C — Parent → Child → Grandchild Subtree Filter Evidence

Capability: subtree filter proving parent → children → grandchildren, with no orphan / no cycle, via the authoritative function. Verdict: PASS. Channel: read-only via shipped DOT wrapper. Mutation: none.

C.1 Command & function

• DOT command: dot_iu_subtree (category=read, mutating=false).
• Wrapper: public.fn_iu_filter_axis_c_subtree(p_root uuid, p_sample_limit integer DEFAULT 100) RETURNS jsonb — STABLE; delegates to authoritative recursion public.fn_iu_subtree(p_root uuid).

C.2 Input

SELECT fn_iu_filter_axis_c_subtree('cb211ee6-2b61-496e-b191-ef502ea28345', 100); (root = canonical D38-DIEU35-S4.)

C.3 Output — the tree (8 nodes, depth 0→2)

relative_depth	canonical_address	iu_id	parent_id
0 (root)	D38-DIEU35-S4	cb211ee6-…-28345	null
1 (child)	D38-DIEU35-S4-P1	3477ff71-…-67ba83	cb211ee6
1 (child)	D38-DIEU35-S4-P2	caa1f95b-…-a785e4	cb211ee6
1 (child)	D38-DIEU35-S4-P3	42d12348-…-7bd768	cb211ee6
1 (child)	D38-DIEU35-S4-P4	3293c8a5-…-1ba77d	cb211ee6
2 (grandchild)	D38-DIEU35-S4-P1-1	5410e681-…-c857115	3477ff71
2 (grandchild)	D38-DIEU35-S4-P1-2	68375024-…-d78f38	3477ff71
2 (grandchild)	D38-DIEU35-S4-P1-3	982677b6-…-da8ede	3477ff71

node_count = 8, min_relative_depth = 0, max_relative_depth = 2. Root → 4 children (P1–P4) → 3 grandchildren under P1 (P1-1/2/3): parent → child → grandchild proven.

C.4 Integrity (no orphan, no cycle)

"subtree_linkage": { "parent_outside_subtree": 0 },
"global_integrity": {
   "orphan_dangling_parent": 0,
   "self_parent_cycle": 0,
   "self_in_ancestors_cycle": 0,
   "root_with_nonzero_depth": 0,
   "depth0_with_parent_stale": 23,
   "stored_depth_parent_mismatch": 23
},
"authoritative_source": "fn_iu_subtree"

• Orphans: 0. Cycles: 0 (self_parent_cycle and self_in_ancestors_cycle both 0). Bad roots: 0.
• Known caveat (not a defect): depth0_with_parent_stale = 23 and stored_depth_parent_mismatch = 23 — these are the stored axis_c_depth column values that are stale because iu_core.three_axis_auto_refresh_enabled = false. The function carries the caveat string and computes structure from fn_iu_subtree.relative_depth, which is authoritative. The 8-node tree above uses relative_depth, so it is correct regardless of the stored-column staleness.

C.5 Cross-validation

fn_iu_subtree recursion agrees with the materialized iu_tree_path ancestor closure and the transitive iu_relation (contains) edge closure. Parent/child/grandchild is represented by iu_relation parent→child contains edges (60 edges) plus iu_tree_path (199 rows).

C.6 What a human can look at

Run SELECT * FROM fn_iu_subtree('cb211ee6-2b61-496e-b191-ef502ea28345') ORDER BY relative_depth, canonical_address; — 8 rows, the tree above, every node's parent_id resolving inside the subtree, depths 0/1/2.

C.7 Safety

Read-only STABLE function. No mutation, no gate touched.