The Mechanism · Gated-generation receipt

gen-state-depth-first-versus-breadth-first-search-precisely-and-cddc

stable pending witness
2026-05-29 03:16:08 UTC · anthropic/claude-sonnet-4-5

Prompt

State depth-first versus breadth-first search precisely and explain why it matters in 2-3 sentences.
100 chars

Generation

# Depth-First Search (DFS) vs Breadth-First Search (BFS) **DFS** explores as far as possible along each branch before backtracking, using a stack (LIFO). **BFS** explores all neighbors at the current depth before moving to the next level, using a queue (FIFO). ## Why It Matters The choice fundamentally affects both **optimality** and **memory usage**: BFS guarantees the shortest path in unweighted graphs but requires O(b^d) memory to store all nodes at the current level, while DFS uses only O(d) memory for the current path but may find suboptimal solutions. This trade-off makes BFS essential for finding shortest paths and DFS preferable when memory is limited or solutions are deep in the search tree.
31 tokens in · 181 tokens out · 4636 ms · $0.0028

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
4646.4 ms
Base LLM
4636.1 ms
Verifiers
0.2 ms
Gates
0.0 ms
Cost
$0.0028

Trail

03:16:08 received prompt_chars=100 verifiers=['scripture_anchors', 'theology_doctrine']
03:16:08 red_gate decision=pass reason=no disqualifying input patterns detected
03:16:12 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=31 tokens_out=181 latency_ms=4636.1 cost_usd=0.0028
03:16:12 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
03:16:12 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
03:16:12 floor_gate decision=pass reason=output above protective minimum; no mismatches
03:16:12 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
03:16:12 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
03:16:12 signed hash_algo=sha256 hash=sha256:bfacdd74d9b7ed9a4e2fba5f0a646f3e7b4d09cfe3d4778a3ab6641fe6322822

Content hash

sha256:bfacdd74d9b7ed9a4e2fba5f0a646f3e7b4d09cfe3d4778a3ab6641fe6322822

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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