The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-balanced-tree-rotation-state-any-93e4

stable pending witness
2026-05-29 08:16:02 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a balanced tree rotation. State any key formula.
74 chars

Generation

A balanced tree rotation is a local restructuring operation used to maintain balance in binary search trees (like AVL or Red-Black trees) after insertions or deletions. During a rotation, nodes are rearranged while preserving the binary search tree property (left < parent < right) to reduce tree height and keep operations efficient. There are two basic types: **right rotation** and **left rotation**. In a right rotation at node y with left child x: `x` becomes the new root, `y` becomes x's right child, and x's original right subtree becomes y's left subtree. **Key formula (AVL trees)**: Balance Factor = height(left subtree) - height(right subtree), where |Balance Factor| ≤ 1 must hold for all nodes.
26 tokens in · 176 tokens out · 4897 ms · $0.0027

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
4910.3 ms
Base LLM
4897.4 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.0027

Trail

08:16:02 received prompt_chars=74 verifiers=['scripture_anchors', 'theology_doctrine']
08:16:02 red_gate decision=pass reason=no disqualifying input patterns detected
08:16:07 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=176 latency_ms=4897.4 cost_usd=0.0027
08:16:07 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
08:16:07 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
08:16:07 floor_gate decision=pass reason=output above protective minimum; no mismatches
08:16:07 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
08:16:07 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
08:16:07 signed hash_algo=sha256 hash=sha256:92a35da508e3a826322a51c5d6bdbfcc6c66bf20b3d4147b5479023e5e2d6c17

Content hash

sha256:92a35da508e3a826322a51c5d6bdbfcc6c66bf20b3d4147b5479023e5e2d6c17

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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