The Mechanism · Gated-generation receipt

gen-briefly-explain-greatest-common-divisor-and-one-common-misco-2266

stable pending witness
2026-05-29 03:38:45 UTC · anthropic/claude-sonnet-4-5

Prompt

Briefly explain greatest common divisor and one common misconception about it.
78 chars

Generation

## Greatest Common Divisor (GCD) The **greatest common divisor** of two or more integers is the largest positive integer that divides all of them without leaving a remainder. **Example:** GCD(12, 18) = 6, because 6 is the largest number that divides both 12 and 18 evenly. ## Common Misconception **"The GCD of two numbers is always smaller than both numbers."** While this is true when the numbers are different, it's false when one number divides the other. For instance, GCD(12, 24) = 12, which equals the smaller number. More specifically, the GCD of any number with itself is that number: GCD(7, 7) = 7.
22 tokens in · 173 tokens out · 4773 ms · $0.0027

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
4780.1 ms
Base LLM
4773.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0027

Trail

03:38:45 received prompt_chars=78 verifiers=['scripture_anchors', 'theology_doctrine']
03:38:45 red_gate decision=pass reason=no disqualifying input patterns detected
03:38:50 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=22 tokens_out=173 latency_ms=4773.1 cost_usd=0.0027
03:38:50 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:38:50 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:38:50 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:38:50 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:38:50 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:38:50 signed hash_algo=sha256 hash=sha256:21dcd635f0a5c9f6464f1dcaa15163ad2fbf95950bf4cf09640589c3cac06bc8

Content hash

sha256:21dcd635f0a5c9f6464f1dcaa15163ad2fbf95950bf4cf09640589c3cac06bc8

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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