Research: shared target donors save 3,288 R420 XORs (no new kappa)

[ellipsi2]

This finite bit-circuit construction / research contribution saves 3,288 binary XOR additions in eumemic's accepted #543 R420 word: 26,916 → 23,628 complete native ADDs. A forest of shared target donors reduces frame-zero compensation D from 19,922 → 16,634, including all 100 preparation and 100 restoration additions. No new κ is claimed.

Sixteen nominated donors serve 100 receivers, with donor and receiver sets disjoint. Helpers remain untouched throughout D. The complete MOVE/COPY/ERASE subsequence, 420 helpers, nine copies, per-register frame paths and paid rank mass 5,112 are unchanged. The inverse positive-prefix bound increases to 3,798,646; the exact native payload bound remains within 104 bits (bit length 102).

Concurrent #713 (Scott Woolsey Biggart) and #716 (Sagar Thakrar) report 3,150 savings using disjoint target pairs. This extends the circuit class to shared donors, yielding 138 additional savings on the same baseline. Their target-basis work and Dugongue's #476/#478 identity are credited; no concurrent code or recipe is imported, and no priority for reversible target factoring is claimed. #686/#694's helper-basis constructions are also credited; #694 saves more overall and is not superseded. No combined saving is claimed.

The original syntactic H2 rule and literal K extractor deliberately reject this word. The package proves and checks the sufficient semantic replacement: D stays at frame zero and implements exactly (x,s,y) -> (x,s,y+Ks) for arbitrary initial targets and helpers. All other inherited interface diagnostics pass. No predecessor checker is patched.

Reproduce with Python 3.9+ and the standard library:

python3 -B research/r420-target-star/verify.py

Expected:

PASS_R420_TARGET_STAR receivers=100 D=19922->16634 native_ADDs=26916->23628 saved=3288 columns=660 rank_mass=5112

The README also gives an optional fresh C++17/Boost replay command, checked against committed normalized NATIVE.json receipts.

Validation completed locally on macOS arm64, Python 3.9.6, Apple Clang 21.0.0 and authenticated Boost 1.85.0 headers:

• All 672 closed frames and 660 symbolic input columns, the exact D operator, and independent set-valued forward/inverse execution of the actual exported records.
• Both words replayed at 5/9/11 stages on 900/1,380/1,620 physical columns in Python and in freshly compiled unchanged C++ checkers. All 48 changed-stream bridge omissions are replayed literally in Python; the native built-in controls pass for both words.
• Nine construction/accounting controls, including a missing preparation invisible to zero-target tests, an already-modified receiver incorrectly used as donor, and an F2-neutral pair charged two ADDs. The C++ checkers reject a missing exported preparation at all three stage counts.
• Optimized/isolated Python, exact native-receipt comparison, minimal relocated reproduction, changed-source/certificate rejection, canonical output equality under gzip recompression, make selected-record-check, and staged whitespace checks pass.

Base: 66849e1475c930fd7732b1a0067ffee7e1e95f60. Reviewed PR543 source: 2065fe4f72a914d907f1046603f5a36f17018535. Selected #626 remains κ = 0.001635527380375392, complex-limited. Exact SHA-256/Git-blob source pins, certificates, proof, validation, overlap metadata and local claim are included.

Assignment seed 0, drawn once from OS randomness, selects the bit track and first donor target 0. The one evidence-driven extension after #713/#716 arrived permits shared donors. All 14,280 oriented pair costs and 1,680 candidate donor sets were evaluated, stopping at the preset 16-donor limit. The best receiver assignment for a fixed donor set is proved; the greedy donor set has no optimality claim. No pinned coordination issue existed. Final overlap was refreshed through #735; main was unchanged. New #731 independently audits the baseline compensation rank, and #733 reports 8,368 savings by combining helper and target bases. They are credited and not imported. #733 changes helper values during D; this result retains the immutable-helper restriction and permits shared target donors. No overall saving record is claimed.

Only research/r420-target-star/ is added. Acceptance of the semantic D interface, hosted-parent/whole-owner reconstruction, global prefix bounds, full finite invoices and changed-word outer assembly remain integration work. All inherited all-size/common-label/mutable-basis/hosting/residual/precision/tape/analytic assumptions remain. Full repository make verify, selected cold reconstruction, remote Linux CI and Lean were not run or claimed. This is not a full multiplication proof or measured runtime improvement. upstream/ and the selected frontier are unchanged.

Prepared for @ellipsi2 with substantial OpenAI Codex assistance in construction, reasoning, implementation, verification and packaging, under Apache-2.0. Original notices and cumulative predecessor attribution are retained. No independent human review is claimed.

[Mister-Meeseeks]

100-PR batch review at 6e7a5d271a123886dc7b54ca3180d0b9f9beda5a.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Target-star compensation saves 3,288 native XORs including preparation/restoration; generalized D semantics and unchanged paid paths.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.