Formalizing Delcourt–Postle's refined absorption in Lean

We describe a Lean formalization of selected principal results from Delcourt and Postle's refined absorption paper and Postle's survey, concentrating on the interfaces between their arguments. Case studies explain reserve matching, avoidance in compatible decompositions, and compatible absorbers. Under the precise definitions discussed in the note, a finite vertex-count obstruction rules out the survey's global embedding conclusion; the proved piecewise variant is treated separately. Completion yields prescribed sparse intersections, finite exact-intersection embeddings and an initial intersection interval of polynomial order. Proved external colouring and Nash-Williams inputs give polynomial excess bounds for partial parallel classes and triangle-decomposition schedules. These are verified derivations and interface clarifications; historical priority for each consequence is not claimed.

Preprint 1.0.1 is an editorial update following three rounds of feedback. It improves the English and Spanish exposition, notation, attribution and coverage statements, and restores the acknowledgements and AI disclosure used in the Nash-Williams papers. The deposit contains four PDFs: the research note and its separate formalization and reproducibility companion, each in English and Spanish.

The Lean proofs, dependency pins and formal-source freeze are unchanged. This release does not formalize every statement of the source papers; the remaining high-girth and other endpoints are identified in the coverage discussion. The internal audit is an agent self-assessment, not independent human peer review, a new kernel replay or a Palomar certificate.

Immutable publication source: https://github.com/jtraverso/refined-absorption-lean/tree/fd36d7d22f35946bdd38c3e092a053cecbf04b49
GitHub release, synchronized sources, audit evidence and checksums: https://github.com/jtraverso/refined-absorption-lean/releases/tag/preprint-v1.0.1
Changelog: https://github.com/jtraverso/refined-absorption-lean/blob/preprint-v1.0.1/CHANGELOG.md

The joint comparison interface covers 18 selected statements. Its historical submission snapshot remains https://github.com/jtraverso/refined-absorption-lean/tree/867d1e3d5e48ef20a8f1ae68237834eb06211cbc . No new official Palomar verification or registration is claimed by this editorial deposit. Version 1.0 remains available unchanged.