The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-the-sieve-of-eratosthenes-answer-14b5

stable pending witness
2026-05-29 08:21:52 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of the sieve of Eratosthenes? Answer concisely in 2-3 sentences.
89 chars

Generation

The Sieve of Eratosthenes is one of the oldest and most efficient algorithms for finding all prime numbers up to a specified integer. It works by iteratively marking the multiples of each prime as composite, leaving only primes unmarked. This ancient method, dating back to the 3rd century BCE, remains widely used in mathematics and computer science for its simplicity and effectiveness.
35 tokens in · 85 tokens out · 2367 ms · $0.0014

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
2379.2 ms
Base LLM
2366.7 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0014

Trail

08:21:52 received prompt_chars=89 verifiers=['scripture_anchors', 'theology_doctrine']
08:21:52 red_gate decision=pass reason=no disqualifying input patterns detected
08:21:55 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=35 tokens_out=85 latency_ms=2366.7 cost_usd=0.0014
08:21:55 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:21:55 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:21:55 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:21:55 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:21:55 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:21:55 signed hash_algo=sha256 hash=sha256:c8bcef3d253620e271e556421cdcf2eb7a44fbec7709daf270276fcd0fda8312

Content hash

sha256:c8bcef3d253620e271e556421cdcf2eb7a44fbec7709daf270276fcd0fda8312

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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