The Mechanism · Gated-generation receipt

gen-explain-prime-factorization-as-you-would-to-a-capable-studen-d541

stable pending witness
2026-05-29 08:54:57 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain prime factorization as you would to a capable student, in 3-4 sentences.
80 chars

Generation

Prime factorization is breaking down a number into the prime numbers that multiply together to create it—like finding the basic building blocks of that number. For example, 12 breaks down into 2 × 2 × 3, where 2 and 3 are prime numbers (numbers only divisible by 1 and themselves). Every whole number greater than 1 has exactly one unique prime factorization, which makes this a powerful tool in mathematics. You can find it by repeatedly dividing by the smallest prime number possible until you're left with only primes.
29 tokens in · 125 tokens out · 3835 ms · $0.002

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
3842.8 ms
Base LLM
3835.0 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.002

Trail

08:54:57 received prompt_chars=80 verifiers=['scripture_anchors', 'theology_doctrine']
08:54:57 red_gate decision=pass reason=no disqualifying input patterns detected
08:55:01 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=125 latency_ms=3835.0 cost_usd=0.002
08:55:01 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:55:01 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:55:01 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:55:01 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:55:01 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:55:01 signed hash_algo=sha256 hash=sha256:23987108b678c447148df560b28a39f36750909ab628b8a101f7d45927fbd0a4

Content hash

sha256:23987108b678c447148df560b28a39f36750909ab628b8a101f7d45927fbd0a4

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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