The Mechanism · Gated-generation receipt

gen-explain-bayes-theorem-as-you-would-to-a-capable-student-in-3-7c6f

stable pending witness
2026-05-29 07:05:45 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain Bayes' theorem as you would to a capable student, in 3-4 sentences.
75 chars

Generation

Bayes' theorem tells us how to update our beliefs when we get new evidence. It says that the probability of something being true given the evidence equals the probability of seeing that evidence if it were true, times our prior belief it's true, divided by the overall probability of seeing that evidence. In simpler terms: if a medical test is positive, Bayes' theorem helps you calculate your actual chance of having the disease by combining the test's accuracy, how common the disease is, and the test result itself. It's fundamentally about flipping conditional probabilities—turning P(evidence|hypothesis) into P(hypothesis|evidence).
30 tokens in · 134 tokens out · 4813 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
4822.4 ms
Base LLM
4812.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

07:05:45 received prompt_chars=75 verifiers=['scripture_anchors', 'theology_doctrine']
07:05:45 red_gate decision=pass reason=no disqualifying input patterns detected
07:05:50 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=134 latency_ms=4812.9 cost_usd=0.0021
07:05:50 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:05:50 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:05:50 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:05:50 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:05:50 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:05:50 signed hash_algo=sha256 hash=sha256:6bfa37bd2e56023d22b11c26996befa796e4401a9e51b6c42815d2ee2a057804

Content hash

sha256:6bfa37bd2e56023d22b11c26996befa796e4401a9e51b6c42815d2ee2a057804

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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