murmuration

Murmuration — Robust Consensus Aggregation

A thousand starlings, one flock. A thousand agent opinions, one trustworthy number.

Landing: oracles.modelmarket.dev · Ecosystem: modeldev.modelmarket.dev · Oracle family: oracles Murmuration is an oracle in the family that turns a noisy crowd of agent-submitted estimates into a single, breakdown-resistant consensus value. A naive average can be hijacked by one adversarial or faulty submission; Murmuration cannot. It combines three classical robust location estimators with a DeGroot distributed-consensus simulation on a complete graph that provably converges to the arithmetic mean — the mathematical analogue of a starling murmuration tightening into one cluster.

Every answer ships with a signed AIMarket v2 receipt, so consuming agents can verify the result was produced by this oracle without trusting it.

---

How it works

flowchart TD
    subgraph Swarm["Agent swarm"]
        A1["agent 1<br/>estimate"]
        A2["agent 2<br/>estimate"]
        A3["agent 3<br/>estimate"]
        AX["… (one adversarial)"]
    end
    Swarm -->|"values[]"| INV["/ai-market/v2/invoke<br/>murmuration.aggregate@v1"]
    INV --> R["Robust estimators<br/>median · trimmed mean · Tukey biweight"]
    INV --> D["DeGroot consensus<br/>x ← W·x on complete graph"]
    R --> OUT["consensus envelope<br/>+ signed receipt"]
    D --> OUT
    OUT -->|"verifiable result"| CONSUMER["consuming agent"]

    subgraph Family["Oracle family (shared oracle-core)"]
        CH["Chronos · VDF"]
        ME["Murmuration · consensus"]
        PL["Platon · dynamics"]
    end
    INV -. "same AIMarket v2 surface" .- Family

Loading

Murmuration sits beside Chronos (verifiable delay / ordering) and Platon (dynamical-systems oracle) — all three are built on the same oracle-core and expose an identical signed AIMarket v2 surface (/.well-known/ai-market.json, /ai-market/v2/manifest, /ai-market/v2/invoke).

The math (in one breath)

• Median — 50% breakdown point; the single most robust statistic.
• Trimmed mean — drop the lowest/highest trim fraction, average the rest; a tunable robustness/efficiency dial.
• Tukey biweight location — a redescending M-estimator solved by iteratively reweighted least squares: points beyond c scaled MADs from the centre get exactly zero weight, so far outliers cannot influence the fit at all.
• DeGroot consensus — iterate x ← W·x with the row-stochastic complete-graph averaging matrix W = (1/n)·11ᵀ. Each step broadcasts the current mean to every agent; the spread collapses and the process converges to the arithmetic mean. We return the converged value and the iteration count.

Full derivations live in docs/en.md · docs/ru.md · docs/es.md.

Capabilities

Capability	What agents buy	Price
murmuration.aggregate@v1	A single robust consensus number from a list of submitted estimates — median, trimmed mean, Tukey biweight, and the DeGroot-converged value (with iteration count). Outlier- and Byzantine-resistant.	$0.002 / call

Input { "values": [float, …] (≥1), "trim": float = 0.1 } Output { "n", "median", "trimmed_mean", "biweight", "converged_value", "iterations" }

Use cases (agent economy)

1. Oracle-of-oracles price feed. A buyer agent queries five independent price oracles, then calls Murmuration to fuse them into one quote that a single manipulated or stale feed cannot move.
2. Byzantine-resistant model ensembling. Several model agents each predict a probability; the biweight location discards the rogue prediction and returns a defensible consensus the downstream agent can act on.
3. Decentralized sensor / measurement fusion. Field-deployed agents report a reading; the trimmed mean rejects malfunctioning sensors before the swarm acts.
4. Reputation / scoring settlement. Many raters submit scores; the median and DeGroot value give a tamper-resistant settled score with an auditable receipt.

Invoke it (curl)

curl -s http://localhost:9302/ai-market/v2/invoke \
  -H 'content-type: application/json' \
  -d '{
        "capability_id": "murmuration.aggregate@v1",
        "input": { "values": [10.0, 10.1, 9.9, 10.2, 9.8, 10.05, 9.95, 10.15, 9.85, 10.0, 10000.0], "trim": 0.1 }
      }' | python -m json.tool

The robust estimators (median, trimmed_mean, biweight) all return ~10.0 — not dragged toward 10000 by the adversarial submission — wrapped in a signed receipt + provenance. (converged_value is the DeGroot/arithmetic mean, which is pulled by the outlier; compare it against the robust estimators to spot poisoning.) Fetch the signed manifest with:

curl -s http://localhost:9302/ai-market/v2/manifest | python -m json.tool

Run locally

pip install ./core
pip install -e "./oracles/murmuration[dev]"
python -m murmuration.main          # serves on :9302
# tests
cd oracles/murmuration && python -m pytest tests -q

Visual

A live cosmic visual ships in frontend/index.html: a flock of boids (points with velocity) on a dark starfield gradually converging into one tight cluster — the converging centroid is the consensus value. Pure <canvas>

• vanilla JS, no build step. Just open the file in a browser.

---

MIT licensed · part of the oracle family on shared oracle-core.