The Mechanism · Gated-generation receipt

gen-explain-the-sieve-of-eratosthenes-as-you-would-to-a-capable-30ba

stable pending witness
2026-05-29 08:48:50 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain the sieve of Eratosthenes as you would to a capable student, in 3-4 sentences.
86 chars

Generation

The Sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to a given limit. You start by listing all numbers from 2 to your limit, then repeatedly cross out multiples of each prime you find: first cross out all multiples of 2 (except 2 itself), then all multiples of 3 (except 3), then 5, and so on. The numbers that remain uncrossed are all the primes, because composite numbers will have been eliminated as multiples of smaller primes. It's called a "sieve" because you're filtering out composite numbers, letting only the primes pass through.
35 tokens in · 145 tokens out · 4352 ms · $0.0023

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
4360.8 ms
Base LLM
4351.6 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0023

Trail

08:48:50 received prompt_chars=86 verifiers=['scripture_anchors', 'theology_doctrine']
08:48:50 red_gate decision=pass reason=no disqualifying input patterns detected
08:48:54 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=35 tokens_out=145 latency_ms=4351.6 cost_usd=0.0023
08:48:54 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:48:54 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:48:54 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:48:54 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:48:54 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:48:54 signed hash_algo=sha256 hash=sha256:908134dd0475b35913348ebeaba2d634dcd482f782b303dc1e18636b629747ec

Content hash

sha256:908134dd0475b35913348ebeaba2d634dcd482f782b303dc1e18636b629747ec

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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