The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-de-morgan-s-laws-state-any-key-form-442f

stable pending witness
2026-05-29 08:43:00 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain De Morgan's laws. State any key formula.
66 chars

Generation

# De Morgan's Laws De Morgan's laws describe how negation distributes over logical operations (AND/OR) or set operations (intersection/union). They state that the negation of a conjunction is equivalent to the disjunction of the negations, and vice versa. **Key formulas:** - **Logic**: ¬(P ∧ Q) ≡ ¬P ∨ ¬Q and ¬(P ∨ Q) ≡ ¬P ∧ ¬Q - **Sets**: (A ∩ B)' = A' ∪ B' and (A ∪ B)' = A' ∩ B' In plain terms: "not (A and B)" equals "not A or not B", and "not (A or B)" equals "not A and not B".
26 tokens in · 209 tokens out · 4786 ms · $0.0032

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
4796.8 ms
Base LLM
4785.9 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0032

Trail

08:43:00 received prompt_chars=66 verifiers=['scripture_anchors', 'theology_doctrine']
08:43:00 red_gate decision=pass reason=no disqualifying input patterns detected
08:43:05 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=209 latency_ms=4785.9 cost_usd=0.0032
08:43:05 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:43:05 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:43:05 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:43:05 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:43:05 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:43:05 signed hash_algo=sha256 hash=sha256:269b7aec5ff533f32b9f7314217cc54e5cdc15f5c69d53dcd8297333946d1f97

Content hash

sha256:269b7aec5ff533f32b9f7314217cc54e5cdc15f5c69d53dcd8297333946d1f97

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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