The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-t-distribution-state-any-key-fo-7126

stable pending witness
2026-05-29 08:56:36 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the t-distribution. State any key formula.
68 chars

Generation

The t-distribution is a probability distribution similar to the normal distribution but with heavier tails, making it more appropriate when working with small sample sizes or unknown population standard deviations. It is characterized by degrees of freedom (df = n - 1), and as the sample size increases, it approaches the standard normal distribution. The key formula for the t-statistic is: **t = (x̄ - μ) / (s/√n)** where x̄ is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size.
26 tokens in · 134 tokens out · 2904 ms · $0.0021

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
2910.7 ms
Base LLM
2903.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

08:56:36 received prompt_chars=68 verifiers=['scripture_anchors', 'theology_doctrine']
08:56:36 red_gate decision=pass reason=no disqualifying input patterns detected
08:56:39 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=134 latency_ms=2903.9 cost_usd=0.0021
08:56:39 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:56:39 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:56:39 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:56:39 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:56:39 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:56:39 signed hash_algo=sha256 hash=sha256:44be91030941e238ca31b1dde02cf42e96ca8bb9642f1509a79fcbb2345e5bea

Content hash

sha256:44be91030941e238ca31b1dde02cf42e96ca8bb9642f1509a79fcbb2345e5bea

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.

Bring another teaching · Run a discernment