ┌────────▼────────┐ │ world-hopping │ │ bisimulation │ │ triad-interleave│ │ (navigation) │ │ (dispersal) │ │ (scheduling) │ └────────┬────────┘ └────────┬────────┘ └────────┬────────┘ │ │ │ └───────────────────┼───────────────────┘ │ ┌────────▼────────┐ │ gay-mcp │ │ (deterministic │ │ coloring) │ └────────┬────────┘ │ ┌────────▼────────┐ │ acsets │ │ (data model) │ └─────────────────┘ ``` ## Unified Protocol ### 1. Schema (ACSets) ```julia @present SchASIWorld(FreeSchema) begin World::Ob Skill::Ob Agent::Ob source::Hom(World, World) target::Hom(World, World) has_skill::Hom(Agent, Skill) inhabits::Hom(Agent, World) Seed::AttrType Trit::AttrType seed::Attr(World, Seed) color_trit::Attr(Skill, Trit) end ``` ### 2. Color Generation (Gay-MCP) ```python from gay import SplitMixTernary, TripartiteStreams def color_world(world_seed: int, skill_index: int) -> dict: gen = SplitMixTernary(world_seed) return gen.color_at(skill_index) ``` ### 3. World Navigation (World-Hopping) ```python def hop_between_worlds(w1, w2, event_name: str): distance = world_distance(w1, w2) if valid_hop(w1, w2): event = Event(site=["skill"], name=event_name) return event.execute(w1) return None ``` ### 4. Skill Dispersal (Bisimulation) ```python async def disperse_skill(skill_path: str, agents: list): game = BisimulationGame() for i, agent in enumerate(agents): trit = (i % 3) - 1 # GF(3) balanced game.attacker_move(agent, skill_path, trit) game.defender_respond(await agent.receive(skill_path)) return game.arbiter_verify() ``` ### 5. Parallel Execution (Triad Interleave) ```python def schedule_skill_updates(seed: int, n_agents: int): interleaver = TriadInterleaver(seed) schedule = interleaver.interleave( n_triplets=n_agents // 3, policy="gf3_balanced" ) return schedule ``` ### 6. Synthesis (Glass Bead Game) ```python def synthesize_skills(*skills): game = GlassBeadGame() for skill in skills: game.add_bead(skill.name, skill.domain) # Connect skills via morphisms game.connect("acsets", "gay-mcp", via="seed_to_color") game.connect("gay-mcp", "triad-interleave", via="color_stream") game.connect("triad-interleave", "bisimulation", via="schedule") game.connect("bisimulation", "world-hopping", via="dispersal") return game.score() ``` ## ~/worlds Letter Index | Letter | Domain | Key Projects | |--------|--------|--------------| | a | Category Theory | ACSets.jl, Catlab.jl, Decapodes.jl | | b | Terminal | bmorphism/trittty | | p | Infrastructure | plurigrid/oni, alpaca.cpp | | t | Collaboration | CatColab | | e | HoTT | infinity-cosmos (Lean 4) | | r | Type Theory | rzk (simplicial HoTT) | | n | Knowledge | nlab-content | | o | Music | rubato-composer | ## GF(3) Conservation Law All operations preserve: ``` ∑ trits ≡ 0 (mod 3) ``` Across: - World hops (Attacker -1, Defender +1, Arbiter 0) - Color triplets (MINUS, ERGODIC, PLUS) - Schedule entries (balanced per triplet) - Skill dispersal (agent assignments) ## Commands ```bash # Generate integrated schedule just asi-schedule 0x42D 10 # Disperse skills to all agents just asi-disperse ~/.claude/skills/ # Verify GF(3) conservation just asi-verify # Play glass bead synthesis just asi-synthesize a b p t # World hop between letters just asi-hop a t ``` ## Starred Gists: Fixpoint & Type Theory Resources Curated from bmorphism's GitHub interactions: ### zanzix: Fixpoints of Indexed Functors [Fix.idr](https://gist.github.com/zanzix/02641d6a6e61f3757e3b703059619e90) - Idris indexed functor fixpoints for graphs, multi-graphs, poly-graphs. ```idris data IFix : (f : (k -> Type) -> k -> Type) -> k -> Type where In : f (IFix f) i -> IFix f i ``` ### VictorTaelin: ITT-Flavored CoC Type Checker [itt-coc.ts](https://gist.github.com/VictorTaelin/dd291148ee59376873374aab0fd3dd78) - Intensional Type Theory CoC in TypeScript. ### VictorTaelin: Affine Types [Affine.lean](https://gist.github.com/VictorTaelin/5584036b0ea12507b78ef883c6ae5acd) - Linear/affine type experiments in Lean 