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Formalize the selected BIT split-residual retractions and conjugation interface - #2728
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PR2195 supplies the written split-rank factorization for selected BIT local-ring residuals. This contribution kernel-checks the explicit block formula, its left/right retractions, image correspondence and injectivity, plus involution and additive coordinate-conjugation behavior.
The abstract proof requires additive maps and VB=id; only involution additionally requires C²=id. Concrete selected matrices, scalar-linearity instantiation, determinant-unit lifting and a dimension/rank-library theorem remain external. The formal result is retractions and image correspondence, not a claim that the full supplier or every selected matrix is certified.
Validation: Lean 4.34.1 compiles the full source with warnings-as-errors and audits 14 roots against standard axioms; four material proof mutations and a genuinely compiled forbidden-axiom declaration are rejected. Registered Python 3.12 checks 252 exact ring cases (42 positive-rank/zero-trace cases), conjugated identities, five premise/boundary controls and four Git-free CLI groups. The generic Python hook does not automatically run Lean; the explicit live command is documented and was run. Independent agent review found no issue; no human review claimed.
Credits Jose Manuel/jmbarrancoml PR2195, original head 3a1cf78, and its retained lineage. Source PROOF.md is byte-identical to that head. Scientific base 21ec98b; current diff base ab4fcd3, unchanged guidance. Claim: #2195 (comment). Bounded live/local overlap and stale Discussion coverage are recorded in TASK.json.
Only research/lean-split-residual is added. No selected cold replay, hosted CI, new supplier or kappa. Substantial OpenAI Codex assistance. Reproduce: python3.12 scripts/research_package.py --package research/lean-split-residual; add the documented verifier --lean executable command for the kernel audit.