feat(Schonhage): implement native shared box-value tables #2176

Native box-value table milestone for #1394, following finite #2160/#2161. Root coordinator/implementation author codex-root-3sum-20261101, ordinary branch work/three-sum-native-box-table-20261101 from exact5a8ad9ba7; reviewed ancestor branches stay unchanged. Fresh issue/PR searches and current reviews show no competing implementation claim or requested source repair.

Acceptance: fixed native standard WordRAM code computes the geometry catalogue/index directory itself and fills a compact per-tile table with every finite canonical box value from the actual left/right signed encoding arrays. Every pointer, digit/P0 scan, validity test, rank/descriptor write, ten-child lookup, signed product/sum, store and loop is charged. Prove actual caller and State.init execution with same-y prefix/halt clients, derived fits, dirty-scratch/outside frames and explicit bounds. Lookup must consume real stored words, with no supplied geometry/rank/layout/run/time/table oracle. Reuse existing alphabets/encoding digits, BoxValues/partition proofs, signed arithmetic, Power/compiler/width APIs; preserve attribution and source mapping.

Investigating one shared geometry catalogue/directory of O((L+1)*10^L) cells computed once in O(poly(L)*10^L), reused across all tiles, with compact B-entry tile values and O(poly(L)*B) per-tile work, where B is the actual finite box count. This is an original native representation alternative to the source trie; its setup/space must remain explicit and amortization must be proved before claiming the improved global bound. No 11^L enumeration or repeated dense setup per tile. If this design fails the required asymptotics, retain the target and use a genuine sparse enumeration/trie; do not close the issue with a kernel.

Primary source: anthropics/formal-math@16a5ce4, 3sum-apsp/ThreeSumApsp/Sec4/Lemma29 and Programs/Sec4/Theorem30 preprocessing/lookup/insert/sum/enumeration routines. Native digit order stays the existing Encoding.leafIndex least-significant level0, P0 digit9; source Horner order differs and cannot be copied silently.

Required concrete tests: complete initialized signed/cancellation/zero-level/threshold-boundary cases, dirty scratch, frames, generic admitted clients, actual table lookup and returned values tied to the same execution state. Scoped checks, hosted full validation, independent nonauthoring review before integration. No abstract impact expected from this data-structure prerequisite. Full native wanted-query construction, Corollary26/global tile/ET integration, improved parameters and tuned1.9992 remain #1394; this issue must deliver the complete reusable table, not claim that endpoint. Keep open until its acceptance criteria integrate. AI assistance: OpenAI Codex.