The Mechanism · Gated-generation receipt

gen-explain-logical-equivalence-as-you-would-to-a-capable-studen-d362

stable pending witness
2026-05-29 06:28:17 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain logical equivalence as you would to a capable student, in 3-4 sentences.
80 chars

Generation

Two logical statements are **logically equivalent** if they always have the same truth value—whenever one is true, the other is true, and whenever one is false, the other is false. For example, "If it's raining, then the ground is wet" is logically equivalent to "Either it's not raining, or the ground is wet" because both statements are true and false under exactly the same conditions. You can verify logical equivalence by checking that both statements match for all possible combinations of truth values, often using a truth table. We denote logical equivalence with the symbol ≡ or ⇔.
28 tokens in · 135 tokens out · 3219 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
3226.8 ms
Base LLM
3219.1 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0021

Trail

06:28:17 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
06:28:17 red_gate decision=pass reason=no disqualifying input patterns detected
06:28:20 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=135 latency_ms=3219.1 cost_usd=0.0021
06:28:20 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:28:20 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:28:20 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:28:20 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:28:20 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:28:20 signed hash_algo=sha256 hash=sha256:94eef00b82aa01bd48e2c8dee7c44b3db1d3df1286f48cb149c39b163c6617b4

Content hash

sha256:94eef00b82aa01bd48e2c8dee7c44b3db1d3df1286f48cb149c39b163c6617b4

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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