615-h · Simplicity/validity rung 5: CP Desc 12–14 + hole containment, MS interiors-disjoint, exact-arithmetic upgrades

[grootstebozewolf]

Umbrella: #615 (the validity lane continues past the epic per confirmed decision 1)
claimId: 615-h (continuation rung)
meso: fork / validity (area-level conditions; exactness upgrades)
Continues: #639 (rung 4: MultiCurve/MultiSurface verdicts + CP Desc-11 counting, landing)

Frontier this rung inherits

After #639, IsSimple is decided for all seven curve-branch types (CS/CC/CP rings from rungs 2–3; MultiCurve per §4.2.25/§10.3.1 Desc 4 and MultiSurface per §4.2.27's definitional simplicity from rung 4), and IsValid answers checked verdicts for CS/CC/MC, definite-false for CP/MS values refuted by an implemented rule — including rung 4's CP ring-pair Desc-11 counting (cross-ring overlap or ≥ 2 contact points) and MS 1-D boundary overlap. Still fail-closed:

1. CP Desc 12–14 + hole containment (§8.2.1): a CP whose ring pairs each meet in ≤ 1 point still throws — deciding it needs hole-inside-shell containment, the spike/cut exclusion, and interior connectivity (a chain of one-point tangencies can disconnect the interior). The canonical pending witness is the internally-tangent hole (shell centre (2,0) r=2, hole centre (3,0) r=1, one contact at (4,0)). Needs arc-aware point-in-ring; the oracle's POINT_IN_CURVE_RING and HOLES_DISJOINT (A_IN_B/B_IN_A answers) lanes are the differential targets.
2. MS interiors-disjoint (§4.2.27 "interiors shall not intersect"): rung 4 refutes 1-D boundary overlap but a pair of elements with area overlap and point-only (or no) boundary contacts still throws — same point-in-ring/containment machinery as item 1.
3. Exact-arithmetic upgrades (inherited from the 615-h · IsSimple rung 2: multi-segment simplicity via arc-arc intersection (continuation) #630 review, deferred again with written reason on 615-h · Simplicity/validity rung 4: MultiCurve/MultiSurface, CP ring-pair conditions, exact-arithmetic upgrades #639): reclaim the conditioning-guard band (eps·r² refusals) and widen cocircular equality beyond canonical triples — exact-rational circle parameters (the oracle's path) or extended precision; any loosening of the guard needs an error analysis, not a constant tweak.
4. Kernel residues stay: degenerate closed segments (Desc-6-invalid) and the nearly-cocircular ambiguity band for genuinely distinct near-equal circles.

Reading room

• Fork: CircularArcGeometry.SegmentPairContacts + CurveSimplicity chains and RingPairContacts (615-h · IsSimple rung 2: multi-segment simplicity via arc-arc intersection (continuation) #630/615-h · Simplicity rung 3: CompoundCurve, CurvePolygon rings, IsValid wiring #634/615-h · Simplicity/validity rung 4: MultiCurve/MultiSurface, CP ring-pair conditions, exact-arithmetic upgrades #639), CurveValidity verdict arms.
• Oracle: POINT_IN_CURVE_RING, HOLES_DISJOINT, RING_ORIENTATION lanes; theories/CurvePolygonDisjoint.v, CurveRingSimple.v, RingContactSound.v.

Witness

At least one CurvePolygon or MultiSurface value that used to throw returns a checked verdict grounded in point-in-ring/containment machinery; the frontier shrinks and is restated.

Definition of Done: fork suites green; next-rung ticket exists (or the lane's remaining frontier is declared closed); umbrella notified.

topics: arc, validity

[grootstebozewolf]

Scope addition from the rung-4 review fold (fork 8429bd9): the kernel now refuses a tangency band in both the circle-circle and circle-chord paths (SegmentPairResult.AmbiguousTangency) — near a zero intersection discriminant, doubles cannot tell one touch from a crossing pair ~√eps·scale apart or a near-miss, and the review demonstrated wrong checked verdicts both ways there. Reclaiming that band is this ticket's exact-arithmetic work, alongside the conditioning guard and the near-cocircular band already listed under item 3: exact-rational circle parameters decide the discriminant's SIGN exactly (the oracle's path — its HOLES_DISJOINT/RING_SIMPLE lanes decide the very vectors NTS now refuses: the tangent-arcs-at-vertex and tangent-line-compound harness rows became fail-closed contract rows, SUMMARY ok=69).

Also carried here from the review's notes: (a) an all-classical MultiSurface's interiors-disjoint could be decided today via the classical MultiPolygon machinery as a special case — an option for this rung; (b) residues now DEFER within a scan (fork 8429bd9), so this ticket's exact upgrades only need to decide pairs, not restructure the walks; (c) member-level residues in MultiCurve.IsSimple still throw before a cross-member refutation elsewhere could decide false — a lesser ordering residue, in scope here if convenient.

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