The Mechanism · Gated-generation receipt

gen-define-de-morgan-s-laws-and-give-one-short-worked-example-3d8d

stable pending witness
2026-05-29 05:37:21 UTC · anthropic/claude-sonnet-4-5

Prompt

Define De Morgan's laws and give one short worked example.
58 chars

Generation

# De Morgan's Laws De Morgan's laws describe how negation distributes over logical operations: **1. NOT (A AND B) = (NOT A) OR (NOT B)** **2. NOT (A OR B) = (NOT A) AND (NOT B)** In set notation: - (A ∩ B)' = A' ∪ B' - (A ∪ B)' = A' ∩ B' ## Worked Example **Statement:** "It is not true that both the light is on AND the door is closed." Let: - A = "light is on" - B = "door is closed" **Original:** NOT (A AND B) **Applying De Morgan's Law:** NOT (A AND B) = (NOT A) OR (NOT B) **Translation:** "Either the light is off OR the door is open (or both)." **Verification with truth table:** ``` A | B | A AND B | NOT(A AND B) | NOT A | NOT B | (NOT A) OR (NOT B) T | T | T | F | F | F | F T | F | F | T | F | T | T F | T | F | T | T | F | T F | F | F | T | T | T | T ``` The columns match, confirming the law. ✓
19 tokens in · 359 tokens out · 7011 ms · $0.0054

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
7017.8 ms
Base LLM
7010.7 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0054

Trail

05:37:21 received prompt_chars=58 verifiers=['scripture_anchors', 'theology_doctrine']
05:37:21 red_gate decision=pass reason=no disqualifying input patterns detected
05:37:28 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=359 latency_ms=7010.7 cost_usd=0.0054
05:37:28 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:37:28 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:37:28 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:37:28 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:37:28 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:37:28 signed hash_algo=sha256 hash=sha256:63616e1f65793acf0fe0eb1eb66e4125f9055e171f7d4628591ab4745ba5439b

Content hash

sha256:63616e1f65793acf0fe0eb1eb66e4125f9055e171f7d4628591ab4745ba5439b

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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