The Mechanism · Gated-generation receipt

gen-explain-perfect-numbers-as-you-would-to-a-capable-student-in-b8e4

stable pending witness
2026-05-29 06:21:45 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain perfect numbers as you would to a capable student, in 3-4 sentences.
76 chars

Generation

A perfect number is a positive integer that equals the sum of all its proper divisors (all divisors except the number itself). For example, 6 is perfect because its proper divisors are 1, 2, and 3, and 1 + 2 + 3 = 6. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28. Perfect numbers are quite rare—only 51 are known to exist, and they're connected to a special class of prime numbers called Mersenne primes.
27 tokens in · 134 tokens out · 4329 ms · $0.0021

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
4335.2 ms
Base LLM
4328.8 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

06:21:45 received prompt_chars=76 verifiers=['scripture_anchors', 'theology_doctrine']
06:21:45 red_gate decision=pass reason=no disqualifying input patterns detected
06:21:50 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=134 latency_ms=4328.8 cost_usd=0.0021
06:21:50 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:21:50 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:21:50 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:21:50 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:21:50 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:21:50 signed hash_algo=sha256 hash=sha256:a31702379896470fbd43f893a9144b92d271df93a2ef1b89cdbff2e1160e0eda

Content hash

sha256:a31702379896470fbd43f893a9144b92d271df93a2ef1b89cdbff2e1160e0eda

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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