The Mechanism · Gated-generation receipt

gen-state-logical-equivalence-precisely-and-explain-why-it-matte-6026

stable pending witness
2026-05-29 04:33:15 UTC · anthropic/claude-sonnet-4-5

Prompt

State logical equivalence precisely and explain why it matters in 2-3 sentences.
80 chars

Generation

# Logical Equivalence **Definition:** Two statements P and Q are logically equivalent (written P ≡ Q) if and only if they have the same truth value in every possible case—that is, P ↔ Q is a tautology. **Why it matters:** Logical equivalence allows us to substitute one statement for another in arguments and proofs without changing the validity or meaning, which is essential for simplifying complex reasoning and revealing hidden relationships between statements. It's the foundation for algebraic manipulation in logic, enabling us to transform arguments into clearer or more useful forms while preserving truth.
25 tokens in · 134 tokens out · 4747 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
4754.8 ms
Base LLM
4747.4 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

04:33:15 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
04:33:15 red_gate decision=pass reason=no disqualifying input patterns detected
04:33:20 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=134 latency_ms=4747.4 cost_usd=0.0021
04:33:20 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:33:20 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:33:20 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:33:20 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:33:20 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:33:20 signed hash_algo=sha256 hash=sha256:8afa2a019d6a92e95838596086fe2db6ac2464ca2004fd32b7ea04215d7bbb0c

Content hash

sha256:8afa2a019d6a92e95838596086fe2db6ac2464ca2004fd32b7ea04215d7bbb0c

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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