The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-priority-queue-state-any-key-form-48e9

stable pending witness
2026-05-29 07:56:09 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a priority queue. State any key formula.
66 chars

Generation

A priority queue is a data structure where each element has an associated priority, and elements are served in order of their priority rather than their insertion order. The highest (or lowest) priority element is always removed first, making it ideal for scheduling tasks or implementing algorithms like Dijkstra's shortest path. **Key formula:** For a binary heap implementation, the parent-child relationships are: - Parent of node at index i: **⌊(i-1)/2⌋** - Left child of node at index i: **2i + 1** - Right child of node at index i: **2i + 2**
25 tokens in · 140 tokens out · 3096 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
3106.0 ms
Base LLM
3096.2 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0022

Trail

07:56:09 received prompt_chars=66 verifiers=['scripture_anchors', 'theology_doctrine']
07:56:09 red_gate decision=pass reason=no disqualifying input patterns detected
07:56:12 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=25 tokens_out=140 latency_ms=3096.2 cost_usd=0.0022
07:56:12 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:56:12 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:56:12 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:56:12 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:56:12 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:56:12 signed hash_algo=sha256 hash=sha256:94c6d1a589207a5a480260c549c48409ae29443d17c30db1738ddbb1975edee3

Content hash

sha256:94c6d1a589207a5a480260c549c48409ae29443d17c30db1738ddbb1975edee3

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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