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title: 02 — Leaf-Set Definition (Branch B) date: 2026-05-31 verdict: LEAF_SET_RULE = EXPLICIT + DATA-DRIVEN (no hardcoded code list); 160 leaf / 9 rollup

02 — Leaf-Set Definition (Branch B)

The accounting invariant total = counted + orphan + phantom is only meaningful over a set with no nested rollups. meta_catalog (169 rows) mixes leaf object-sets with rollup/meta summary rows; a blind SUM double-counts — the exact disguised-math trap Đ28 forbids.

composition_level distribution (live, all 169 rows)

composition_level	rows	Σrecord	Σactual	Σorphan
atom	77	3,635,579	3,836,259	0
molecule	51	1,670	1,677	0
compound	34	846	749	0
material	2	58	113	0
meta	3	517	null	161
product	1	0	0	0
building	1	0	0	0

The 9 rollup/meta rows (must be EXCLUDED from the invariant)

code	entity_type	composition_level	record	actual	note
CAT-ALL	all	atom	1,682,270	1,919,748	grand rollup of all atoms — sits inside the atom level → the double-count trap
CAT-MOL	molecule_total	molecule	774	766	per-layer rollup
CAT-CMP	compound_total	compound	423	326	per-layer rollup
CAT-MAT	material_total	material	0	55	per-layer rollup
CAT-BLD	building_total	building	0	0	per-layer rollup
CAT-PRD	product_total	product	0	0	per-layer rollup
CAT-DOT	dot_total	meta	307	null	DOT registry rollup (carries 140 orphans)
CAT-COL	collection_total	meta	168	null	collection registry rollup (20 orphans)
CAT-SPE	species_total	meta	42	null	species rollup (1 orphan)

LEAF-SET RULE (data-driven; no hardcoded code list)

leaf_set := meta_catalog
  WHERE composition_level <> 'meta'        -- excludes CAT-DOT/COL/SPE
    AND entity_type NOT LIKE '%_total'     -- excludes CAT-MOL/CMP/MAT/BLD/PRD
    AND entity_type <> 'all'               -- excludes CAT-ALL (lives inside 'atom')

• Live result: 160 leaf rows (169 − 9). Cross-check inside the rehearsal: meta_rollup_record_excluded = 517 = 307+168+42 ✓ (the three meta rows), and CAT-ALL/layer-totals excluded by entity_type.
• The rule keys on existing data columns only (composition_level, entity_type) — there is no hardcoded list of CAT codes. It survives new categories: any new *_total/all/meta row is auto-excluded; any new real object-set is auto-included.

Which rows are what

• Leaf / real object-set (160): each maps to a concrete substrate via source_location (e.g. Directus:birth_registry, Directus:entity_labels, File:dot/bin/). Top leaves: CAT-023 birth 980,378 · CAT-068 entity_labels 690,341 · CAT-017 system_issue 171,939 · CAT-016 changelog 66,095 · CAT-141 measurement_log 31,984.
• Rollup / derived-summary (9): the table re-aggregates leaves (per-layer *_total, the global all, and the three meta registry totals). These are display conveniences, not object-sets.
• Excluded from invariant computation: the 9 rollups.

Residual gaps (recorded, not hidden)

• LEAF_SET is necessary but not provably MECE. Even within the 160 leaves there may be overlap (e.g. a "junction_table" count vs an "all" count of the same physical rows). The rule removes the known rollups; it cannot guarantee mutual exclusivity. → The true cross-check anchor is PIV-500 (a grand-total pivot over the universal object substrate, e.g. birth_registry), not a catalog re-sum. PIV-500 is PIVOT_MISSING (doc 03).
• 5 leaf rows have actual_count IS NULL (leaf_actual_null = 5) → those leaves are count_integrity_status='unverified' (can't be reconciled until scanned).
• The leaf rule lives in PG (a view v_registry_leaf_set, rehearsed in doc 04). It must never be re-implemented as a Nuxt filter (Đ28 NT-D1).