The Mechanism · Gated-generation receipt

gen-state-material-implication-precisely-and-explain-why-it-matt-e1a8

stable pending witness
2026-05-29 06:18:10 UTC · anthropic/claude-sonnet-4-5

Prompt

State material implication precisely and explain why it matters in 2-3 sentences.
81 chars

Generation

# Material Implication **Precise statement:** A conditional statement "If P, then Q" (P → Q) is false if and only if P is true and Q is false; it is true in all other cases (when P is false, or when Q is true, or both). **Why it matters:** Material implication is the foundation of logical reasoning in mathematics, computer science, and formal argumentation, allowing us to construct valid proofs and algorithms. Its counterintuitive feature—that false antecedents make conditionals vacuously true—is essential for mathematical theorems (e.g., "if x > 5, then x² > 25" remains valid even when considering numbers ≤ 5) and ensures logical consistency in formal systems.
25 tokens in · 168 tokens out · 5084 ms · $0.0026

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
5092.1 ms
Base LLM
5084.1 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0026

Trail

06:18:10 received prompt_chars=81 verifiers=['scripture_anchors', 'theology_doctrine']
06:18:10 red_gate decision=pass reason=no disqualifying input patterns detected
06:18:15 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=168 latency_ms=5084.1 cost_usd=0.0026
06:18:15 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:18:15 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:18:15 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:18:15 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:18:15 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:18:15 signed hash_algo=sha256 hash=sha256:8c3e1b40b92052234c00f2682cdb4d9e4efadfa278ef4df18f00462fcc38e95d

Content hash

sha256:8c3e1b40b92052234c00f2682cdb4d9e4efadfa278ef4df18f00462fcc38e95d

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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