The Mechanism · Gated-generation receipt

gen-define-greatest-common-divisor-and-give-one-short-worked-exa-828a

stable pending witness
2026-05-29 04:46:11 UTC · anthropic/claude-sonnet-4-5

Prompt

Define greatest common divisor and give one short worked example.
65 chars

Generation

# Greatest Common Divisor (GCD) **Definition:** The greatest common divisor of two integers is the largest positive integer that divides both numbers evenly (with no remainder). ## Worked Example Find the GCD of 48 and 18. **Method: List the divisors** Divisors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Divisors of 18: 1, 2, 3, 6, 9, 18 Common divisors: 1, 2, 3, 6 Therefore, **GCD(48, 18) = 6** --- *Alternative quick method (Euclidean algorithm):* - 48 = 18 × 2 + 12 - 18 = 12 × 1 + 6 - 12 = 6 × 2 + 0 **GCD = 6** (the last non-zero remainder)
19 tokens in · 242 tokens out · 5375 ms · $0.0037

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
5381.9 ms
Base LLM
5374.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0037

Trail

04:46:11 received prompt_chars=65 verifiers=['scripture_anchors', 'theology_doctrine']
04:46:11 red_gate decision=pass reason=no disqualifying input patterns detected
04:46:16 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=242 latency_ms=5374.6 cost_usd=0.0037
04:46:16 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:46:16 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:46:16 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:46:16 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:46:16 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:46:16 signed hash_algo=sha256 hash=sha256:7c599c576f187534597bdbc3ae86b4e7aefcd12b598d996b0aafa1c5312e1c90

Content hash

sha256:7c599c576f187534597bdbc3ae86b4e7aefcd12b598d996b0aafa1c5312e1c90

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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