--- name: pre-agent-ontology description: Pre-Agent Ontology Skill version: 1.0.0 --- # Pre-Agent Ontology Skill **Trit**: 0 (ERGODIC - coordinates the ontology) Foundational 5-layer ontology for agent-o-rama. Agents are not primitives—they emerge from derivations, stalks, and sections when gluing succeeds. ## Related Skills - **unworld**: Derivational succession (Layer 1) - **sheaf-cohomology**: Gluing verification (Layer 2) - **bisimulation-game**: Observational equivalence (Layer 2) - **acsets**: Categorical database structure (Layer 2) --- ## 5-Layer Hierarchy ``` Layer 4: EMERGENT agent, skill, experiment ↑ Layer 3: OPERATIONAL node, emit, aggregation, result ↑ Layer 2: SHEAF stalk, section, cohomology ↑ Layer 1: DERIVATIONAL derivation, chain ↑ Layer 0: PRE-ONTOLOGICAL seed, trit, γ (gamma) ``` ### Layer 0: Pre-Ontological (Absolute Primitives) | Term | Type | Definition | |------|------|------------| | seed | uint64 | Deterministic state replacing time | | trit | {-1, 0, +1} | GF(3) charge element | | γ | constant | 0x9E3779B97F4A7C15 (golden ratio bits) | ### Layer 1: Derivational | Term | Type | Definition | |------|------|------------| | derivation | (Seed × Trit) → (Seed × Section) | Fundamental computation unit | | chain | [Seed] | Sequence of derived seeds | **Rule**: `seed_{n+1} = splitmix64(seed_n ⊕ (trit_n × γ))` ### Layer 2: Sheaf-Theoretic | Term | Type | Definition | |------|------|------------| | stalk | Set(Section) | Collection of sections over one trit | | section | local data | Output of derivation, can glue | | cohomology | (H⁰, H¹) | Global sections and obstructions | **Stalk Distribution (2-3-2)**: ``` MINUS: 2 elements, trit=-1, role=validator ERGODIC: 3 elements, trit=0, role=coordinator PLUS: 2 elements, trit=+1, role=generator Verification: 2(-1) + 3(0) + 2(+1) = 0 ✓ ``` ### Layer 3: Operational | Term | Sheaf Correspondence | |------|---------------------| | node | section-producer | | emit | stalk transition | | aggregation | gluing (cocycle check) | | result | global section (H⁰ element) | ### Layer 4: Emergent | Term | Definition | |------|------------| | agent | Fiber bundle over trit poset {-1, 0, +1} | | skill | Executable section (self-contained knowledge) | | experiment | Derivation chain evaluation | **Key**: `Agent = Observation(Bundle(Stalk₋₁, Stalk₀, Stalk₊₁))` --- ## 5 Stability Invariants | ID | Invariant | Formula | Verified By | |----|-----------|---------|-------------| | I1 | GF(3) Conservation | `Σ trits ≡ 0 (mod 3)` | aggregation, trifurcate | | I2 | Determinism | `derive(s,t) = derive(s,t)` | seed chaining | | I3 | Order Independence (SPI) | `parallel(f) = sequential(f)` | spi-parallel-verify | | I4 | Gluing (Cocycle) | `g_ij ∘ g_jk = g_ik` | cohomology check | | I5 | Bisimulation | `A ~ B ⟺ ∀obs. obs(A) = obs(B)` | bisimulation-game | --- ## Key Primitives ### Seed 64-bit unsigned integer replacing temporal state. Same seed → identical derivation chains. ### Trit GF(3) element in {-1, 0, +1}. Forms a field under modular arithmetic. ### Derivation Fundamental computation: `(Seed × Trit) → (Seed × Section)` Replaces temporal succession with seed-based chaining. ### Stalk Collection of sections over a single trit value. Organized as fiber bundle. ### Section Local data produced by derivation. Sections glue to form global sections when cocycle condition holds. --- ## Trifurcation Pattern (MANDATORY) Every operation MUST split into three sub-derivations: ``` intent │ ┌────────┼────────┐ ▼ ▼ ▼ MINUS ERGODIC PLUS (-1) (0) (+1) validate coordinate generate │ │ │ └────────┼────────┘ ▼ aggregate (verify Σ=0) ``` | Sub-Agent | Trit | Role | Skills | |-----------|------|------|--------| | MINUS | -1 | Validator | spi-parallel-verify, bisimulation-game | | ERGODIC | 0 | Coordinator | glass-bead-game, triad-interleave | | PLUS | +1 | Generator | gflownet, self-evolving-agent | --- ## Clojure Implementation ### Constants ```clojure (def GENESIS-SEED 0x42D) (def GAMMA 0x9E3779B97F4A7C15) (def MIX1 0xBF58476D1CE4E5B9) (def MIX2 0x94D049BB133111EB) ``` ### Derivation ```clojure (defn derive-seed [seed trit] (let [adjusted (bit-xor seed (* trit GAMMA))] (splitmix64-next adjusted))) (defn derivation-chain [genesis-seed trits] (reductions derive-seed genesis-seed trits)) ``` ### GF(3) Arithmetic ```clojure (defn gf3-add [a b] (let [sum (+ a b)] (cond (> sum 1) (- sum 3) (< sum -1) (+ sum 3) :else sum))) (defn gf3-conserved? [trits] (zero? (reduce gf3-add 0 trits))) ``` ### Trifurcate Pattern ```clojure ;; Scatter: emit three roles (aor/agg-start-node "scatter" "execute-role" (fn [agent-node {:keys [intent]}] (aor/emit! agent-node "execute-role" {:intent intent :role :minus}) (aor/emit! agent-node "execute-role" {:intent intent :role :ergodic}) (aor/emit! agent-node "execute-role" {:intent intent :role :plus}))) ;; Gather: verify conservation (aor/agg-node "execute-role" nil aggs/+vec-agg (fn [agent-node requests _] (let [results (mapv execute-role requests) trits (mapv :trit results) conserved? (gf3-conserved? trits)] (aor/result! agent-node {:conserved conserved? :trits trits})))) ``` --- ## Verification Checklist Before any operation completes: - [ ] GF(3) sum ≡ 0 (mod 3) - [ ] All three trits represented (trifurcation) - [ ] Cocycle condition satisfied (sections glue) - [ ] Deterministic (same seed → same result) - [ ] Order-independent (SPI holds) --- ## Sources - [ONTOLOGY.md](file:///Users/alice/agent-o-rama/agent-o-rama/dev/terms/ONTOLOGY.md) - [derivation.md](file:///Users/alice/agent-o-rama/agent-o-rama/dev/terms/derivation.md) - [CONTINUITY.md](file:///Users/alice/agent-o-rama/agent-o-rama/examples/clj/src/com/rpl/agent/CONTINUITY.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 ## 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.