The Mechanism · Gated-generation receipt

gen-define-the-euclidean-algorithm-and-give-one-short-worked-exa-dcab

stable pending witness
2026-05-29 07:30:33 UTC · anthropic/claude-sonnet-4-5

Prompt

Define the Euclidean algorithm and give one short worked example.
65 chars

Generation

# Euclidean Algorithm The **Euclidean algorithm** is a method for finding the greatest common divisor (GCD) of two integers. It's based on the principle that: **gcd(a, b) = gcd(b, a mod b)** The algorithm repeatedly replaces the larger number with the remainder of dividing the larger by the smaller, until the remainder is 0. The last non-zero remainder is the GCD. ## Worked Example Find gcd(48, 18): ``` 48 = 18 × 2 + 12 18 = 12 × 1 + 6 12 = 6 × 2 + 0 ``` Since the remainder is now 0, we stop. The last non-zero remainder is **6**. Therefore, **gcd(48, 18) = 6**.
21 tokens in · 201 tokens out · 4421 ms · $0.0031

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
4429.2 ms
Base LLM
4420.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0031

Trail

07:30:33 received prompt_chars=65 verifiers=['scripture_anchors', 'theology_doctrine']
07:30:33 red_gate decision=pass reason=no disqualifying input patterns detected
07:30:38 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=21 tokens_out=201 latency_ms=4420.7 cost_usd=0.0031
07:30:38 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:30:38 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:30:38 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:30:38 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:30:38 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:30:38 signed hash_algo=sha256 hash=sha256:1727644b4cf10004b8b79b86b044dd12c20274dd1d92fc4cfb6e97f1753f4a0e

Content hash

sha256:1727644b4cf10004b8b79b86b044dd12c20274dd1d92fc4cfb6e97f1753f4a0e

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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