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Prove a common-reference numerical splice from nonlinear rounded finite-core inverses to a complete cyclic/tensor inverse, using sparse inputs copied before core mutation. An explicit direct-Neumann halo replaces the original normal-equation correction. The error bound has no core-count factor; rounding, actual input radii and normalization scales remain charged.
Consumes #4205's finite-core contract, retained via #4253. Complements #4217/#4517's locality/lift and #5081's suffix result by supplying the alternative local defect; predecessor methods are not claimed anew.
Base: 7c49fe3. Exact seven live input Git/SHA256 pins and separate provenance: SOURCES.json.
Reproduce (Python 3.12, stdlib):
Expected: PASS_REGISTERED_RESEARCH_PACKAGE.
Executed: normal/optimized exact checks on four fixtures, 1,408 outputs and 2,024 saved copies. Twelve controls cover stale inputs, missing period paths, premature cropping, ideal-only radii, unpaid normalizers and recovery-scale/norm errors. Source/commit bytes and both read-only Git-free export replays pass; remote tree matches tested contents. Core test doubles are not executions of the fast predecessor circuit.
No new κ. Reference row gap and finite-core contract are premises. Global reference/page generation, physical delivery/cost, full suffix/recovery scaling and all five selected assumptions remain. No complete multiplier or human/kernel acceptance.
By @CubeJerry with substantial OpenAI Codex assistance and separate adversarial review. Credit Cinna Davis (#4100), Jose Manuel (#4205/#4253), Nick Petalas (#4217), Ryanson Jonathan (#4517), JoyboyBrian (#5081), Mason Hale (#2313), and retained analytic lineage. Apache-2.0.
Proof, pins, validation and open questions:
https://github.com/CubeJerry/integer-mult-bounds/tree/e212af981b49c299de515f8c23dfb0e5b73e2e95/research/rounded-core-halo-splice