What was already known
The prior Buys–Polak–Zuiddam lower bound was 5.295492315784620 in dimension 207. The exact capacity remains unknown.
AI involvement
Protti directed the work and credits Astra 6 Pro and Codex GPT-6 Astra with retained certificate refinements. The underlying framework and base constructions are due to Buys, Polak and Zuiddam.
The disclosed model work supplies retained R10 certificate refinements under Protti’s direction, building on BPZ’s human framework.
- Supporting source (vibemathed.com) — What was actually shown; What the AI did; Verification
Importance
Sets a slightly higher explicit lower bound for the Shannon capacity of the 11-cycle.
Limitations
The improvement is small. The reported Lean replay uses disclosed native Boolean-check axioms and has not had independent expert review; the release does not prove an upper bound or optimality.
Technical verification
The v0.5.0 release reports a cited Lean 4.32.2 development build and fresh replay of the actual C11 independent set, exact cardinality and lower-bound theorem. Numerical proofs retain disclosed native Boolean-check axioms and compiler/runtime trust; the statement has not received independent expert review. The upper diagnostics and search optimality are outside this rating.
Formal checking
The release reports a pinned Lean build, fresh replay, theorem and axiom audits, and negative controls; native Boolean checking remains in the trust boundary.
- Checker
- Lean 4.32.2 and the author-side fresh replay
- Scope
- R10 independent set in C11 strong power 213, exact cardinality, capacity lower bound 5.295526013632343 and strict comparisons
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
Protti directed and assessed certificates, but the reviewed disclosure does not establish a human explanation of the full R10 terminal construction. Few is the evidence default, not a claim that humans cannot understand it.
Correction and publication history
A new explicit independent set slightly raises the C₁₁ lower bound.
Read this published revision