The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-euclidean-algorithm-state-any-k-f710

stable pending witness
2026-05-29 05:34:42 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the Euclidean algorithm. State any key formula.
73 chars

Generation

The Euclidean algorithm is a method for finding the greatest common divisor (GCD) of two integers by repeatedly applying the division algorithm. It works by dividing the larger number by the smaller number, then replacing the larger number with the smaller number and the smaller number with the remainder, repeating until the remainder is zero. The last non-zero remainder is the GCD. The key formula is: **gcd(a, b) = gcd(b, a mod b)**, where "a mod b" is the remainder when a is divided by b.
28 tokens in · 122 tokens out · 6055 ms · $0.0019

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
6073.9 ms
Base LLM
6054.6 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0019

Trail

05:34:42 received prompt_chars=73 verifiers=['scripture_anchors', 'theology_doctrine']
05:34:42 red_gate decision=pass reason=no disqualifying input patterns detected
05:34:48 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=122 latency_ms=6054.6 cost_usd=0.0019
05:34:48 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:34:48 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:34:48 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:34:48 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:34:48 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:34:48 signed hash_algo=sha256 hash=sha256:bc3a67f73fe1775ba6074e987ad136b63092b974341f0c771760a8eb5c83367f

Content hash

sha256:bc3a67f73fe1775ba6074e987ad136b63092b974341f0c771760a8eb5c83367f

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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