The Mechanism · Gated-generation receipt

gen-state-de-morgan-s-laws-precisely-and-explain-why-it-matters-f2ec

stable pending witness
2026-05-29 07:02:20 UTC · anthropic/claude-sonnet-4-5

Prompt

State De Morgan's laws precisely and explain why it matters in 2-3 sentences.
77 chars

Generation

# De Morgan's Laws **Precise Statement:** 1. ¬(A ∧ B) ≡ (¬A ∨ ¬B) — "Not (A and B)" is equivalent to "(Not A) or (Not B)" 2. ¬(A ∨ B) ≡ (¬A ∧ ¬B) — "Not (A or B)" is equivalent to "(Not A) and (Not B)" **Why It Matters:** De Morgan's laws are fundamental for simplifying logical expressions and converting between equivalent forms in mathematics, computer science, and digital circuit design. They allow us to push negations inward through logical operators, which is essential for proof techniques, database queries, programming conditionals, and optimizing Boolean circuits. Without these laws, many logical manipulations and simplifications would be impossible.
26 tokens in · 199 tokens out · 4314 ms · $0.0031

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
4325.3 ms
Base LLM
4314.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0031

Trail

07:02:20 received prompt_chars=77 verifiers=['scripture_anchors', 'theology_doctrine']
07:02:20 red_gate decision=pass reason=no disqualifying input patterns detected
07:02:24 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=199 latency_ms=4314.1 cost_usd=0.0031
07:02:24 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:02:24 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:02:24 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:02:24 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:02:24 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:02:24 signed hash_algo=sha256 hash=sha256:f0ddd1f0e3e8db3152f492a26cb541e90f588c2b4e2527bd1d5d414ff8fa8010

Content hash

sha256:f0ddd1f0e3e8db3152f492a26cb541e90f588c2b4e2527bd1d5d414ff8fa8010

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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