The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-perfect-numbers-state-any-key-formu-d002

stable pending witness
2026-05-29 08:06:22 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain perfect numbers. State any key formula.
65 chars

Generation

A perfect number is a positive integer that equals the sum of its proper divisors (all positive divisors excluding the number itself). For example, 6 is perfect because 6 = 1 + 2 + 3, and 28 is perfect because 28 = 1 + 2 + 4 + 7 + 14. The **Euclid-Euler theorem** provides the formula for even perfect numbers: **n = 2^(p-1) × (2^p - 1)**, where both p and (2^p - 1) must be prime. It remains unknown whether any odd perfect numbers exist.
24 tokens in · 150 tokens out · 3705 ms · $0.0023

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
3716.2 ms
Base LLM
3705.1 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0023

Trail

08:06:22 received prompt_chars=65 verifiers=['scripture_anchors', 'theology_doctrine']
08:06:22 red_gate decision=pass reason=no disqualifying input patterns detected
08:06:25 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=150 latency_ms=3705.1 cost_usd=0.0023
08:06:25 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:06:25 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:06:25 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:06:25 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:06:25 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:06:25 signed hash_algo=sha256 hash=sha256:0cfb28582e4f3019606225cbd2468483950a8f01a240ac5ca46a738fc52f52da

Content hash

sha256:0cfb28582e4f3019606225cbd2468483950a8f01a240ac5ca46a738fc52f52da

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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