The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-merge-sort-state-any-key-formula-0f9a

stable pending witness
2026-05-29 08:23:35 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain merge sort. State any key formula.
60 chars

Generation

Merge sort is a divide-and-conquer sorting algorithm that recursively splits an array into two halves until each subarray contains a single element, then merges these subarrays back together in sorted order. The merging process compares elements from two sorted subarrays and combines them into a larger sorted array. The time complexity is **O(n log n)** in all cases, where n is the number of elements, because the array is divided log n times and merging takes O(n) time at each level. The space complexity is O(n) due to the temporary arrays needed for merging.
24 tokens in · 135 tokens out · 3443 ms · $0.0021

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
3450.2 ms
Base LLM
3442.5 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0021

Trail

08:23:35 received prompt_chars=60 verifiers=['scripture_anchors', 'theology_doctrine']
08:23:35 red_gate decision=pass reason=no disqualifying input patterns detected
08:23:38 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=24 tokens_out=135 latency_ms=3442.5 cost_usd=0.0021
08:23:38 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:23:38 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:23:38 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:23:38 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:23:38 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:23:38 signed hash_algo=sha256 hash=sha256:27b3e7e581c03ef685ae9e465ee9f5904622cab05e2b598b077126fc36d73f6c

Content hash

sha256:27b3e7e581c03ef685ae9e465ee9f5904622cab05e2b598b077126fc36d73f6c

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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