The Mechanism · Gated-generation receipt

gen-explain-asymptotic-big-o-complexity-as-you-would-to-a-capabl-3d88

stable pending witness
2026-05-29 05:46:19 UTC · anthropic/claude-sonnet-4-5

Prompt

Explain asymptotic (big-O) complexity as you would to a capable student, in 3-4 sentences.
90 chars

Generation

# Big-O Complexity Big-O notation describes how an algorithm's runtime or memory usage grows as the input size increases, focusing on the worst-case scenario. Instead of measuring exact execution time (which varies by computer), we classify algorithms by their growth rate—for example, O(n) means time grows linearly with input size, while O(n²) means it grows quadratically. We ignore constants and lower-order terms because we care about behavior with very large inputs: an O(n) algorithm will always eventually outperform an O(n²) one as data gets big enough. This helps us compare algorithms and choose the right approach before writing any code.
34 tokens in · 145 tokens out · 5427 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
5434.8 ms
Base LLM
5427.0 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0023

Trail

05:46:19 received prompt_chars=90 verifiers=['scripture_anchors', 'theology_doctrine']
05:46:19 red_gate decision=pass reason=no disqualifying input patterns detected
05:46:24 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=34 tokens_out=145 latency_ms=5427.0 cost_usd=0.0023
05:46:24 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:46:24 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:46:24 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:46:24 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:46:24 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:46:24 signed hash_algo=sha256 hash=sha256:0b154efdf9e2aae5cf1191292ad6d105260dd9903446fbc6a7637c70ff115368

Content hash

sha256:0b154efdf9e2aae5cf1191292ad6d105260dd9903446fbc6a7637c70ff115368

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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