The Mechanism · Gated-generation receipt

gen-state-greatest-common-divisor-precisely-and-explain-why-it-m-576a

stable pending witness
2026-05-29 04:11:10 UTC · anthropic/claude-sonnet-4-5

Prompt

State greatest common divisor precisely and explain why it matters in 2-3 sentences.
84 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. The GCD matters because it's fundamental to simplifying fractions (divide numerator and denominator by their GCD), solving problems involving periodic patterns or grouping, and forms the basis for important algorithms in cryptography and number theory. It reveals the deepest multiplicative relationship between numbers.
26 tokens in · 95 tokens out · 2791 ms · $0.0015

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
2797.8 ms
Base LLM
2790.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0015

Trail

04:11:10 received prompt_chars=84 verifiers=['scripture_anchors', 'theology_doctrine']
04:11:10 red_gate decision=pass reason=no disqualifying input patterns detected
04:11:13 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=95 latency_ms=2790.7 cost_usd=0.0015
04:11:13 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:11:13 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:11:13 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:11:13 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:11:13 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:11:13 signed hash_algo=sha256 hash=sha256:23bcef659b19cdbb4295d654b8a612633574b97cbee3342284fa9ae4e96e807e

Content hash

sha256:23bcef659b19cdbb4295d654b8a612633574b97cbee3342284fa9ae4e96e807e

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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