The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-the-sieve-of-eratosthenes-state-any-ba0f

stable pending witness
2026-05-29 08:56:16 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain the sieve of Eratosthenes. State any key formula.
75 chars

Generation

The Sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to a given limit n. It works by iteratively marking the multiples of each prime as composite, starting with 2: mark all multiples 2k, 3k, 5k, etc. as non-prime. An optimization is that you only need to check primes up to √n, since any composite number ≤ n must have a prime factor ≤ √n. The unmarked numbers that remain are all the primes up to n.
32 tokens in · 125 tokens out · 4863 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
4870.0 ms
Base LLM
4863.0 ms
Verifiers
0.4 ms
Gates
0.1 ms
Cost
$0.002

Trail

08:56:16 received prompt_chars=75 verifiers=['scripture_anchors', 'theology_doctrine']
08:56:16 red_gate decision=pass reason=no disqualifying input patterns detected
08:56:20 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=32 tokens_out=125 latency_ms=4863.0 cost_usd=0.002
08:56:20 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:56:20 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:56:20 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:56:20 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:56:20 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:56:20 signed hash_algo=sha256 hash=sha256:06a8107b9dfb65352a1a3e136c171b45489605e213b91af679205940193a8963

Content hash

sha256:06a8107b9dfb65352a1a3e136c171b45489605e213b91af679205940193a8963

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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