The Mechanism · Gated-generation receipt

gen-in-3-4-sentences-explain-depth-first-versus-breadth-first-se-b1fc

stable pending witness
2026-05-29 07:32:25 UTC · anthropic/claude-sonnet-4-5

Prompt

In 3-4 sentences, explain depth-first versus breadth-first search. State any key formula.
89 chars

Generation

# Depth-First vs Breadth-First Search **Depth-First Search (DFS)** explores a graph by going as deep as possible down one branch before backtracking, typically using a stack (or recursion). **Breadth-First Search (BFS)** explores level by level, visiting all neighbors at the current depth before moving deeper, using a queue. **Space complexity:** DFS uses O(h) space where h is the maximum depth, while BFS uses O(w) space where w is the maximum width of the tree/graph. **Key property for unweighted graphs:** BFS guarantees the shortest path with path length = number of edges traversed, while DFS does not guarantee optimality.
31 tokens in · 162 tokens out · 5191 ms · $0.0025

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
5198.9 ms
Base LLM
5191.3 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0025

Trail

07:32:25 received prompt_chars=89 verifiers=['scripture_anchors', 'theology_doctrine']
07:32:25 red_gate decision=pass reason=no disqualifying input patterns detected
07:32:31 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=162 latency_ms=5191.3 cost_usd=0.0025
07:32:31 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
07:32:31 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
07:32:31 floor_gate decision=pass reason=output above protective minimum; no mismatches
07:32:31 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
07:32:31 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
07:32:31 signed hash_algo=sha256 hash=sha256:958a52b8801bf76c9c00b203b04ac5ceb9233e12ca6637717d4a791c2ae14122

Content hash

sha256:958a52b8801bf76c9c00b203b04ac5ceb9233e12ca6637717d4a791c2ae14122

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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