[tekuuu]

PR2999 shows that independently nearest-rounded native calls can lose input information and leave a nonzero private residue in the first P104 collector. This construction changes the numerical map: integer-lifting butterflies use a literal paired inverse, restoring all five dirty sources and the private field exactly without retaining rounding residues or per-coordinate history.

Both completed calls meet relative Hilbert error at most 2^-b on the paired execution. The query remains approximate on its retained working grid; the absolute outbound error is at most 112*2^-F. The inverse schedule and grid must be preserved. Standard reversible lifting is credited; the contribution is its binding to PR2586 events 2025–2039, the paired accuracy/cleanup proof, and a fully charged scalar-reference recurrence.

Evidence:

• All 512 ideal native basis columns and a separate tensor-convolution oracle agree; 6,561 signed pair cases verify the parity/error identity and both inverse directions.
• Fifteen same-grid comparisons separate the predecessor's collision inputs. Fourteen dense/cancellation fixtures include 400-bit dirty inputs and eight nonzero-error cases.
• Eight behavioral groups pass, including wrong inverse chronology, independently rounded return, changed native phase/occurrence, dirty wrapper scratch, underprecision, nonexact downshift, broken cleanup, source/receipt drift and read-only Git-free execution.
• Registered CPython 3.12.14 replay and optimized CPython 3.14.7 controls pass on Linux. All 15 committed package/input files pass publication-byte checks. Hosted CI is separate.

python3.12 -B scripts/research_package.py --package research/p104-reversible-lifting

Exact base: d8e0f83f00191df62174b641e9fff055c357f641, priority revision 6. Native source: ywz65/PR2586 7953c9a8f788a8de5cf2ced63d9a61b67c22c6f1; collision predecessor: Arham Tahir/PR2999 ac6025235b6f1233291000d35a067198628569e9. All consumed bytes are pinned in SOURCES.json. Package proof, result and remaining questions. Canonical claim.

Scope: a local numerical construction. It is nonlinear and evaluates every butterfly; it does not inherit a cheap recursive child tariff. A complete numerical consumer, physical hosting/routing, all-size admission and a favorable supplier moment remain unresolved. No new kappa, selected-frontier change, full selected replay or formal/human review is claimed. Latest PR3019's relaxed matching support and PR3024's packing cap address distinct obligations. Fresh complete overlap pagination failed; the retained historical corpus, recent PRs, canonical thread and relevant bodies were checked, with limits recorded in TASK.json.

Credit Arham Tahir/PR2999/2891/2665, ywz65/PR2586/2730/2555, Nick Petalas/PR2754/2771, Chafik Boukhalfa/PR628 and the retained native/geometry/compiler lineage. Prepared by Tekalign with substantial OpenAI Codex assistance. Apache-2.0.

The change is eight additive research-package files. Frozen sources, shared checkers, upstream/ and the selected frontier are unchanged.