06 — Count Integrity Equation & UI Status Model (Workstream E)

Count status taxonomy (the model the UI renders)

status	meaning	source field	UI render
FINAL	scalar pivot-backed count, live	node contract count_status='pivot_backed' (scalar pivots)	the number, plain
DRILLDOWN	grouped pivot; total = Σ group rows	grouped pivot in pivot_results	expandable group list
CANDIDATE	computable but law not ratified	register aggregate_status='CANDIDATE_REPORT_ONLY'	number + CANDIDATE badge
PIVOT_MISSING	no pivot exists for the concept	node contract count_status='PIVOT_MISSING' / register	"not yet defined" + propose_pivot
LAW_DEFINITION_NEEDED	concept undefined	register aggregate_status='NEEDS_LAW_DEFINITION'	"not yet ratified", never 0
WARNING_DRILL_MISMATCH	parent ≠ Σ children where a partition law holds	v_rp_drill_reconciliation.drill_status	warning banner
UNVERIFIABLE	grand-total closure impossible	count_integrity_status='unverifiable_at_grand_total'	equation-incomplete banner

Did the base view need extending? Yes — two additive read-only views (applied, DROP-reversible)

The base v_registries_pivot_node_contract already exposes count_value, count_status, drift_status, orphan_count, phantom_count, unmanaged_count (NULL), pin_state, warning_flags. It lacked (a) parent↔child drill reconciliation and (b) a candidate/law register. Both were added without touching the base view (so the existing UI contract is byte-identical and stable).

View 1 — v_rp_drill_reconciliation

Compares each parent's scalar count to the sum of its children's group/scalar totals, but only asserts a verdict when a partition law holds: a single, same-source, non-matrix, full-population (same filter) grouped child. Otherwise it is advisory.

parent           parent_count  n_children  children_total  partition_defined  drill_status
MTX-L1-OVERVIEW  1,132,013     1           2,262,884       f                  ADVISORY_NO_PARTITION_LAW  (matrix = cross-tab, not a partition)
PIV-001          169           3           492             f                  ADVISORY_NO_PARTITION_LAW  (3 facet children, overlap)
PIV-007          309           1           309             t                  RECONCILES                  ← DOT drill fixed
PIV-009          168           1           168             t                  RECONCILES
PIV-016          42            1           42              t                  RECONCILES
PIV-101          (null)        6           146             f                  PARENT_NOT_SCALAR

No WARNING_DRILL_MISMATCH remains after the PIV-104 fix. The matrix case was deliberately excluded from the partition law (a matrix sums to ~2× its parent because it counts cells, not a partition) — otherwise it would be a false positive.

View 2 — v_rp_aggregate_candidate_register

The explicit, honest aggregate surface (live counts where a single relation exists):

code     concept      live_count  aggregate_status            ui_render
PIV-301  orphan       59          CANDIDATE_REPORT_ONLY       CANDIDATE_BADGE
PIV-302  phantom      289         CANDIDATE_REPORT_ONLY       CANDIDATE_BADGE
PIV-303  count_drift  3           CANDIDATE_REPORT_ONLY       CANDIDATE_BADGE
PIV-312  kg_edges     2,259       NEEDS_LAW_DEFINITION        PROPOSE_PIVOT
PIV-304  unmanaged    (null)      NEEDS_LAW_DEFINITION        PROPOSE_PIVOT
PIV-500  grand_total  (null)      NOT_A_PIVOT_EQUATION_VIEW   EQUATION_VIEW

The accounting equation (honest, leaf-scoped)

total_system_objects = counted (FINAL, pivot-backed leaf sum, no Nuxt math)
                     + orphan      (59, CANDIDATE)
                     + phantom     (289, CANDIDATE)
                     + unmanaged   (NULL, LAW_DEFINITION_NEEDED)

From v_count_integrity (160 leaf rows): Σcounted = 2,275,591 · Σactual = 2,254,409 · net record-surplus = 21,197 · drift-flagged rows = 3 · pivot-backed leaves = 21. Because unmanaged is NULL and PIV-500's anchor is unratified, the equation cannot close to one number → count_integrity_status = unverifiable_at_grand_total. This is surfaced as a warning, not a silent green.

UI render rules (no client math, no hardcoded depth)

• Tree/structure — read parent_code / is_root / has_children / child_pivot_codes / child_layer_kind only.
• Counts — read count_value (scalar) or the group rows (drilldown). Never compute in Nuxt.
• Final counts render plain. Candidate counts render with a badge (from the register). Missing/law render as "not yet defined / ratified", never as 0.
• Drill — read v_rp_drill_reconciliation.drill_status; show a warning only on WARNING_DRILL_MISMATCH (currently none); ADVISORY_NO_PARTITION_LAW is informational.
• Drift — keep showing drift_status from the node contract (e.g. dot_tools record-surplus 146); it is independent of drill reconciliation.
• Grand total — render the equation with the UNVERIFIABLE banner; do not invent a number.

Completion

The UI can represent current truth — final, candidate, missing, law-needed, drill, drift, and unverifiable — without misleading users. ✅