The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-quicksort-and-its-pivot-state-any-k-8678

stable pending witness
2026-05-29 05:46:00 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain quicksort and its pivot. State any key formula.
73 chars

Generation

Quicksort is a divide-and-conquer sorting algorithm that works by selecting a "pivot" element from the array and partitioning the other elements into two sub-arrays: those less than the pivot and those greater than the pivot. The pivot can be chosen in various ways (first element, last element, random, or median), and this choice affects performance. The sub-arrays are then recursively sorted. **Key formula:** Average time complexity is **O(n log n)**, but worst-case is **O(n²)** when the pivot consistently splits the array poorly (e.g., already sorted array with first/last element as pivot).
28 tokens in · 143 tokens out · 4490 ms · $0.0022

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
4498.7 ms
Base LLM
4489.7 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0022

Trail

05:46:00 received prompt_chars=73 verifiers=['scripture_anchors', 'theology_doctrine']
05:46:00 red_gate decision=pass reason=no disqualifying input patterns detected
05:46:04 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=28 tokens_out=143 latency_ms=4489.7 cost_usd=0.0022
05:46:04 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:46:04 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:46:04 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:46:04 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:46:04 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:46:04 signed hash_algo=sha256 hash=sha256:1e3083392c8e85c3a639843dc9cb6fef9d1b50c46895576c5a8bb5e7e694f23a

Content hash

sha256:1e3083392c8e85c3a639843dc9cb6fef9d1b50c46895576c5a8bb5e7e694f23a

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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