Original question and givens
The finite simple undirected graph has V={-11, -10, -9, -8} and E={{-11, -10}, {-10, -9}, {-9, -8}}. There are no loops or multiple edges, and repeated representations of the same unordered edge count once. The vertex v=-9 belongs to V. List N(v) in increasing order with no duplicates.
G001 — The finite simple undirected graph has V={-11, -10, -9, -8} and E={{-11, -10}, {-10, -9}, {-9, -8}}. There are no loops or multiple edges, and repeated representations of the same unordered edge count once. The vertex v=-9 belongs to V. List N(v) in increasing order with no duplicates.
Step-by-step derivation
S001 · implies
Before
source roles = [qf-simple-graph-neighbors, [E, V, operation, v]]
After
derived = [neighbors, no-invented-domain]
Conditions: none
Keep EACH bank’s keys/operation/domain distinct:LDL/PULSE/function legacy table underscores,TREE full tree_* with its declared domain,and permissive BASE signed without invented op/domain.All arithmetic respects the binary-primitive contract.
Step identifiers and dependencies
Rule: R69_SOURCE_specific_keys_operation_domain_AND_binary_contract · Uses: G001
S002 · implies
Before
source roles = [LDL graph vertices ORIGINAL, 100, [-11, -10, -9, -8]]
After
derived = [[-11, -10, -9, -8]]
Conditions: none
Type EVERY RAW SAFE label,distinctness and THIS bank’s cardinality bound;empty is allowed.Sort ONLY the derived representation,not original JSON.Do not exchange TREE and LDL limits.
Step identifiers and dependencies
Rule: Finite_RAW_ALL_SAFE_distinct_labels_then_derived_sort · Uses: G001, S001
S003 · implies
Before
source roles = [LDL raw edges ORIGINAL, 0, [-11, -10]]
After
derived = [[-11, -10]]
Conditions: none
BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.
Step identifiers and dependencies
Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S002
S004 · implies
Before
source roles = [LDL raw edges ORIGINAL, 1, [-10, -9]]
After
derived = [[-10, -9]]
Conditions: none
BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.
Step identifiers and dependencies
Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S003
S005 · implies
Before
source roles = [LDL raw edges ORIGINAL, 2, [-9, -8]]
After
derived = [[-9, -8]]
Conditions: none
BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded.
Step identifiers and dependencies
Rule: Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup · Uses: G001, S004
S006 · implies
Before
source roles = [[-11, -10, -9, -8], [[-11, -10], [-10, -9], [-9, -8]], No]
After
derived = [[[-11, -10], [-10, -9], [-9, -8]], [[-11, [-10]], [-10, [-11, -9]], [-9, [-10, -8]], [-8, [-9]]]]
Conditions: none
Type the WHOLE raw edge list,then normalize undirected endpoints/deduplicate;reversed duplicates are allowed.INPUT edges have no loops/outside endpoints,while isolated vertices stay in V.TREE raw E does NOT acquire LDL’s200-entry limit.
Step identifiers and dependencies
Rule: Graph_WHOLE_simple_undirected_edges_normalized_NO_loops_or_outside · Uses: G001, S005
S007 · implies
Before
source roles = [-9, [-11, -10, -9, -8]]
After
derived = [[-10, -8], 2]
Conditions: none
A degree/neighbor QUERY first requires v∈V.Find distinct neighbors through ALL edges,not sketch crossings or raw duplicate rows.
Step identifiers and dependencies
Rule: Graph_QUERY_vertex_must_belong_V_complete_distinct_neighbors · Uses: G001, S006