Research: save 3,150 R420 XORs with a restored target basis

[swbiggart]

This finite bit-circuit construction reduces PR543 R420's complete native word by 3,150 XOR additions: 26,916 → 23,766. It conjugates the frame-zero dirt correction by 57 disjoint target transvections, including all 57 preparation and 57 restoration ADDs. No new κ is claimed.

The complete MOVE/COPY/ERASE subsequence, 420 helpers, nine copies and rank mass 5,112 remain unchanged. D falls from 19,922 to 16,772 ADDs. The reverse positive prefix grows from 2,270,064 to 3,703,810; the recomputed local payload allowance is 102 bits, below the 104-bit cap. No inherited global invoice is claimed for the changed word.

Concurrent #686 and #694 are credited for helper-column factoring and the semantic D-prefix contract. This contribution factors target rows and restores arbitrary target inputs. A control demonstrates that omitting preparation escapes zero-target testing but fails the complete input basis. #708 shares separate FULL-frame decoder operands. None of these circuits is imported or composed here.

The original literal H2 and K extractor reject the new syntax as expected. A written conjugation proof and complete operator check establish the sufficient semantic replacement; no predecessor checker is patched.

python3 -B research/r420-target-basis/verify.py
# With C++17 and Boost headers:
python3 -B research/r420-target-basis/native.py

Expected local result: PASS_R420_TARGET_BASIS D=19922->16772 native_ADDs=26916->23766 saved=3150 columns=660 rank_mass=5112 kappa=unchanged.

Validation:

• Focused Linux CI passed on Python 3.11 and 3.13 at 1a19af5c5ddb6de9797a6d085e5df0b90ed6d58b, including fresh C++ multistage checks on 3.13 and clean-tree checks.
• Exact certificate and four obligation tests passed on Python 3.9.6, 3.11.16 and 3.13.16.
• All 660 dirty-input columns in both directions, exact E8/frame checks, independent set interpretation, full official exporter agreement and eight rejection controls.
• Fresh unchanged C++ legality and 5/9/11-stage checks on both words: 900/1,380/1,620 columns, 96 bridge controls total and six missing-D controls. Apple Clang 21.0.0, pinned Boost 1.85.0.
• Minimal relocated/recompressed-source replay, corrupted-source/certificate rejection, optimized-mode refusal, selected-record integrity and whitespace checks passed.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. PR543: 2065fe4f72a914d907f1046603f5a36f17018535. Source pins, exact certificates, proof, frozen recipe and local seed-5 claim are included. All 14,280 ordered target pairs were scored, followed by one seeded greedy disjoint pass; no optimality is asserted. Final overlap refresh covered open PRs through #709; no pinned coordination issue existed.

Only the new research package and its focused workflow are added. Hosted-parent reconstruction, revised global invoices, outer assembly and acceptance of the semantic interface remain integration obligations. All inherited compiler/common-label/mutable-basis/physical/hosting/precision/tape/analytic assumptions remain. No full theorem, repository-wide suite pass or practical runtime improvement is claimed. upstream/ and the selected frontier are unchanged.

Prepared by Scott Woolsey Biggart (@swbiggart) with substantial OpenAI Codex assistance, under Apache-2.0. Full predecessor attribution and original notices are linked in the README. No independent human review is claimed.