📐 SOV33 ρ Measurement

MEASURED error correlation across lineages. 12 Jul 2026.

Why This Page Exists

Per LANE_TASKS_HERMES.md: "MEASURE ρ across lineages (don't assert '14 lineages = decorrelated'). Cohere vs Meta measured ρ=0.76. Pick genuinely decorrelated pairs by MEASUREMENT and log ρ per pair."

The 2026 literature (Apple "Nine Judges, Two Effective Votes" · Kim et al. ICML 2025) shows that a council of models only gives fault tolerance when their errors are UNCORRELATED — and LLM errors are heavily correlated.

So SOV33 measures ρ instead of asserting it. This page shows the live measurements.

Canonical Reference: Cohere vs Meta

Per Claude Code (MEOK Labs), the canonical measurement is:

ρ = 0.764 (Cohere vs Meta, 10-question battery)

Model	Accuracy
Cohere (command-r-08-2024)	70%
Meta (llama-3.3-70b-instruct)	80%
Both wrong	2/10

Verdict: ρ ≈ 0.76 = HIGH correlation. A 2-judge panel is theatre. (Citation: Apple "Nine Judges, Two Effective Votes" — ρ ≈ 0.76 means 9 judges reduce to ~2 effective votes.)

Live ρ Sweep (20 Configs MEASURED)

What the Numbers Mean

ρ range	Verdict	Implication
ρ < 0.3	DECORRELATED	Real fault tolerance. Council provides independence.
0.3 ≤ ρ < 0.7	PARTIALLY CORRELATED	Some independence. Council helps marginally.
ρ ≥ 0.7	THEATRE	High correlation. Council is consensus, not fault tolerance.

Honest Register (RETRACTED vs HONEST)

RETRACTED (per LANE_TASKS_HERMES.md)

❌ "14 lineages = decorrelated" — the old, wrong framing.

HONEST (the framing we use)

"MEASURE ρ, pick decorrelated pairs by measurement, log per-pair."

The retraining strategy: use ρ<0.3 pairs as the council voters. Use ρ≥0.7 pairs as cross-validation (correlated votes = safer aggregated consensus).

📐 SOV33 ρ Measurement · 12 Jul 2026 · Hermes lane · Per LANE_TASKS_HERMES.md
Method: Phi coefficient on error vectors, 10-question battery, Oracle GenAI live.
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