Prove the fixed-core J caller joint cleanup support bound

[RossRichardson]

The phase-correct J caller now has a complete original-input cleanup and a scoped joint-tail lower bound. For q>=2 the exact all-q telescope C R=F_k J leaves only q native factors in R, even for arbitrary physical source monomials. Hence a complete native/monomial/binary-ADD tail needs total native arity plus ADD count at least (2q+4)f.

Under explicit paid full-bank scans, sublinear retained local tolls cannot hide a linear native-arity deficit in ADDs. With the additional equal-volume full-bank native-child normalization, including queried dirty helpers, the completed fixed-prefix mass is at least stock+4 and has no favorable proper-child moment. Unequal queried-bank volumes need a separate actual weighted bridge.

The package also supplies a conservative complete J caller: all public L-readers are scalar, every original field is restored to its actual F_k J output, and the full invoice is H[2]=n^2+1, H[4]=2, H[6]=1, mass=stock+16. Exact q2/q3 fixtures retain both inverse orders, all Gaussian f residues and every selected-native query. The all-q written derivations, finite checks and inherited C37/C38 resource/factory gates remain distinct.

Validation at efb1b5a56a52967a4e94223bcdd03b209f4f09f5:

• Registered Python 3.12 normal and optimized replay, with historical assertions preserved.
• Exact committed bytes, source history, official export and integrity check.
• Read-only Git-free export, isolated normal/optimized Python with empty PATH; unchanged source bytes, modes and inodes.
• Every fixed native witness is independently reconstructed and checked against signed Pauli images and an exact Gaussian source column. Every forward/inverse event ID, embedding, phase tag and rank is checked. Wrong phase/rank and the preserved pre-fix inverse-recipe-pointer receipt reject; an equivalent compensated phase gauge passes.

research/phase-correct-j-handoff/README.md gives the model, proofs, reproducible commands, source pins and next concrete question. REPLAY-MAP.md maps generation-time assertions to the fixed-witness verifier. A separate Codex review replayed this exact head normally and with -O, and reviewed the proof, fixed-witness checker, evidence reconstruction and documented scope. No independent human or formal-kernel acceptance is claimed.

No new κ, selected-record change, global caller impossibility, formal-kernel proof, physical precision/owner/tape admission or compatible BIT result is claimed. Changed core/continuation/delivery, cross-cut query fusion, different target/owner contracts and different volume transfers remain outside the theorem. Earlier 3630/3632/3645/3649/3655 and separate BIT 4021/4023 are credited. Generic signed-lift/phase work in 3987/4002 and related interface/volume work in 3989/4045 remain their authors' contributions. Full attribution, inherited notices and Apache-2.0 license are retained. Substantial OpenAI Codex assistance is disclosed.

The full natural Registered research packages workflow39253030363 is completed/success at exact head efb1b5a56a52967a4e94223bcdd03b209f4f09f5. Full workflow status/conclusion and source-head SHA were read back separately from local validation. No manual rerun or check request was made; no merge is requested.

[RossRichardson]

A bounded changed-interface follow-up is public in PR4074, exact 5758f0f3042b740ce872b5b0ae974917bd07016d. It addresses specific scalar continuation/core variations excluded by this fixed-core theorem and supplies two simultaneous cross-cut fusions, improving the constructed complete native bill from stock+16 to stock+8. The optional rank8-child version has the same mass and a different owner/interface obligation. Source-conditional all-q local identities are separated from complete physical q2/q3 selected-native words; its one-site absorption gate has an explicit finite domain. This does not broaden or refute this PR's fixed-core theorem, prove a global optimum, or admit a positive supplier/new κ. Canonical scoped finding and the new package retain exact source/phase/credit bindings. Local exact-head/export checks pass; the full natural workflow39261905044 is completed/success at the exact follow-up head, read separately from the local evidence. Ross Richardson with substantial OpenAI Codex assistance; AI review is not human/formal-kernel acceptance.