The Mechanism · Gated-generation receipt

gen-state-np-completeness-precisely-and-explain-why-it-matters-i-1d6e

stable pending witness
2026-05-29 04:40:36 UTC · anthropic/claude-sonnet-4-5

Prompt

State NP-completeness precisely and explain why it matters in 2-3 sentences.
76 chars

Generation

# NP-Completeness **Precise Definition:** A problem is NP-complete if (1) it is in NP (solutions can be verified in polynomial time), and (2) every problem in NP can be reduced to it in polynomial time (it is NP-hard). **Why It Matters:** If any NP-complete problem has a polynomial-time solution, then P=NP and thousands of important problems become efficiently solvable. Conversely, proving a new problem is NP-complete provides strong evidence that no efficient algorithm exists, suggesting we should focus on approximations or heuristics instead of searching for optimal polynomial-time solutions.
27 tokens in · 146 tokens out · 3655 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
3664.2 ms
Base LLM
3655.0 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0023

Trail

04:40:36 received prompt_chars=76 verifiers=['scripture_anchors', 'theology_doctrine']
04:40:36 red_gate decision=pass reason=no disqualifying input patterns detected
04:40:40 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=27 tokens_out=146 latency_ms=3655.0 cost_usd=0.0023
04:40:40 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:40:40 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:40:40 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:40:40 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:40:40 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:40:40 signed hash_algo=sha256 hash=sha256:6cb86e9359026265f74c9f548ce528984c72e081bb9cee2db31157185a66b389

Content hash

sha256:6cb86e9359026265f74c9f548ce528984c72e081bb9cee2db31157185a66b389

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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