Implicit Coordination Skill

"The trace IS the message." "22 frames with OCR in 10ms, one causality trip."

Overview

Implicit Coordination enables multi-agent systems to coordinate WITHOUT explicit message passing:

                    ┌─────────────────────────┐
                    │     ENVIRONMENT         │
                    │  (DuckDB + Seed Chain)  │
                    └───────────┬─────────────┘
                                │
            ┌───────────────────┼───────────────────┐
            │                   │                   │
    ┌───────▼───────┐   ┌───────▼───────┐   ┌───────▼───────┐
    │   Agent -1    │   │   Agent  0    │   │   Agent +1    │
    │  (Validator)  │   │ (Coordinator) │   │  (Generator)  │
    │   READS       │   │   DERIVES     │   │   WRITES      │
    └───────────────┘   └───────────────┘   └───────────────┘
            │                   │                   │
            └───────────────────┼───────────────────┘
                                │
                        NO MESSAGES
                     Only environment traces

Core Principle: Stigmergy

Stigmergy (Grassé 1959): Agents coordinate through environment modification.

Traditional:   Agent A --[message]--> Agent B
Stigmergic:    Agent A --[writes]--> Environment <--[reads]-- Agent B

Key insight: The seed chain IS the coordination mechanism:

• Agent +1 (Generator): Writes seed to environment
• Agent 0 (Coordinator): Derives next seed via SplitMix64
• Agent -1 (Validator): Reads and verifies GF(3) conservation

Vehicle Semantics

The carrier encodes meaning (not separate payload):

Performance: One Causality Trip

22 frames OCR → 10ms total → single DuckDB write

vs. Traditional:
22 frames → 22 messages → 22 round trips → 22 acknowledgments

Latency reduction: O(n) → O(1) for n frames.

GF(3) Triads

shadow-goblin (-1) ⊗ implicit-coordination (0) ⊗ gay-mcp (+1) = 0 ✓  [Core Stigmergy]
three-match (-1) ⊗ implicit-coordination (0) ⊗ agent-o-rama (+1) = 0 ✓  [Validation]
temporal-coalgebra (-1) ⊗ implicit-coordination (0) ⊗ world-runtime (+1) = 0 ✓  [Verse Traces]
polyglot-spi (-1) ⊗ implicit-coordination (0) ⊗ gay-mcp (+1) = 0 ✓  [Cross-Lang]
ramanujan-expander (-1) ⊗ implicit-coordination (0) ⊗ influence-propagation (+1) = 0 ✓  [Network]

Implementation

Environment Trace Schema (DuckDB)

CREATE TABLE IF NOT EXISTS stigmergy_traces (
  trace_id VARCHAR PRIMARY KEY,
  seed_hex VARCHAR NOT NULL,
  trit INT CHECK (trit IN (-1, 0, 1)),
  color_hex VARCHAR(7),
  agent_role VARCHAR,  -- 'generator', 'coordinator', 'validator'
  environment_key VARCHAR,  -- What was modified
  environment_value VARCHAR,  -- Serialized state
  causality_ms FLOAT,  -- Time for this trace
  parent_trace_id VARCHAR,
  gf3_running_sum INT DEFAULT 0,
  created_at TIMESTAMP DEFAULT CURRENT_TIMESTAMP
);

-- Index for fast derivation lookup
CREATE INDEX IF NOT EXISTS idx_stigmergy_parent ON stigmergy_traces(parent_trace_id);

-- View for GF(3) validation
CREATE VIEW IF NOT EXISTS stigmergy_gf3_check AS
SELECT 
  parent_trace_id,
  SUM(trit) as trit_sum,
  COUNT(*) as trace_count,
  SUM(trit) % 3 = 0 as gf3_conserved
FROM stigmergy_traces
GROUP BY parent_trace_id;

Babashka Implementation

(ns implicit-coordination
  (:require [babashka.process :refer [shell]]
            [cheshire.core :as json]))

(def STIGMERGY_DB "gh_interactome.duckdb")

(defn write-trace
  "Agent writes to environment (stigmergic deposit)"
  [seed trit agent-role env-key env-value parent-id]
  (let [trace-id (str "stg-" (subs (Long/toHexString seed) 0 8))
        color-hex (format "#%06X" (bit-and seed 0xFFFFFF))
        sql (format "INSERT INTO stigmergy_traces 
                     (trace_id, seed_hex, trit, color_hex, agent_role, 
                      environment_key, environment_value, parent_trace_id)
                     VALUES ('%s', '%s', %d, '%s', '%s', '%s', '%s', %s)"
                    trace-id (Long/toHexString seed) trit color-hex agent-role
                    env-key env-value (if parent-id (str "'" parent-id "'") "NULL"))]
    (shell {:out :string :continue true}
           "duckdb" STIGMERGY_DB "-c" sql)
    {:trace-id trace-id :seed seed :trit trit}))

