[tekuuu]

PR3025 restores the P104 collector exactly, but evaluates every nonlinear lifting butterfly at full precision. This package reduces the identical map to one wide exact linear evaluation plus bounded-width residue work. At rank seven only four input bits per real component are needed for the nonlinear part. The paired inverse, query values and private-zero cleanup are unchanged.

The written proof establishes L_r(x+2^g z)=L_r(x)+2^g U_r(z) for g=floor(r/2)+1, including the literal inverse and Gaussian monomial wrappers. Explicit witnesses show the forward uniform threshold is sharp. An exact integer Walsh backend makes the reduction executable. Same-input, alternating-order Python 3.12 measurements on the actual outbound recipe give 2.08× at 4,096 bits and 3.75× at 65,536 bits; 64-bit inputs are slower (0.76×). All seven timing pairs at each of five widths are retained.

This is a research reduction and reference implementation improvement, not a completed fast recursive supplier or a new κ. The full ledger pays both wrapper sets, extraction/recombination, narrow arithmetic, owned buffers and reset. It identifies the exact/certified-integer backend contract and its W-dependent precision requirement. If an admitted exact backend costs O(NW r^(1−a)), the reduction preserves that rate for W=Omega(r^(1+a)), with n=Theta(r); its current narrow algorithm does not establish the saving at W=Theta(r). Mutable buffer reset is not a physical dirty-workspace or reversible-uncomputation proof.

Validation:

• Ranks 1–10 in both directions; 2,592 exhaustive signed pair cases; one-bit-short counterexamples.
• All 512 ideal native columns in each direction, five wide paired fixtures, and four full dirty collector comparisons against byte-identical PR3025 code.
• Eight control groups cover signed residues, missing correction, faulty backend, native occurrence/phase, wrong inverse order, scratch, source pins, typed receipts and an optimized read-only Git-free export.
• Registered CPython 3.12.14 replay and optimized CPython 3.14.7 controls pass. All 15 committed package/input byte checks pass. Hosted CI and independent mathematical review are separate.

python3.12 scripts/research_package.py --package research/p104-lifting-residue-reduction

Base: d8e0f83f00191df62174b641e9fff055c357f641, priority revision 6. PR3025 source: a544ef068a46f4de3bc47d1d02149cbdc3ba547f. Actual collector/native recipes: ywz65/PR2586 7953c9a8f788a8de5cf2ced63d9a61b67c22c6f1. Source hashes, proof, recurrence, benchmark and unresolved obligations are in research/p104-lifting-residue-reduction/.

Canonical claim. Canonical main and dependency head were refreshed before publication. Recent PRs through PR3030 were checked: the T148/T740 packing releases address a distinct obligation. The overlap check uses retained historical metadata and fresh deltas, not a claim to have reviewed every diff or unpublished result.

Credit Tekalign/PR3025 for the unchanged lifting map and collector; Arham Tahir/PR2999 for the collision predecessor and occurrence-binding lineage; ywz65/PR2586/2555 for the physical recipes and rounded-shear precedent; and the retained native/geometry lineage. Standard lifting and Walsh factorization are not claimed as new. Prepared by Tekalign with substantial OpenAI Codex assistance. Apache-2.0.

The diff adds 12 scoped package files, about 1,570 lines including the 233-line unchanged predecessor reference. No shared checker, frozen source, upstream file or selected frontier is modified.