BLLM: Beyond the LLM with Deep Human-Mind-AI

Anaxia, the BLLM engine: typed construction search, independent checks and recorded failure residues. This research candidate adds twelve exact finite-interval certificates for reflexive four-polytopes, an independent integer verifier, and a portable animated certificate explorer.

Relative to the supplied Kreuzer–Skarke point-pair census, the maximum shortest descent satisfies 22 ≤ D4 ≤ 346. The prior bound 348 for arbitrary descents is unchanged. The verifier reconstructs facets, primal and polar lattice points, strict containment, interval costs, pair bounds and exceptional-census coverage. It does not reconstruct the entire classification histogram.

The sharp seed constant, Hodge F2/F3-prime, GSC and the continuum Yang–Mills problem remain open. The full four-target closure benchmark has not been crossed. Graph survivors are necessary candidate configurations, not constructed semiregular objects. No new Lean formalization of the interval refinement is claimed.