Lattice · low-discrepancy (quasi-random) sequences

Fill space more evenly than random. Lattice is a deterministic quasi-random oracle: it serves Halton / van der Corput low-discrepancy points that blanket the unit cube far more uniformly than white noise — the substrate for faster quasi-Monte-Carlo integration, sampling, and space-filling search.

Landing: oracles.modelmarket.dev · Ecosystem: ecosystem.modelmarket.dev · Oracle family: oracles Part of the alexar76 AI agent economy — discoverable via AIMarket Protocol v2 (signed manifest), built on the shared oracle-core, and a sibling of Chronos (verifiable delay) and Platon (chaotic randomness beacon).

White noise clumps. Lattice doesn't. Random sampling leaves gaps and clusters by chance (star discrepancy ~ O(1/√N)). A low-discrepancy sequence is engineered so every prefix is already spread out (O((log N)^d / N)). Same number of samples, lower error.

How it works

flowchart LR
  AGENT["Autonomous agents<br/>QMC · sampling · search"] --> HUB["AIMarket Hub<br/>modelmarket.dev"]
  MESH["AI service mesh"] --> HUB
  HUB -->|"routes signed, paid calls"| LAT["Lattice Oracle<br/>lattice.sequence@v1"]
  LAT --> VDC["van der Corput<br/>radical inverse φ_b(n)"]
  VDC --> PTS["Halton points in [0,1)^d<br/>coprime prime bases 2,3,5,7…"]
  PTS -->|"signed receipt + provenance"| HUB

  subgraph FAMILY["Oracle family on oracle-core"]
    LAT
    CHR["Chronos · VDF"]
    PLA["Platon · chaos beacon"]
  end

The oracle maps each sample index n to a point by taking the radical inverse of n in successive coprime prime bases. Coordinate k uses the k-th prime base, so the per-axis 1D sequences are jointly equidistributed and the point set fills [0,1)^d without lattice-alignment artefacts.

n  = Σ aᵢ · bⁱ            (base-b digits of n)
φ_b(n) = Σ aᵢ · b^-(i+1)   ∈ [0,1)     ← reflect digits around the radix point
point(n) = ( φ₂(n), φ₃(n), φ₅(n), … )  ∈ [0,1)^d

AIMarket capabilities

Every invoke returns a signed 7-field protocol receipt and a sha256 input_hash. Manifest p50_latency_ms / success_rate_30d are measured from real calls (rolling window), not hardcoded.

Use-cases in the agent economy

• Quasi-Monte-Carlo integration — a pricing/risk agent estimating an integral or expectation gets the same accuracy as plain Monte-Carlo with far fewer samples (lower variance, deterministic and reproducible for audit).
• Hyperparameter & design-of-experiments search — an AutoML agent sweeps a 6-D config space; Halton points cover every region instead of clustering, so no corner of the search space is missed early.
• Procedural / texture / scatter placement — a generative agent places N objects, dither samples, or sensor probes that look evenly spread with no visible clumps, fully reproducible from (count, dim, skip).
• Stratified A/B and survey sampling — pick representative points across a normalized feature cube without the gaps that uniform random leaves at small N.

Invoke it

# Discover
curl -s http://localhost:9301/.well-known/ai-market.json | jq .
curl -s http://localhost:9301/ai-market/v2/manifest | jq '.tools[].capability_id'

# Buy 256 quasi-random points in 2D
curl -X POST http://localhost:9301/ai-market/v2/invoke \
  -H "Content-Type: application/json" \
  -d '{"capability_id":"lattice.sequence@v1","input":{"count":256,"dim":2,"skip":0}}'

Response (truncated):

{
  "ok": true,
  "capability_id": "lattice.sequence@v1",
  "output": {
    "sequence": "halton/van-der-corput",
    "points": [[0.5, 0.3333], [0.25, 0.6667], "…"],
    "dim": 2, "count": 256, "skip": 0, "bases": [2, 3]
  },
  "price_usd": 0.002,
  "provenance": {"source": "prod-lattice", "input_hash": "…"},
  "receipt": {"…signed 7-field receipt…"}
}

Run

# from the monorepo root, with oracle-core installed in the venv
PYTHONPATH=oracles/lattice .venv/bin/python -m lattice.main   # serves on :9301

Tests

cd /path/to/oracles
PYTHONPATH=oracles/lattice .venv/bin/python -m pytest oracles/lattice/tests -q

The suite proves the math (radical-inverse values, determinism, points in [0,1), skip semantics) and the product claim (1D max-gap far smaller than random; 2D cell occupancy beats random; QMC integration error below MC) plus the app (signed manifest, invoke round-trip).

Visual

A live cosmic visualization ships in frontend/index.html — open the file directly (no build, no CDN). Quasi-random points drop in one-by-one and tile a square ultra-evenly, beside a faint clumpy white-noise cloud for contrast. You can see the lower discrepancy.

Docs

Detailed write-ups (math, diagrams, use-cases) in English · Русский · Español.

License

MIT — alexar76 ecosystem