The Mechanism · Gated-generation receipt

gen-state-bayes-theorem-precisely-and-explain-why-it-matters-in-c6f0

stable pending witness
2026-05-29 05:26:05 UTC · anthropic/claude-sonnet-4-5

Prompt

State Bayes' theorem precisely and explain why it matters in 2-3 sentences.
75 chars

Generation

# Bayes' Theorem **Precise statement:** P(A|B) = P(B|A) × P(A) / P(B) Or equivalently: P(A|B) = P(B|A) × P(A) / [P(B|A) × P(A) + P(B|¬A) × P(¬A)] **Why it matters:** Bayes' theorem provides the mathematically correct way to update beliefs in light of new evidence, forming the foundation of rational inference. It reveals that the probability of a hypothesis given observed data depends not just on how well the hypothesis explains the data, but also on the prior probability of the hypothesis itself—a insight crucial for everything from medical diagnosis to machine learning to scientific reasoning.
27 tokens in · 175 tokens out · 4154 ms · $0.0027

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
4160.8 ms
Base LLM
4153.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0027

Trail

05:26:05 received prompt_chars=75 verifiers=['scripture_anchors', 'theology_doctrine']
05:26:05 red_gate decision=pass reason=no disqualifying input patterns detected
05:26:09 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=175 latency_ms=4153.6 cost_usd=0.0027
05:26:09 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:26:09 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:26:09 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:26:09 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:26:09 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:26:09 signed hash_algo=sha256 hash=sha256:5e5306d15e2c7884b78f44eb64ee985caf7be1c2b0e7a780150e64f5fa45a44b

Content hash

sha256:5e5306d15e2c7884b78f44eb64ee985caf7be1c2b0e7a780150e64f5fa45a44b

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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