# Research index

- v0.7.0, 26 September 2026: strict semantic realization, excisive event reconstruction, and integral prime/matrix interaction kernels. K32–K41 have written proofs under explicit hypotheses; arithmetic globalization and Lean remain open. [Route record](research/records/2026-09-26_v070_semantic_excision_arithmetic.md). Base hashes and source diff are in `audit/`.

- v0.8.0, 27 September 2026: nonidentity derived arithmetic resolution, nilpotent excision collapse, explicit completion/repair generic-fiber defect, and effective lattice/operator gluing. K42–K52 have written proofs; K15 has a restricted lattice instance. [Route record](research/records/2026-09-27_v080_arithmetic_towers_completion_gluing.md). No Lean or automorphic-existence claim.

- v0.9.0, 27 September 2026: intrinsic kernel/invariant residuals, sharp precision lifting, a canonical non-scalar derived exchange defect, one-step action nonlifting, and exact exchange for coefficient-lifted inputs. K53–K61 have written proofs and self-review. [Route record](research/records/2026-09-27_v090_intrinsic_exchange_lifting.md). All four finite suites pass. No sufficient general lifting or reciprocity claim.

- v0.10.0, 27 September 2026: complete next-level H² obstruction, refuted sufficiency of the single derived-invariant comparison, known finite-group stability with a direct averaging proof, finite lifting horizon and class catalogue, and a profinite scope boundary. K62–K71 have written proofs. [Route record](research/records/2026-09-27_v0100_finite_group_lifting.md). Five suites pass; no all-profinite or Langlands claim.

- v0.11.0: [Continuous source resolution and normalized abelian lifting](research/records/2026-09-27_v0110_profinite_abelian_lifting.md). K72–K82, complete rank-two test, sharp horizon, mixed-variance correction, six exact suites, and certificate tool.