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**Trit**: 0 (ERGODIC - coordinates the ontology)
Coordinates multi-agent systems using GF(3) trit assignments (-1,0,+1) and conservation checks (sum ≡0 mod 3) for triadic compositions. For ALIFE diffing, counterfactual navigation, categorical rewriting.
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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.
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)
| Term | Type | Definition |
|---|---|---|
| seed | uint64 | Deterministic state replacing time |
| trit | {-1, 0, +1} | GF(3) charge element |
| γ | constant | 0x9E3779B97F4A7C15 (golden ratio bits) |
| 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))
| 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 ✓
| Term | Sheaf Correspondence |
|---|---|
| node | section-producer |
| emit | stalk transition |
| aggregation | gluing (cocycle check) |
| result | global section (H⁰ element) |
| 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))
| 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 |
64-bit unsigned integer replacing temporal state. Same seed → identical derivation chains.
GF(3) element in {-1, 0, +1}. Forms a field under modular arithmetic.
Fundamental computation: (Seed × Trit) → (Seed × Section)
Replaces temporal succession with seed-based chaining.
Collection of sections over a single trit value. Organized as fiber bundle.
Local data produced by derivation. Sections glue to form global sections when cocycle condition holds.
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 |
(def GENESIS-SEED 0x42D)
(def GAMMA 0x9E3779B97F4A7C15)
(def MIX1 0xBF58476D1CE4E5B9)
(def MIX2 0x94D049BB133111EB)
(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))
(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)))
;; 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}))))
Before any operation completes:
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
general: 734 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.