The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-prime-factorization-answer-conci-4974

stable pending witness
2026-05-29 06:45:22 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of prime factorization? Answer concisely in 2-3 sentences.
83 chars

Generation

Prime factorization is significant because it reveals the unique building blocks of any whole number—every integer greater than 1 can be expressed as a product of primes in exactly one way (Fundamental Theorem of Arithmetic). This property is essential for many mathematical operations like finding greatest common divisors and least common multiples, and forms the foundation of modern cryptography systems like RSA encryption.
29 tokens in · 84 tokens out · 2420 ms · $0.0013

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
2427.2 ms
Base LLM
2420.5 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0013

Trail

06:45:22 received prompt_chars=83 verifiers=['scripture_anchors', 'theology_doctrine']
06:45:22 red_gate decision=pass reason=no disqualifying input patterns detected
06:45:25 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=29 tokens_out=84 latency_ms=2420.5 cost_usd=0.0013
06:45:25 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:45:25 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:45:25 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:45:25 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:45:25 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:45:25 signed hash_algo=sha256 hash=sha256:7322d0c30ab2ce8f62db0ff84264bf76b5b2ebdd25a7ca7722e8952a33aa3763

Content hash

sha256:7322d0c30ab2ce8f62db0ff84264bf76b5b2ebdd25a7ca7722e8952a33aa3763

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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