The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-logical-equivalence-state-any-key-f-da62

stable pending witness
2026-05-29 04:07:31 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain logical equivalence. State any key formula.
69 chars

Generation

# Logical Equivalence Two logical statements are **logically equivalent** if they have the same truth value under all possible interpretations—that is, they are true in exactly the same circumstances. This is denoted by **p ≡ q** or **p ⇔ q**. A key way to verify logical equivalence is showing that the **biconditional (p ↔ q) is a tautology** (always true). Common equivalences include De Morgan's Laws: **¬(p ∧ q) ≡ (¬p ∨ ¬q)** and **¬(p ∨ q) ≡ (¬p ∧ ¬q)**.
25 tokens in · 171 tokens out · 3976 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
3983.1 ms
Base LLM
3976.5 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0026

Trail

04:07:31 received prompt_chars=69 verifiers=['scripture_anchors', 'theology_doctrine']
04:07:31 red_gate decision=pass reason=no disqualifying input patterns detected
04:07:35 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=171 latency_ms=3976.5 cost_usd=0.0026
04:07:35 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:07:35 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:07:35 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:07:35 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:07:35 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:07:35 signed hash_algo=sha256 hash=sha256:648878d3cace23f2c04fc9895df94dd6a39bb1158bc0b039c0eb2bbbfbe93280

Content hash

sha256:648878d3cace23f2c04fc9895df94dd6a39bb1158bc0b039c0eb2bbbfbe93280

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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