The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-bayes-theorem-answer-concisely-i-a232

stable pending witness
2026-05-29 06:30:28 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of Bayes' theorem? Answer concisely in 2-3 sentences.
78 chars

Generation

Bayes' theorem provides a mathematical framework for updating beliefs or probabilities when new evidence becomes available. It's fundamental to statistical inference, machine learning, and decision-making under uncertainty, allowing us to reverse conditional probabilities and calculate the probability of causes given observed effects. The theorem forms the foundation of Bayesian statistics, which has applications across science, medicine, AI, and many other fields.
30 tokens in · 84 tokens out · 3063 ms · $0.0014

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
3074.5 ms
Base LLM
3063.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0014

Trail

06:30:28 received prompt_chars=78 verifiers=['scripture_anchors', 'theology_doctrine']
06:30:28 red_gate decision=pass reason=no disqualifying input patterns detected
06:30:32 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=84 latency_ms=3063.2 cost_usd=0.0014
06:30:32 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:30:32 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:30:32 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:30:32 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:30:32 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:30:32 signed hash_algo=sha256 hash=sha256:2da1e57b2d54108a4fcf1e8a276af77c8614ba899d300921cfaac20c69a3c74f

Content hash

sha256:2da1e57b2d54108a4fcf1e8a276af77c8614ba899d300921cfaac20c69a3c74f

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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