C11 R6: Lean-checked bound 5.295515544509239

Explicit independent sets in the 186th, 198th, and 213th strong powers of C11 give Lean-checked capacity lower bounds 5.295498536418623, 5.295510441529957, and 5.295515544509239. Each constructed root strictly exceeds its matching R5 root and all four older frozen BPZ/R3/R4 comparison roots, using full integers.

R6 verifies the supplied ordinary 58-letter certificates within BPZ's generic framework. The general avoidance-profile calculus remains a written proof. R5 is preserved in v0.2.0 and in this source tree; all earlier sealed packages are unchanged.

The attached original checked ZIP has SHA256 f9255ff24766c736593e31469df82857ee038809078274cbac5ed1e09a4feeb2. It includes the sources, pinned fresh-build evidence, 24 scope aliases, 232 audited declarations, actual-type inspection of all 234 native axioms in the audit union, six intended failing compile controls, and reproducibility tools. Native evaluation and dependency-cache trust are disclosed; this is not kernel-only arithmetic replay. Publication integrity checks do not themselves rerun Lean.

The source tree additionally preserves the author's supplied automated receipt review. That receiving review did not rerun Lean and is not a human referee report. No new global priority clearance or independent expert endorsement is claimed.

AI co-developed under Matthew Protti's direction with OpenAI's Astra 6 Pro and Codex GPT-6 Astra Extra-High. The underlying BPZ work and earlier seed authors retain their attribution.