The Mechanism · Gated-generation receipt

gen-state-the-sieve-of-eratosthenes-precisely-and-explain-why-it-4ddd

stable pending witness
2026-05-29 05:01:54 UTC · anthropic/claude-sonnet-4-5

Prompt

State the sieve of Eratosthenes precisely and explain why it matters in 2-3 sentences.
86 chars

Generation

## The Sieve of Eratosthenes **Precise statement:** To find all prime numbers up to n, list all integers from 2 to n, then iteratively mark as composite all multiples of each prime p (starting with p² up to n), beginning with p=2 and continuing with each unmarked number. **Why it matters:** The sieve is one of the most efficient algorithms for finding all small primes and has remained relevant for over 2000 years because it's simple to implement yet remarkably fast for its purpose. It provides a concrete, constructive method for generating primes rather than just testing individual numbers, making it foundational in number theory and computational mathematics.
32 tokens in · 153 tokens out · 4441 ms · $0.0024

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
4448.8 ms
Base LLM
4440.8 ms
Verifiers
0.4 ms
Gates
0.1 ms
Cost
$0.0024

Trail

05:01:54 received prompt_chars=86 verifiers=['scripture_anchors', 'theology_doctrine']
05:01:54 red_gate decision=pass reason=no disqualifying input patterns detected
05:01:59 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=32 tokens_out=153 latency_ms=4440.8 cost_usd=0.0024
05:01:59 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:01:59 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:01:59 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:01:59 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:01:59 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:01:59 signed hash_algo=sha256 hash=sha256:a8b849c30f73756b80f3e2ca0cb8f7be0a7da789f951058cd5c8da356dcdc784

Content hash

sha256:a8b849c30f73756b80f3e2ca0cb8f7be0a7da789f951058cd5c8da356dcdc784

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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