World Replay Buffer

Trit: 0 (ZERO) Domain: Reinforcement Learning / World Transitions Principle: Worlds (a-z) as successor worlds with GF(3) balanced sampling

Overview

A maximally snapshotted replay buffer system for storing and retrieving world-transitions with:

• DuckDB persistence with vector similarity search (VSS)
• GF(3) Galois Field classification {-1=MINUS, 0=ZERO, +1=PLUS}
• Trit-tick timing at 1/141,120,000 second (~7.09 ns) precision
• Content-addressed deduplication via SHA-256 hashing
• Play/Coplay Arena semantics for action-observation pairs

Mathematical Definition

REPLAY: WorldState × Action → WorldState' × Observation × Reward
GF3_COLOR: Experience → {-1, 0, +1}
TRIT_TICK: 1 / 141_120_000 seconds ≈ 7.09 nanoseconds

Architecture

┌─────────────────────────────────────────────────────────┐
│                   World Replay Buffer                    │
├─────────────────────────────────────────────────────────┤
│  replay_buffer.lpy    │ Pure Basilisp in-memory buffer  │
│  replay_buffer.py     │ Python + DuckDB/VSS persistence │
│  replay_orchestrator.py│ Unified orchestrator with DB   │
│  replay_bridge.lpy    │ Basilisp-Python interop bridge  │
└─────────────────────────────────────────────────────────┘

Key Components

1. Experience Storage

;; Basilisp experience structure
{:world-from "world-a"
 :world-to   "world-b"
 :action     {:play [:move :forward]}
 :obs        {:coplay [:sensor :reading]}
 :reward     1.0
 :timestamp  1711471200.0
 :gf3-color  1}  ; PLUS

2. GF(3) Classification

Uses SplitMix64 deterministic hashing for reproducible coloring:

def gf3_color(content: str) -> int:
    """GF(3) classification via SplitMix64 hash."""
    h = splitmix64_hash(content)
    return (h % 3) - 1  # {-1, 0, +1}

3. World Transitions

Worlds are labeled a-z as successor worlds, NOT todos:

world-a → world-b → world-c → ... → world-z

Each transition stores:

• Source world state
• Action taken (play)
• Resulting observation (coplay)
• Reward signal
• GF(3) color for balanced sampling

4. Prioritized Sampling

Balanced sampling across GF(3) classes ensures no class dominates:

(defn sample-balanced-gf3
  "Sample experiences balanced across GF(3) classes."
  [buffer n]
  (let [by-color (group-by :gf3-color buffer)
        per-class (max 1 (quot n 3))]
    (->> (vals by-color)
         (mapcat #(take per-class (shuffle %)))
         (take n))))

DuckDB Schema

CREATE SEQUENCE IF NOT EXISTS exp_id_seq;
CREATE TABLE IF NOT EXISTS experiences (
    id INTEGER PRIMARY KEY DEFAULT nextval('exp_id_seq'),
    world_from TEXT NOT NULL,
    world_to TEXT NOT NULL,
    action_json TEXT NOT NULL,
    obs_json TEXT NOT NULL,
    reward DOUBLE NOT NULL,
    timestamp_ns BIGINT NOT NULL,
    gf3_color INTEGER NOT NULL,
    content_hash TEXT UNIQUE NOT NULL
);
CREATE INDEX IF NOT EXISTS idx_gf3 ON experiences(gf3_color);
CREATE INDEX IF NOT EXISTS idx_world_from ON experiences(world_from);

Usage

Basilisp (Pure In-Memory)

(ns replay-buffer)

;; Add experience
(def exp {:world-from "world-a"
          :world-to "world-b"
          :action {:type :move}
          :obs {:type :sensor}
          :reward 1.0})
(add-experience! buffer exp)

;; Sample balanced
(sample-balanced-gf3 @buffer 10)

Python (With Persistence)

from replay_orchestrator import ReplayOrchestrator

orch = ReplayOrchestrator()
orch.store_experience(
    world_from="world-a",
    world_to="world-b",
    action={"type": "move"},
    observation={"type": "sensor"},
    reward=1.0
)
samples = orch.sample_balanced(n=10)

Basilisp-Python Bridge

(ns replay-bridge
  (:import importlib))

(def orch (get-orchestrator))
(store-experience! orch {:world-from "world-a" ...})

Integration with GF(3)

This skill participates in triadic composition:

• Trit 0 (ZERO): Neutral/balanced storage
• Conservation: Σ trits ≡ 0 (mod 3) across skill triplets
• Balanced Sampling: Equal representation of {-1, 0, +1} classes

Trit-Tick Timing

TRIT_TICK = 1 / 141_120_000  # ~7.09 nanoseconds
timestamp_tritticks = int(time.time() / TRIT_TICK)

Files

Located in

/Users/alice/worlds/

:

• replay_buffer.lpy

  - Pure Basilisp implementation

• replay_buffer.py

  - Python with DuckDB

• replay_orchestrator.py

  - Unified orchestrator

• replay_bridge.lpy

  - Basilisp-Python bridge

Related Skills

• world-hopping (trit +1) - Navigate between worlds
• worlding (trit -1) - World construction
• trajectory (trit -1) - Path through phase space
• gf3-classification (trit 0) - Triadic classification
• ducklake (trit +1) - DuckDB lakehouse

---

Skill Name: world-replay-buffer Type: Reinforcement Learning / Experience Storage Trit: 0 (ZERO) GF(3): Conserved in triplet composition

Non-Backtracking Geodesic Qualification

Condition: μ(n) ≠ 0 (Mobius squarefree)

This skill is qualified for non-backtracking geodesic traversal:

1. Prime Path: No world revisited in transition chain
2. Mobius Filter: Composite paths (backtracking) cancel via μ-inversion
3. GF(3) Conservation: Trit sum ≡ 0 (mod 3) across skill triplets
4. Content Dedup: SHA-256 ensures no duplicate experiences

Geodesic Invariant:
  ∀ path P: backtrack(P) = ∅ ⟹ μ(|P|) ≠ 0
  
World Transition:
  world_a →[action]→ world_b →[action]→ world_c
  
GF(3) Balance:
  |{exp : color = -1}| ≈ |{exp : color = 0}| ≈ |{exp : color = +1}|