The Mechanism · Gated-generation receipt

gen-define-prime-factorization-and-give-one-short-worked-example-9a70

stable pending witness
2026-05-29 05:58:26 UTC · anthropic/claude-sonnet-4-5

Prompt

Define prime factorization and give one short worked example.
61 chars

Generation

# Prime Factorization **Definition:** Prime factorization is the process of expressing a composite number as a product of prime numbers. Every composite number can be written uniquely as a product of primes (this is called the Fundamental Theorem of Arithmetic). ## Worked Example Find the prime factorization of **60**. **Solution:** ``` 60 = 2 × 30 = 2 × 2 × 15 = 2 × 2 × 3 × 5 = 2² × 3 × 5 ``` Therefore, the prime factorization of 60 is **2² × 3 × 5**.
19 tokens in · 160 tokens out · 2794 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
2802.3 ms
Base LLM
2793.9 ms
Verifiers
0.1 ms
Gates
0.1 ms
Cost
$0.0025

Trail

05:58:26 received prompt_chars=61 verifiers=['scripture_anchors', 'theology_doctrine']
05:58:26 red_gate decision=pass reason=no disqualifying input patterns detected
05:58:29 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=160 latency_ms=2793.9 cost_usd=0.0025
05:58:29 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:58:29 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:58:29 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:58:29 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:58:29 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:58:29 signed hash_algo=sha256 hash=sha256:47e413eea1a90b733deec135ce3ccd6ec62bf39643cfbdc7707e17a1380f112c

Content hash

sha256:47e413eea1a90b733deec135ce3ccd6ec62bf39643cfbdc7707e17a1380f112c

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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