The Mechanism · Gated-generation receipt

gen-explain-the-euclidean-algorithm-as-you-would-to-a-capable-st-7d30

stable pending witness
2026-05-29 03:42:27 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain the Euclidean algorithm as you would to a capable student, in 3-4 sentences.
84 chars

Generation

The Euclidean algorithm is an efficient method for finding the greatest common divisor (GCD) of two numbers. It works by repeatedly replacing the larger number with the remainder when the larger is divided by the smaller, until you reach a remainder of zero—at that point, the last non-zero remainder is the GCD. For example, to find GCD(48, 18): 48 = 2(18) + 12, then 18 = 1(12) + 6, then 12 = 2(6) + 0, so the GCD is 6. This method is much faster than factoring both numbers, especially for large integers.
31 tokens in · 149 tokens out · 3364 ms · $0.0023

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
3371.6 ms
Base LLM
3364.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0023

Trail

03:42:27 received prompt_chars=84 verifiers=['scripture_anchors', 'theology_doctrine']
03:42:27 red_gate decision=pass reason=no disqualifying input patterns detected
03:42:31 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=149 latency_ms=3364.2 cost_usd=0.0023
03:42:31 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:42:31 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:42:31 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:42:31 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:42:31 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:42:31 signed hash_algo=sha256 hash=sha256:0aa899c31ae1e01479da50b22a2710b71a85952919183b9034ae869cf93b32c1

Content hash

sha256:0aa899c31ae1e01479da50b22a2710b71a85952919183b9034ae869cf93b32c1

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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