The Mechanism · Gated-generation receipt

gen-briefly-explain-np-completeness-and-one-common-misconception-dcac

stable pending witness
2026-05-29 08:11:48 UTC · anthropic/claude-sonnet-4-5

Prompt

Briefly explain NP-completeness and one common misconception about it.
70 chars

Generation

# NP-Completeness **NP-complete** problems are the "hardest" problems in NP (problems verifiable in polynomial time). A problem is NP-complete if: 1. It's in NP (solutions can be verified quickly) 2. Every other problem in NP can be reduced to it in polynomial time If you could solve any NP-complete problem efficiently, you could solve *all* NP problems efficiently. ## Common Misconception **"NP means 'not polynomial' or unsolvable"** ❌ Actually, NP stands for **Nondeterministic Polynomial time**. NP-complete problems may very well have polynomial-time solutions—we just haven't found any yet (and most experts believe none exist). The question of whether P = NP remains one of the biggest open problems in computer science.
23 tokens in · 194 tokens out · 5010 ms · $0.003

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
5017.6 ms
Base LLM
5009.7 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.003

Trail

08:11:48 received prompt_chars=70 verifiers=['scripture_anchors', 'theology_doctrine']
08:11:48 red_gate decision=pass reason=no disqualifying input patterns detected
08:11:53 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=23 tokens_out=194 latency_ms=5009.7 cost_usd=0.003
08:11:53 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:11:53 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:11:53 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:11:53 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:11:53 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:11:53 signed hash_algo=sha256 hash=sha256:31799a0fd64a08c3da6253b90a3dc2a0077aa021f1fd1c47ec378f1c8cbed0d9

Content hash

sha256:31799a0fd64a08c3da6253b90a3dc2a0077aa021f1fd1c47ec378f1c8cbed0d9

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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