The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-correlation-coefficient-state-a-a7fa

stable pending witness
2026-05-29 08:00:42 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the correlation coefficient. State any key formula.
77 chars

Generation

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables, ranging from -1 to +1. A value of +1 indicates a perfect positive linear relationship, -1 indicates a perfect negative linear relationship, and 0 indicates no linear relationship. The key formula is: **r = Σ[(x - x̄)(y - ȳ)] / √[Σ(x - x̄)² × Σ(y - ȳ)²]** where x̄ and ȳ are the means of variables x and y respectively.
25 tokens in · 140 tokens out · 3303 ms · $0.0022

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
pass
no declared way_path (Way check NA); no coercion language
EXECUTION
deferred
no witnesses available (Witness Roll not yet constituted)

Verifier results

scripture_anchors NOT_APPLICABLE
0 Scripture citation(s) extracted
theology_doctrine NOT_APPLICABLE
no doctrine keyword patterns detected

Metrics

Total latency
3309.8 ms
Base LLM
3303.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0022

Trail

08:00:42 received prompt_chars=77 verifiers=['scripture_anchors', 'theology_doctrine']
08:00:42 red_gate decision=pass reason=no disqualifying input patterns detected
08:00:46 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=140 latency_ms=3303.2 cost_usd=0.0022
08:00:46 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:00:46 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:00:46 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:00:46 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:00:46 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:00:46 signed hash_algo=sha256 hash=sha256:73a0033a8e618e0227aec91ff5acb2d6031761a2df9539ef1e79d028550c8354

Content hash

sha256:73a0033a8e618e0227aec91ff5acb2d6031761a2df9539ef1e79d028550c8354

SHA256 over the canonical JSON (excluding this field). Tamper detection. Ed25519 signing planned for v2 once the operator’s signing key is provisioned on disk.

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