4. ### rdivyanshu: Streams & Unique Fixed Points [Nats.dfy](https://gist.github.com/rdivyanshu/2042085421d5f0762184dd7fe7cfb4cb) - Dafny streams with unique fixpoint theorems. ### Keno: Abstract Lattice [abstractlattice.jl](https://gist.github.com/Keno/fa6117ae0bf9eea3f041c0cf1f33d675) - Julia abstract lattice. Comment: "a quantum of abstract solace ∞" ### norabelrose: Fast Kronecker Decomposition [kronecker_decompose.py](https://gist.github.com/norabelrose/3f7a553f4d69de3cf5bda93e2264a9c9) - Optimal Kronecker decomposition. ### borkdude: UUID v1 in Babashka [uuidv1.clj](https://gist.github.com/borkdude/18b18232c00c2e2af2286d8bd36082d7) - Deterministic UUID generation in Clojure. ## QuickCheck/Adhesive Rewriting Integration Property-based testing connects to ASI through **autopoietic generators**: ```julia # QuickCheck-style recursive generator with GF(3) conservation function autopoietic_tree(seed::UInt64, depth::Int) rng = SplitMix64(seed) trit = mod(next_u64!(rng), 3) - 1 if depth == 0 || trit == -1 # MINUS = terminate return Leaf(color_at(seed)) else left_seed, right_seed = split(rng) return Node( trit = trit, left = autopoietic_tree(left_seed, depth-1), right = autopoietic_tree(right_seed, depth-1) ) end end ``` ### Shrinking as Adhesive Complement QuickCheck shrinking = finding minimal ∼Q_G in adhesive categories: - **Decomposition**: Q ≅ Q_G +_{Q_L} Q_R - **Complement**: ∼A is smallest subobject where X = A ∨ ∼A - **Shrunk value** = complement of failed portion ### Transitive Closure (Kris Brown) From [Incremental Query Updating in Adhesive Categories](https://topos.institute/blog/2025-08-15-incremental-adhesive/): ``` path(X,Z) :- path(X,Y), edge(Y,Z). Incremental update: When we apply rule to add path(a,b), new matches = outgoing edges from b (rooted search) ``` ## References - [Towards Foundations of Categorical Cybernetics](https://arxiv.org/abs/2105.06332) - Capucci, Gavranović, Hedges, Rischel - [Modeling autopoiesis and cognition with reaction networks](https://www.sciencedirect.com/science/article/pii/S0303264723001120) - Bickhard - [Bicategories of Automata, Automata in Bicategories](https://arxiv.org/pdf/2303.03865) - ACT 2023 ## Directory Tree ``` plurigrid/asi/ ├── package.json ├── bin/cli.js ├── README.md └── skills/ ├── a/SKILL.md # AlgebraicJulia ├── b/SKILL.md # bmorphism ├── c/SKILL.md # cognitect ├── d/SKILL.md # claykind ├── e/SKILL.md # infinity-cosmos ├── f/SKILL.md # clojure-site ├── g/SKILL.md # archiver-bot ├── h/SKILL.md # gdlog ├── i/SKILL.md # InverterNetwork ├── k/SKILL.md # kubeflow ├── l/SKILL.md # pretty-bugs ├── m/SKILL.md # awesome-category-theory ├── n/SKILL.md # nlab-content ├── o/SKILL.md # oeis, rubato-composer ├── p/SKILL.md # plurigrid ├── q/SKILL.md # quadrat ├── r/SKILL.md # rzk ├── s/SKILL.md # mathematicians ├── t/SKILL.md # CatColab ├── v/SKILL.md # viro └── _integrated/ # This skill └── SKILL.md ``` ## Scientific Skill Interleaving This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem: ### Graph Theory - **networkx** [○] via bicomodule - Universal graph hub ### Bibliography References - `general`: 734 citations in bib.duckdb ## SDF Interleaving This skill connects to **Software Design for Flexibility** (Hanson & Sussman, 2021): ### Primary Chapter: 10. Adventure Game Example **Concepts**: autonomous agent, game, synthesis ### GF(3) Balanced Triad ``` _integrated (−) + SDF.Ch10 (+) + [balancer] (○) = 0 ``` **Skill Trit**: -1 (MINUS - verification) ### Secondary Chapters - Ch3: Variations on an Arithmetic Theme - Ch1: Flexibility through Abstraction - Ch4: Pattern Matching ### Connection Pattern Adventure games synthesize techniques. This skill integrates multiple patterns. ## Cat# Integration This 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 ``` ### GF(3) Naturality The skill participates in triads satisfying: ``` (-1) + (0) + (+1) ≡ 0 (mod 3) ``` This ensures compositional coherence in the Cat# equipment structure.