feat(Schonhage): implement native sparse box queries #2203

Complete native Section 4 box-query milestone toward #1394, reusing #2185's actual table and #2161's finite partition. Owner/session codex-root-3sum-20261101, ordinary branch work/three-sum-native-box-query-20261101 from exact7b88ef0d; published suppliers remain untouched. Fresh open issue/PR searches and current parent reviews show no competing claim or requested source repair.

Acceptance: fixed native standard WordRAM program reads an ordinary output code and original canonical signed leaf arrays, traverses only contributing prefixes with order<=t, multiplies low-order leaves and consumes actual compact table words for exact-threshold leaves. Prove native stack/descriptor construction, no repeated/dropped query terms, complete signed result equal existing boxQuery/bilinearProduct, charged O(poly(L)*(sum d<=t alpha(m,d))) query work, derived fits/logwidth, dirty scratch/source/outside frames, actual caller and State.init same-y prefix/charged halt clients. Complete initialized constructor must build real geometry/table itself; reusable query kernel may consume the resulting pure memory readback, never an execution/time/list/layout/table oracle. No dense10^m or11^L per-query scan. Native original explicit work stack is an alternative to source bounded-nine-string enumeration; its workspace and preparation costs stay explicit. Shared global table/encoding amortization, actual all-tile selection, Corollary26/ET integration and tuned1.9992 remain #1394; this milestone cannot claim that endpoint.

Implementation direction: worklist of contributing prefixes; P0 branch always available at an inner coordinate, nine indexed branches only while used<t; outer coordinates have their private term. Each task's raw native fields are depth, decimal prefix, used non-P0 inner count, initial-P0 star count and power. At a threshold leaf, the actual key is e*10^L+leafIndex and the canonical box is existing starBelow. A finite work potential (remaining depth+1)*number of possible leaves charges all native nodes and bounds stack allocation. One-time table setup remains separate from query cost; signed partials derive from original array envelopes.

Primary: anthropics/formal-math@16a5ce4, Sec4/Lemma27_28, BoxesFromLeaves and Programs/Sec4/Theorem30/{QuerySum,Query,Contracts}. Reuse existing output/term digits, leafIndex, lowLeaves, starBelow/boxes, alpha counts, native signed/compiler/table APIs. Preserve native least-significant level0 and source credit; no machine/run-semantics import.

Require fully admitted signed/cancellation/zero-depth/threshold boundary and actual traversal/dirty-memory tests, scoped strict/static checks, hosted full six, fresh exact-head nonauthoring correctness/API/source/resource review. No curated abstract impact expected. Keep open until integration. AI assistance: OpenAI Codex.