The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-greatest-common-divisor-state-any-k-7e50

stable pending witness
2026-05-29 08:42:11 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain greatest common divisor. State any key formula.
73 chars

Generation

The greatest common divisor (GCD) of two or more integers is the largest positive integer that divides all of them without leaving a remainder. For example, GCD(12, 18) = 6 since 6 is the largest number that divides both 12 and 18 evenly. A key formula is the **Euclidean algorithm**: GCD(a, b) = GCD(b, a mod b), which is applied recursively until b = 0, at which point GCD(a, 0) = a. Additionally, **Bézout's identity** states that for any integers a and b, there exist integers x and y such that ax + by = GCD(a, b).
26 tokens in · 163 tokens out · 3769 ms · $0.0025

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
3775.7 ms
Base LLM
3768.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

08:42:11 received prompt_chars=73 verifiers=['scripture_anchors', 'theology_doctrine']
08:42:11 red_gate decision=pass reason=no disqualifying input patterns detected
08:42:15 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=163 latency_ms=3768.7 cost_usd=0.0025
08:42:15 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:42:15 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:42:15 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:42:15 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:42:15 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:42:15 signed hash_algo=sha256 hash=sha256:95503b5e59f0d3044cbff8ecb7745e45a7c573b2292793e2e144063e33121543

Content hash

sha256:95503b5e59f0d3044cbff8ecb7745e45a7c573b2292793e2e144063e33121543

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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