Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 351-03. Path selection and an elliptic inequality on degenerating Ricci-flat trees
Manuscript map · lines 9185–9194
OpenAI@2026-10-07#rem:oai-p-351-03
Authors: OpenAI. Family 351.
Title: Path selection and an elliptic inequality on degenerating Ricci-flat trees.
Abstract: We prove a sequential elliptic inequality for the renormalized Einstein–Hilbert functional on a fixed finite tree of four-dimensional Ricci-flat spaces. As the joining lengths diverge and the scale-neutral weighted Ricci error M tends to zero, the functional satisfies $E=o(M)$. The root end has decay exponent greater than one, and every joined quotient group is nontrivial. We also prove the multivariable path-selection theorem for asymptotic expansions used to obtain this estimate.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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