The Mechanism · Gated-generation receipt

gen-explain-the-t-distribution-as-you-would-to-a-capable-student-d2f7

stable pending witness
2026-05-29 06:16:47 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain the t-distribution as you would to a capable student, in 3-4 sentences.
79 chars

Generation

The t-distribution is like a slightly more spread-out version of the normal distribution that we use when we're working with small sample sizes and don't know the true population standard deviation. It has heavier "tails," meaning there's a higher probability of getting extreme values, which accounts for the extra uncertainty that comes from estimating parameters from limited data. As your sample size increases, the t-distribution gradually approaches the normal distribution, eventually becoming nearly identical when you have around 30 or more observations. You'll encounter it most commonly in t-tests and when constructing confidence intervals for means.
29 tokens in · 126 tokens out · 4689 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
4701.5 ms
Base LLM
4689.3 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.002

Trail

06:16:47 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
06:16:47 red_gate decision=pass reason=no disqualifying input patterns detected
06:16:51 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=126 latency_ms=4689.3 cost_usd=0.002
06:16:51 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:16:51 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:16:51 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:16:51 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:16:51 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:16:51 signed hash_algo=sha256 hash=sha256:e31c4a83637660193235843d6e359d80883a8855ba457697ac2fcccdb1787866

Content hash

sha256:e31c4a83637660193235843d6e359d80883a8855ba457697ac2fcccdb1787866

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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