[Clear1nsight]

Result

Bind one proposed joint-child transfer to the actual PR3945 native interface. Helpers 600, 601, 602 and 604 have four rank-4 frame climbs with the same entrance and destination. Their native residuals each have 16 nonzero entries per row; a single inherited rank-16 child has 65,536. Arbitrary monomial pre/post maps and auxiliary coordinates restored identically on all arbitrary dirty inputs cannot bridge that support mismatch. Valid selector batching retains active Fourier rank 4.

This addresses one missing physical implication in Gonzalo Mier's PR4031 zero-charge block screen. Its matrix direct-sum identity is valid and its physical costs are explicitly waived. This result is scoped to a one-call monomial/dirty-return transfer, not a general batching obstruction or a defect claim against that screen. Nonmonomial encoders, multiple queries, clean initialization and changed consumer contracts remain open. No new κ is claimed.

The exact optimistic allowance at the pinned PR3945 endpoint is
0.038249447579079975271991 < 4 H4 - H16 < 0.038249447579079975271992, with H_r = r^(1-κ). One additional positive-rank recursive child exceeds it if every other bill and inventory is fixed. Unknown gathering, routing, hosting, precision and restoration costs are not zero; compensating savings elsewhere are outside this local comparison.

Evidence and verification

Only research/staged544-joint-child-rank-interface/ changes: 15 files. Both immutable source prefixes are traced with native events at their literal positions. The common actual residual is evaluated on all 512 basis columns using credited PR3987 Gaussian arithmetic. Five mathematical controls and four actual production-CLI mutation runs distinguish spectator axes, reject rank-12/rank-16 substitutions, reject an invalid source frame and detect changed source bytes/stale results. Normal and optimized Python pass.

The canonical main checkpoint remains 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. The root round checked 733 open PR bodies, newer deltas and a partial live handoff thread; this is not exhaustive novelty coverage. The source/operator definition and exact assumption boundary received a separate agent review; no independent human or proof-kernel review is claimed.

GitHub-authored commit 91afbb643f7f4ccf6f34b685ecd959eb790a0f94 has one canonical-main parent. All committed raw bytes and declared history pass the repository gate. The official committed export passes integrity checking; all verifier/control commands pass from a read-only Git-free export in normal and optimized Python with unchanged bytes. Hosted CI is reported separately.

python3 scripts/research_package.py --package research/staged544-joint-child-rank-interface
python3 scripts/check_research_commit.py --package research/staged544-joint-child-rank-interface --check-source-history

No rewritten whole provider, full dirty-word replay, owner realization, native supplier implementation or complete root calculation is claimed. The proof, source pins, complete cost-status ledger and open next questions are retained in the package.

Credit and next boundary

Gonzalo Mier/PR4031 supplies the motivating screen; Dugongue/PR3945 supplies the current words; PR3969 supplies the owner-cost bridge; PR3987 supplies the retained exact native arithmetic/compiler snapshots. The source notices preserve dataisfire, zxv, Ross Richardson, DreamingOfClouds, chafreaky/PR458, PR2226 and the detailed native/owner lineage. New proof and checker: Chris R / Clear1nsight with substantial OpenAI Codex assistance, Apache-2.0.

The next useful test is an explicit nonmonomial or multi-query encoding that preserves all four inputs and their consumers, restores borrowed state, and fits its complete allowance or identifies an independently credited offsetting saving. A larger zero-charge grouping alone does not remove this boundary.