The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-confidence-interval-state-any-key-f20a

stable pending witness
2026-05-29 04:12:26 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a confidence interval. State any key formula.
71 chars

Generation

A confidence interval is a range of values that likely contains an unknown population parameter, with a specified level of confidence (commonly 95%). It's calculated from sample data and provides both a point estimate and a measure of uncertainty around that estimate. The key formula for a confidence interval for a population mean is: **CI = x̄ ± (critical value) × (s/√n)** where x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and the critical value comes from the t-distribution (or z-distribution for large samples).
25 tokens in · 129 tokens out · 3005 ms · $0.002

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
3011.9 ms
Base LLM
3004.8 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.002

Trail

04:12:26 received prompt_chars=71 verifiers=['scripture_anchors', 'theology_doctrine']
04:12:26 red_gate decision=pass reason=no disqualifying input patterns detected
04:12:29 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=129 latency_ms=3004.8 cost_usd=0.002
04:12:29 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:12:29 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:12:29 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:12:29 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:12:29 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:12:29 signed hash_algo=sha256 hash=sha256:f40b65ab78bc24e231a7f00156f54fc1e2fed34f85b2df6d77a9dcd9bb82875f

Content hash

sha256:f40b65ab78bc24e231a7f00156f54fc1e2fed34f85b2df6d77a9dcd9bb82875f

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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