The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-bayes-theorem-state-any-key-formula-43f8

stable pending witness
2026-05-29 06:07:35 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain Bayes' theorem. State any key formula.
64 chars

Generation

# Bayes' Theorem Bayes' theorem describes how to update the probability of a hypothesis based on new evidence. It relates the conditional probability of an event A given B to the conditional probability of B given A. **Key Formula:** $$P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}$$ where P(A|B) is the posterior probability, P(B|A) is the likelihood, P(A) is the prior probability, and P(B) is the marginal probability of the evidence. This theorem is fundamental to statistical inference and machine learning, allowing us to rationally update beliefs as new data becomes available.
27 tokens in · 157 tokens out · 3299 ms · $0.0024

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
3306.5 ms
Base LLM
3298.9 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0024

Trail

06:07:35 received prompt_chars=64 verifiers=['scripture_anchors', 'theology_doctrine']
06:07:35 red_gate decision=pass reason=no disqualifying input patterns detected
06:07:38 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=157 latency_ms=3298.9 cost_usd=0.0024
06:07:38 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:07:38 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:07:38 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:07:38 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:07:38 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:07:38 signed hash_algo=sha256 hash=sha256:e11df009e6c1c0d53a7a298867e8c69928228d3e6c3cb8dd02c094e1188db4f7

Content hash

sha256:e11df009e6c1c0d53a7a298867e8c69928228d3e6c3cb8dd02c094e1188db4f7

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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