The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-t-distribution-answer-concis-0d73

stable pending witness
2026-05-29 06:13:23 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the t-distribution? Answer concisely in 2-3 sentences.
82 chars

Generation

The t-distribution is crucial for statistical inference when sample sizes are small (typically n < 30) and the population standard deviation is unknown. It accounts for the additional uncertainty from estimating the standard deviation from sample data, having heavier tails than the normal distribution to reflect this uncertainty. As sample size increases, the t-distribution converges to the normal distribution.
29 tokens in · 78 tokens out · 2379 ms · $0.0013

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
2386.2 ms
Base LLM
2379.4 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0013

Trail

06:13:23 received prompt_chars=82 verifiers=['scripture_anchors', 'theology_doctrine']
06:13:23 red_gate decision=pass reason=no disqualifying input patterns detected
06:13:25 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=78 latency_ms=2379.4 cost_usd=0.0013
06:13:25 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:13:25 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:13:25 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:13:25 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:13:25 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:13:25 signed hash_algo=sha256 hash=sha256:d777aa7e1bade3603ebbc3c8802e710c7c1042e6a0f6f1f95e151180f4e1184d

Content hash

sha256:d777aa7e1bade3603ebbc3c8802e710c7c1042e6a0f6f1f95e151180f4e1184d

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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