The Mechanism · Gated-generation receipt

gen-explain-the-binomial-distribution-as-you-would-to-a-capable-7d1b

stable pending witness
2026-05-29 03:13:57 UTC · anthropic/claude-sonnet-4-5

Prompt

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

Generation

The binomial distribution describes the number of successes you'll get in a fixed number of independent trials, where each trial has only two possible outcomes (like heads/tails) and the same probability of success each time. For example, if you flip a coin 10 times, the binomial distribution tells you the probability of getting exactly 5 heads, or 3 heads, or any other number. It's characterized by two parameters: n (the number of trials) and p (the probability of success on each trial). This distribution is incredibly useful for modeling situations like quality control testing, survey responses, or any scenario with repeated yes/no outcomes.
29 tokens in · 139 tokens out · 6369 ms · $0.0022

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
6375.5 ms
Base LLM
6369.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0022

Trail

03:13:57 received prompt_chars=86 verifiers=['scripture_anchors', 'theology_doctrine']
03:13:57 red_gate decision=pass reason=no disqualifying input patterns detected
03:14:03 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=139 latency_ms=6369.1 cost_usd=0.0022
03:14:03 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:14:03 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:14:03 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:14:03 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:14:03 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:14:03 signed hash_algo=sha256 hash=sha256:bcdec31a87bce838be5f51a0b247356381866fa375433a4b7923e2ff33beb71a

Content hash

sha256:bcdec31a87bce838be5f51a0b247356381866fa375433a4b7923e2ff33beb71a

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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