(defn read-latest-trace
  "Agent reads from environment (stigmergic sensing)"
  [env-key]
  (let [sql (format "SELECT trace_id, seed_hex, trit, environment_value 
                     FROM stigmergy_traces 
                     WHERE environment_key = '%s' 
                     ORDER BY created_at DESC LIMIT 1" env-key)
        result (shell {:out :string :continue true}
                      "duckdb" STIGMERGY_DB "-c" sql)]
    (when (= 0 (:exit result))
      (:out result))))

(defn derive-next-seed
  "Coordinator derives next seed (no message needed)"
  [parent-seed trit]
  (let [GOLDEN 0x9e3779b97f4a7c15
        MIX1 0xbf58476d1ce4e5b9
        MIX2 0x94d049bb133111eb
        z (unchecked-add parent-seed GOLDEN)
        z (unchecked-multiply (bit-xor z (unsigned-bit-shift-right z 30)) MIX1)
        z (unchecked-multiply (bit-xor z (unsigned-bit-shift-right z 27)) MIX2)
        z (bit-xor z (unsigned-bit-shift-right z 31))]
    (unchecked-add z (* trit GOLDEN))))

(defn stigmergic-coordination
  "Three agents coordinate via environment only"
  [initial-seed env-key]
  (let [;; Generator (+1) writes
        gen-trace (write-trace initial-seed 1 "generator" 
                               env-key "proposal" nil)
        ;; Coordinator (0) derives (reads implicitly via seed chain)
        coord-seed (derive-next-seed initial-seed 1)
        coord-trace (write-trace coord-seed 0 "coordinator"
                                  env-key "derived" (:trace-id gen-trace))
        ;; Validator (-1) reads and verifies
        val-seed (derive-next-seed coord-seed 0)
        val-trace (write-trace val-seed -1 "validator"
                               env-key "verified" (:trace-id coord-trace))
        ;; GF(3) check: 1 + 0 + (-1) = 0 ✓
        gf3-sum (+ 1 0 -1)]
    {:traces [gen-trace coord-trace val-trace]
     :gf3-sum gf3-sum
     :gf3-conserved (= 0 gf3-sum)
     :messages-sent 0
     :causality-trips 1}))

Integration with WorldRuntime

;; Verses coordinate stigmergically
(defn verse-stigmergy
  "Parallel verses coordinate via shared environment"
  [parent-seed]
  (let [;; push_down: split into 3 verses
        verse-nash (write-trace parent-seed -1 "verse-nash"
                                "multiverse" "selfish" nil)
        verse-optimal (write-trace (derive-next-seed parent-seed -1) 0 "verse-optimal"
                                   "multiverse" "cooperative" (:trace-id verse-nash))
        verse-chaos (write-trace (derive-next-seed parent-seed 0) 1 "verse-chaos"
                                 "multiverse" "random" (:trace-id verse-optimal))
        ;; No messages between verses - only environment traces
        ;; pull_up: resolve via oracle (reads traces)
        resolution (read-latest-trace "multiverse")]
    {:verses [verse-nash verse-optimal verse-chaos]
     :resolution resolution
     :coordination :stigmergic
     :messages 0}))

Justfile Commands

# Stigmergic coordination demo
just stigmergy-demo

# Check GF(3) conservation in traces
just stigmergy-gf3-check

# View trace chain
just stigmergy-traces

# Verse stigmergy
just verse-stigmergy

Performance Comparison

Key Insights

1. No coordination protocol needed - agents read/write same environment
2. Seed chain IS causality - no separate ordering mechanism
3. GF(3) emerges from structure - not enforced by messages
4. Vehicle semantics - the carrier (seed) encodes the meaning

References

1. Grassé, P.P. (1959) - "La reconstruction du nid et les coordinations inter-individuelles"
2. Susi, T. & Ziemke, T. (2001) - "Social cognition, artefacts, and stigmergy"
3. Theraulaz & Bonabeau (1999) - "A Brief History of Stigmergy"
4. Dave White/Paradigm (2025) - "Multiverse Finance"

See Also

• world-runtime - Verse execution substrate
• world-extractable-value - WEV at Markov blanket
• chromatic-walk - 3-agent exploration
• shadow-goblin - Trace observation

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.