The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-asymptotic-big-o-complexity-state-a-f213

stable pending witness
2026-05-29 05:42:16 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain asymptotic (big-O) complexity. State any key formula.
79 chars

Generation

# Asymptotic (Big-O) Complexity Big-O notation describes how an algorithm's runtime or space requirements grow as the input size increases, focusing on the dominant term while ignoring constants and lower-order terms. It provides an upper bound on the growth rate, allowing us to compare algorithm efficiency at scale. **Key formula:** f(n) = O(g(n)) means there exist constants c > 0 and n₀ such that f(n) ≤ c·g(n) for all n ≥ n₀. For example, an algorithm with runtime 3n² + 5n + 2 is O(n²) because the quadratic term dominates as n becomes large.
31 tokens in · 165 tokens out · 3614 ms · $0.0026

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
3626.3 ms
Base LLM
3613.5 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0026

Trail

05:42:16 received prompt_chars=79 verifiers=['scripture_anchors', 'theology_doctrine']
05:42:16 red_gate decision=pass reason=no disqualifying input patterns detected
05:42:19 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=165 latency_ms=3613.5 cost_usd=0.0026
05:42:19 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:42:19 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:42:19 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:42:19 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:42:19 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:42:19 signed hash_algo=sha256 hash=sha256:e2a0f0891112c19e57bd81333646ab1f41bba6b6e72cb9ad5f85b8cb8a3fb551

Content hash

sha256:e2a0f0891112c19e57bd81333646ab1f41bba6b6e72cb9ad5f85b8cb8a3fb551

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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