The Mechanism · Gated-generation receipt

gen-what-is-the-significance-of-perfect-numbers-answer-concisely-0c98

stable pending witness
2026-05-29 08:58:42 UTC · anthropic/claude-sonnet-4-5

Prompt

What is the significance of perfect numbers? Answer concisely in 2-3 sentences.
79 chars

Generation

Perfect numbers are integers equal to the sum of their proper divisors (e.g., 6 = 1+2+3). They have fascinated mathematicians since ancient Greece due to their rarity and elegant mathematical properties. They remain significant today because many unsolved problems surround them, including whether any odd perfect numbers exist and whether infinitely many perfect numbers exist.
27 tokens in · 80 tokens out · 2952 ms · $0.0013

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
2959.7 ms
Base LLM
2951.9 ms
Verifiers
0.1 ms
Gates
0.0 ms
Cost
$0.0013

Trail

08:58:42 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
08:58:42 red_gate decision=pass reason=no disqualifying input patterns detected
08:58:44 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=80 latency_ms=2951.9 cost_usd=0.0013
08:58:44 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:58:44 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:58:44 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:58:44 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:58:44 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:58:44 signed hash_algo=sha256 hash=sha256:e9cc705d0c0ee7345083a737aab3522b865e6921e4f393c4dacbac761cf5b03a

Content hash

sha256:e9cc705d0c0ee7345083a737aab3522b865e6921e4f393c4dacbac761cf5b03a

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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