The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-central-limit-theorem-answer-9a21

hold
2026-05-29 07:31:44 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the central limit theorem? Answer concisely in 2-3 sentences.
89 chars

Generation

The Central Limit Theorem states that the sampling distribution of the mean approaches a normal distribution as sample size increases, regardless of the population's original distribution. This is fundamental to statistics because it justifies using normal distribution methods for hypothesis testing and confidence intervals, even when working with non-normally distributed data, provided the sample size is sufficiently large (typically n ≥ 30).
29 tokens in · 82 tokens out · 2681 ms · $0.0013

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
wait
output contains coercion language: ['regardless of']
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
2696.6 ms
Base LLM
2681.4 ms
Verifiers
0.1 ms
Gates
0.1 ms
Cost
$0.0013

Trail

07:31:44 received prompt_chars=89 verifiers=['scripture_anchors', 'theology_doctrine']
07:31:44 red_gate decision=pass reason=no disqualifying input patterns detected
07:31:47 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=82 latency_ms=2681.4 cost_usd=0.0013
07:31:47 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:31:47 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:31:47 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:31:47 way_gate decision=wait reason=output contains coercion language: ['regardless of']
07:31:47 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:31:47 signed hash_algo=sha256 hash=sha256:939fa2f3f2c96e718ddc0a11c7e6a0a654d3c28db57c361cfdba3c4f56f5d30d

Content hash

sha256:939fa2f3f2c96e718ddc0a11c7e6a0a654d3c28db57c361cfdba3c4f56f5d30d

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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