The Mechanism · Gated-generation receipt

gen-explain-np-completeness-as-you-would-to-a-capable-student-in-481c

stable pending witness
2026-05-29 03:59:43 UTC · anthropic/claude-sonnet-4-5

Prompt

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

Generation

NP-completeness is about problems where we can quickly verify a proposed solution, but don't know any efficient way to find that solution in the first place. An NP-complete problem has the special property that if you could solve it efficiently, you could solve thousands of other hard problems efficiently too—they're the "hardest" problems in NP. The classic example is the traveling salesman problem: given a proposed route, you can easily check its length, but finding the shortest route among all possibilities seems to require checking exponentially many options. Whether these problems actually *require* exponential time or we just haven't been clever enough to find faster algorithms is the famous unsolved P vs NP question.
30 tokens in · 149 tokens out · 5792 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
5803.0 ms
Base LLM
5792.5 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0023

Trail

03:59:43 received prompt_chars=76 verifiers=['scripture_anchors', 'theology_doctrine']
03:59:43 red_gate decision=pass reason=no disqualifying input patterns detected
03:59:49 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=30 tokens_out=149 latency_ms=5792.5 cost_usd=0.0023
03:59:49 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:59:49 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:59:49 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:59:49 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:59:49 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:59:49 signed hash_algo=sha256 hash=sha256:a26692c810581ea4550c88500fc7171aa592ac741c1cdc256aec6c6ab1981bc7

Content hash

sha256:a26692c810581ea4550c88500fc7171aa592ac741c1cdc256aec6c6ab1981bc7

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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