The Mechanism · Gated-generation receipt

gen-state-a-balanced-tree-rotation-precisely-and-explain-why-it-1691

stable pending witness
2026-05-29 06:18:27 UTC · anthropic/claude-sonnet-4-5

Prompt

State a balanced tree rotation precisely and explain why it matters in 2-3 sentences.
85 chars

Generation

# Balanced Tree Rotation **Right Rotation**: Given a node Y with left child X, make X the new parent by setting Y's left child to X's right child, then set X's right child to Y. **Why it matters**: Rotations preserve the binary search tree property (in-order traversal remains unchanged) while reducing tree height, which keeps operations like search, insert, and delete at O(log n) time complexity instead of degrading to O(n) in unbalanced cases. They are the fundamental operation used by self-balancing trees like AVL and Red-Black trees to maintain logarithmic performance guarantees.
26 tokens in · 141 tokens out · 4330 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
4341.9 ms
Base LLM
4329.9 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0022

Trail

06:18:27 received prompt_chars=85 verifiers=['scripture_anchors', 'theology_doctrine']
06:18:27 red_gate decision=pass reason=no disqualifying input patterns detected
06:18:32 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=141 latency_ms=4329.9 cost_usd=0.0022
06:18:32 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
06:18:32 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
06:18:32 floor_gate decision=pass reason=output above protective minimum; no mismatches
06:18:32 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
06:18:32 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
06:18:32 signed hash_algo=sha256 hash=sha256:ab5f556de0604c4c9d98e5145b750099b2a6e79cbd20ba070aad4cadfac8dce6

Content hash

sha256:ab5f556de0604c4c9d98e5145b750099b2a6e79cbd20ba070aad4cadfac8dce6

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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