06 — Count Integrity and Accounting Equation

Count integrity (live, post-commit)

From v_count_integrity (160 leaf rows):

metric	value
Σ counted	2,275,591
Σ actual	2,254,409
Σ orphan (leaf-grain)	0
net record-surplus	21,197
drift-flagged rows	3
pivot-backed leaves	21

Safety-net (birth-grain) counts: orphan v_birth_orphan=59, phantom v_birth_phantom=289, IU=219, KG edges=2,259, system_issues(open)=207,940.

No Nuxt math required

Every L1 and wired-layer count is pivot-backed (v_registries_pivot_node_contract.count_value). The UI renders values verbatim. The backend contract needs no client-side arithmetic.

The accounting equation (explicit, leaf-scoped, honest)

total_system_objects  =  counted_in_registries_pivot
                       +  orphan      (unborn / missing-birth)
                       +  phantom     (registered-but-absent / stranded)
                       +  unmanaged   (no registry / unknown)

• counted = Σ pivot-backed leaf counts over the leaf set (composition_level<>'meta', not a _total/all rollup) — never a blind SUM of meta+rollup rows.
• orphan = 59 (v_birth_orphan, birth-grain) — CANDIDATE (not legally stable at RP grain).
• phantom = 289 (v_birth_phantom, birth-grain) — CANDIDATE.
• unmanaged = NULL / CANDIDATE — no ratified definition; surfaced as unmanaged_count=NULL, never faked.
• cross-check anchor = PIV-500 grand total = PIVOT_MISSING ⇒ count_integrity_status = unverifiable_at_grand_total.

Which terms are FINAL vs CANDIDATE

term	status
per-leaf counted (L1 totals, wired layers)	FINAL — pivot-backed, live
orphan (59)	CANDIDATE (birth-grain; RP-grain law not ratified)
phantom (289)	CANDIDATE
unmanaged	CANDIDATE (undefined)
grand total / equation closure	UNVERIFIABLE until PIV-500 ratified

Warning, not silent green

Because the grand-total anchor (PIV-500) is missing and orphan/phantom/unmanaged are CANDIDATE, the equation cannot be closed to a single number. The contract surfaces this honestly: count_status=PIVOT_MISSING on the missing aggregates, unmanaged_count=NULL, and count_integrity_status=unverifiable_at_grand_total. A mismatched equation raises a warning state — it does not silently pass.

DOT-category drill discrepancy (surfaced drift flag)

PIV-104 (status='published' only) child Σ = 16 (pivot 8 / uncategorised 4 / Vòng đời 2 / Giám sát 2) ≠ parent PIV-007 = 309 (all dot_tools). This is a real published-only drill-integrity gap — documented, not silently reconciled. Fix (owner decision): drop the published filter or add a status sub-axis so child Σ reconciles to parent.