The Mechanism · Gated-generation receipt

gen-explain-bezout-s-identity-as-you-would-to-a-capable-student-6f63

stable pending witness
2026-05-29 06:34:25 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain Bezout's identity as you would to a capable student, in 3-4 sentences.
78 chars

Generation

Bezout's identity states that for any two integers a and b, there exist integers x and y such that ax + by = gcd(a,b), where gcd(a,b) is their greatest common divisor. In other words, you can always write the GCD of two numbers as a linear combination of those numbers using integer coefficients. For example, since gcd(12,8) = 4, we can find integers x and y where 12x + 8y = 4 (one solution is x = -1, y = 2, giving -12 + 16 = 4). The extended Euclidean algorithm provides a systematic way to find these coefficients x and y.
30 tokens in · 158 tokens out · 3744 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
3750.3 ms
Base LLM
3743.5 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

06:34:25 received prompt_chars=78 verifiers=['scripture_anchors', 'theology_doctrine']
06:34:25 red_gate decision=pass reason=no disqualifying input patterns detected
06:34:29 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=158 latency_ms=3743.5 cost_usd=0.0025
06:34:29 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:34:29 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:34:29 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:34:29 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:34:29 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:34:29 signed hash_algo=sha256 hash=sha256:db4b1474597d2ce19edbb4f7d9e8da41474ceb2530b5686f87898e18bb4483d9

Content hash

sha256:db4b1474597d2ce19edbb4f7d9e8da41474ceb2530b5686f87898e18bb4483d9

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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