The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-binomial-distribution-answer-7a57

stable pending witness
2026-05-29 05:12:54 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the binomial distribution? Answer concisely in 2-3 sentences.
89 chars

Generation

The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success. It's fundamental in statistics for analyzing yes/no outcomes, like coin flips, quality control testing, or survey responses. This makes it essential for probability calculations, hypothesis testing, and real-world decision-making across fields from medicine to manufacturing.
29 tokens in · 79 tokens out · 2911 ms · $0.0013

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
2918.7 ms
Base LLM
2911.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0013

Trail

05:12:54 received prompt_chars=89 verifiers=['scripture_anchors', 'theology_doctrine']
05:12:54 red_gate decision=pass reason=no disqualifying input patterns detected
05:12:57 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=79 latency_ms=2911.3 cost_usd=0.0013
05:12:57 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:12:57 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:12:57 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:12:57 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:12:57 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:12:57 signed hash_algo=sha256 hash=sha256:347eecec7d166b87ad294e3f23b806120f7e40f7ad48fee5387662cc0ec40aaf

Content hash

sha256:347eecec7d166b87ad294e3f23b806120f7e40f7ad48fee5387662cc0ec40aaf

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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