The Mechanism · Gated-generation receipt

gen-define-a-minimum-spanning-tree-and-give-one-short-worked-exa-ffb2

stable pending witness
2026-05-29 05:38:52 UTC · anthropic/claude-sonnet-4-5

Prompt

Define a minimum spanning tree and give one short worked example.
65 chars

Generation

# Minimum Spanning Tree (MST) ## Definition A **minimum spanning tree** of a weighted, connected graph is a subset of edges that: 1. Connects all vertices (spanning) 2. Forms a tree (no cycles) 3. Has the minimum possible total edge weight ## Worked Example Consider this weighted graph: ``` A ---2--- B | | 3 4 | | C ---1--- D ``` **Edge weights:** - A-B: 2 - A-C: 3 - B-D: 4 - C-D: 1 **Finding the MST (using Kruskal's algorithm):** 1. Sort edges by weight: C-D (1), A-B (2), A-C (3), B-D (4) 2. Add C-D (weight 1) ✓ 3. Add A-B (weight 2) ✓ 4. Add A-C (weight 3) ✓ — now all vertices connected 5. Skip B-D (would create cycle) **MST:** ``` A ---2--- B | 3 | C ---1--- D ``` **Total weight: 1 + 2 + 3 = 6** This is minimal because any other spanning tree would have a larger total weight.
19 tokens in · 329 tokens out · 6293 ms · $0.005

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
6309.1 ms
Base LLM
6293.0 ms
Verifiers
0.3 ms
Gates
0.1 ms
Cost
$0.005

Trail

05:38:52 received prompt_chars=65 verifiers=['scripture_anchors', 'theology_doctrine']
05:38:52 red_gate decision=pass reason=no disqualifying input patterns detected
05:38:58 base_llm_call model=anthropic/claude-sonnet-4-5 tokens_in=19 tokens_out=329 latency_ms=6293.0 cost_usd=0.005
05:38:58 verifier:scripture_anchors verdict=NOT_APPLICABLE summary=0 Scripture citation(s) extracted
05:38:58 verifier:theology_doctrine verdict=NOT_APPLICABLE summary=no doctrine keyword patterns detected
05:38:58 floor_gate decision=pass reason=output above protective minimum; no mismatches
05:38:58 way_gate decision=pass reason=no declared way_path (Way check NA); no coercion language
05:38:58 execution_gate decision=deferred reason=no witnesses available (Witness Roll not yet constituted)
05:38:58 signed hash_algo=sha256 hash=sha256:c6a86ec9d88f8b9f1397b96f939055140d547ae8b94a7cd98e7f2a09b3c7eabc

Content hash

sha256:c6a86ec9d88f8b9f1397b96f939055140d547ae8b94a7cd98e7f2a09b3c7eabc

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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