The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-np-completeness-state-any-key-formu-084a

stable pending witness
2026-05-29 05:12:50 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain NP-completeness. State any key formula.
65 chars

Generation

NP-completeness refers to a class of decision problems that are among the hardest in NP (problems verifiable in polynomial time). A problem is NP-complete if: (1) it is in NP, and (2) every problem in NP can be reduced to it in polynomial time. The key relationship is: if any NP-complete problem can be solved in polynomial time, then P = NP, meaning **P ⊆ NP** and if an NP-complete problem has a polynomial solution, then **NP ⊆ P**, thus **P = NP**. Classic NP-complete problems include SAT (Boolean satisfiability), the traveling salesman problem, and graph coloring.
27 tokens in · 162 tokens out · 4213 ms · $0.0025

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
4220.9 ms
Base LLM
4213.5 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

05:12:50 received prompt_chars=65 verifiers=['scripture_anchors', 'theology_doctrine']
05:12:50 red_gate decision=pass reason=no disqualifying input patterns detected
05:12:54 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=162 latency_ms=4213.5 cost_usd=0.0025
05:12:54 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:12:54 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:12:54 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:12:54 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:12:54 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:12:54 signed hash_algo=sha256 hash=sha256:933d20c9c208d0240eed36ef4b563aa208059c1abbb0123fb89603d341cac0e7

Content hash

sha256:933d20c9c208d0240eed36ef4b563aa208059c1abbb0123fb89603d341cac0e7

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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