The Mechanism · Gated-generation receipt

gen-state-asymptotic-big-o-complexity-precisely-and-explain-why-61f3

stable pending witness
2026-05-29 04:09:50 UTC · anthropic/claude-sonnet-4-5

Prompt

State asymptotic (big-O) complexity precisely and explain why it matters in 2-3 sentences.
90 chars

Generation

# Big-O Complexity **Definition**: Big-O notation describes the upper bound of an algorithm's growth rate as input size approaches infinity. For example, O(n) means runtime grows linearly with input size, O(n²) means quadratic growth, and O(log n) means logarithmic growth. **Why it matters**: Big-O allows developers to predict how algorithms scale with larger inputs and compare efficiency between different approaches, independent of hardware or implementation details. The difference between O(n) and O(n²) can mean the difference between a program running in seconds versus hours on large datasets—making it critical for writing performant, production-ready code.
31 tokens in · 146 tokens out · 7058 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
7064.5 ms
Base LLM
7057.7 ms
Verifiers
0.3 ms
Gates
0.0 ms
Cost
$0.0023

Trail

04:09:50 received prompt_chars=90 verifiers=['scripture_anchors', 'theology_doctrine']
04:09:50 red_gate decision=pass reason=no disqualifying input patterns detected
04:09:57 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=146 latency_ms=7057.7 cost_usd=0.0023
04:09:57 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
04:09:57 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
04:09:57 floor_gate decision=pass reason=output above protective minimum; no mismatches
04:09:57 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
04:09:57 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
04:09:57 signed hash_algo=sha256 hash=sha256:28c1653fbc5c6009f547c2b1029ae64ff70ad5356eb7ed4b47bb450b27e1dfde

Content hash

sha256:28c1653fbc5c6009f547c2b1029ae64ff70ad5356eb7ed4b47bb450b27e1dfde

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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