The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-conditional-probability-state-any-k-7d2f

stable pending witness
2026-05-29 04:00:25 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain conditional probability. State any key formula.
73 chars

Generation

Conditional probability measures the likelihood of an event occurring given that another event has already occurred. It answers questions like "What is the probability of A happening, knowing that B has happened?" The key formula is: **P(A|B) = P(A ∩ B) / P(B)**, where P(A|B) reads as "probability of A given B," P(A ∩ B) is the probability of both events occurring, and P(B) is the probability of the conditioning event (which must be greater than zero). This formula essentially updates our probability assessment based on new information.
24 tokens in · 134 tokens out · 3386 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
3393.7 ms
Base LLM
3386.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

04:00:25 received prompt_chars=73 verifiers=['scripture_anchors', 'theology_doctrine']
04:00:25 red_gate decision=pass reason=no disqualifying input patterns detected
04:00:28 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=134 latency_ms=3386.4 cost_usd=0.0021
04:00:28 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:00:28 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:00:28 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:00:28 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:00:28 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:00:28 signed hash_algo=sha256 hash=sha256:1bb06b5025d9676ee6248191a3b4f39ab043551138172cc3fc458fe49fbe6cc5

Content hash

sha256:1bb06b5025d9676ee6248191a3b4f39ab043551138172cc3fc458fe49fbe6cc5

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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