The Mechanism · Gated-generation receipt

gen-define-perfect-numbers-and-give-one-short-worked-example-fc88

stable pending witness
2026-05-29 07:42:24 UTC · anthropic/claude-sonnet-4-5

Prompt

Define perfect numbers and give one short worked example.
57 chars

Generation

# Perfect Numbers A **perfect number** is a positive integer that equals the sum of its proper divisors (all positive divisors excluding the number itself). ## Worked Example: 6 Let's verify that 6 is a perfect number. **Proper divisors of 6:** 1, 2, 3 **Sum of proper divisors:** 1 + 2 + 3 = 6 ✓ Since the sum equals the original number, **6 is perfect**. --- *Note: The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28*
17 tokens in · 153 tokens out · 3681 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
3686.0 ms
Base LLM
3680.5 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0023

Trail

07:42:24 received prompt_chars=57 verifiers=['scripture_anchors', 'theology_doctrine']
07:42:24 red_gate decision=pass reason=no disqualifying input patterns detected
07:42:28 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=17 tokens_out=153 latency_ms=3680.5 cost_usd=0.0023
07:42:28 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:42:28 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:42:28 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:42:28 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:42:28 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:42:28 signed hash_algo=sha256 hash=sha256:05a434fcdf665d202ef3aa099ac37c49a368f0332c7e23137ddd88ed57960539

Content hash

sha256:05a434fcdf665d202ef3aa099ac37c49a368f0332c7e23137ddd88ed57960539

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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