The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-a-binary-search-tree-state-any-key-c00e

stable pending witness
2026-05-29 05:13:02 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain a binary search tree. State any key formula.
70 chars

Generation

A binary search tree (BST) is a hierarchical data structure where each node has at most two children (left and right), and for every node, all values in its left subtree are smaller and all values in its right subtree are larger. This ordering property enables efficient searching, insertion, and deletion operations. The average time complexity for these operations is **O(log n)** where n is the number of nodes, though it degrades to **O(n)** in the worst case when the tree becomes unbalanced. The maximum number of nodes at depth d is **2^d**, and a complete binary tree with n nodes has height **⌊log₂ n⌋**.
26 tokens in · 151 tokens out · 3890 ms · $0.0023

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
3902.0 ms
Base LLM
3889.7 ms
Verifiers
0.2 ms
Gates
0.1 ms
Cost
$0.0023

Trail

05:13:02 received prompt_chars=70 verifiers=['scripture_anchors', 'theology_doctrine']
05:13:02 red_gate decision=pass reason=no disqualifying input patterns detected
05:13:06 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=26 tokens_out=151 latency_ms=3889.7 cost_usd=0.0023
05:13:06 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:13:06 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:13:06 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:13:06 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:13:06 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:13:06 signed hash_algo=sha256 hash=sha256:48d6b2eb92a42323ac0bf9340fa36352880eb603227c71fb6959059e7764db25

Content hash

sha256:48d6b2eb92a42323ac0bf9340fa36352880eb603227c71fb6959059e7764db25

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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