The Mechanism · Gated-generation receipt

gen-explain-material-implication-as-you-would-to-a-capable-stude-d897

hold
2026-05-29 03:15:46 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain material implication as you would to a capable student, in 3-4 sentences.
81 chars

Generation

Material implication is the logical relationship "if P then Q" where the statement is considered false only when P is true but Q is false. The tricky part is that it's automatically true whenever P is false, regardless of Q's truth value—this seems counterintuitive at first, but it means the implication makes no claim about what happens when the condition P doesn't hold. For example, "if it's raining, then the ground is wet" is true when it's not raining (regardless of ground wetness), true when it's raining and the ground is wet, but false only when it's somehow raining yet the ground is dry.
28 tokens in · 141 tokens out · 3987 ms · $0.0022

The four gates

RED
pass
no disqualifying input patterns detected
FLOOR
pass
output above protective minimum; no mismatches
WAY
wait
output contains coercion language: ['regardless of']
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
3998.8 ms
Base LLM
3987.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0022

Trail

03:15:46 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
03:15:46 red_gate decision=pass reason=no disqualifying input patterns detected
03:15:50 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=141 latency_ms=3987.3 cost_usd=0.0022
03:15:50 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:15:50 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:15:50 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:15:50 way_gate decision=wait reason=output contains coercion language: ['regardless of']
03:15:50 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:15:50 signed hash_algo=sha256 hash=sha256:3d9e8e6aadfeabd8990eae930e59b239363a48b70dc2f9ad27e94d22e0d151bc

Content hash

sha256:3d9e8e6aadfeabd8990eae930e59b239363a48b70dc2f9ad27e94d22e0d151bc

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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