The Mechanism · Gated-generation receipt

gen-define-the-sieve-of-eratosthenes-and-give-one-short-worked-e-e436

stable pending witness
2026-05-29 05:22:20 UTC · anthropic/claude-sonnet-4-5

Prompt

Define the sieve of Eratosthenes and give one short worked example.
67 chars

Generation

# Sieve of Eratosthenes **Definition:** An ancient algorithm for finding all prime numbers up to a given limit by iteratively marking the multiples of each prime as composite. ## How it works: 1. List all numbers from 2 to n 2. Start with the first unmarked number (it's prime) 3. Mark all its multiples as composite 4. Repeat with the next unmarked number 5. Continue until you've processed all numbers ## Worked Example: Find all primes up to 30 **Initial list:** 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 **Step 1:** 2 is prime. Cross out multiples of 2: - 2, 3, ~~4~~, 5, ~~6~~, 7, ~~8~~, 9, ~~10~~, 11, ~~12~~, 13, ~~14~~, 15, ~~16~~, 17, ~~18~~, 19, ~~20~~, 21, ~~22~~, 23, ~~24~~, 25, ~~26~~, 27, ~~28~~, 29, ~~30~~ **Step 2:** 3 is prime. Cross out multiples of 3: - 2, 3, 5, 7, ~~9~~, 11, 13, ~~15~~, 17, 19, ~~21~~, 23, 25, ~~27~~, 29 **Step 3:** 5 is prime. Cross out multiples of 5: - 2, 3, 5, 7, 11, 13, 17, 19, 23, ~~25~~, 29 **Step 4:** 7 is prime, but 7² = 49 > 30, so we're done! **Primes up to 30:** 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
25 tokens in · 547 tokens out · 7019 ms · $0.0083

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
7032.4 ms
Base LLM
7018.6 ms
Verifiers
1.1 ms
Gates
0.1 ms
Cost
$0.0083

Trail

05:22:20 received prompt_chars=67 verifiers=['scripture_anchors', 'theology_doctrine']
05:22:20 red_gate decision=pass reason=no disqualifying input patterns detected
05:22:27 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=547 latency_ms=7018.6 cost_usd=0.0083
05:22:27 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:22:27 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:22:27 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:22:27 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:22:27 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:22:27 signed hash_algo=sha256 hash=sha256:66a3e4986e94eedf2f5c0bc27666a1be27fb73b8acd37ac71a4c88adfb443fe1

Content hash

sha256:66a3e4986e94eedf2f5c0bc27666a1be27fb73b8acd37ac71a4c88adfb443fe1

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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