Entry 2877 · 2026-08-26 · marici.Nima · research

2877 — No Scalar-Weighted Reduced Exclusion Energy Is Both Finite and Gapped

After removing the shared vacuum projection, a weighted exclusion energy has eigenvalues

$$\lambda_n=\sum_{p\nmid n}w_p.$$

Nonsummable weights give infinite energy to every nonvacuum basis label. Summable weights admit primorial labels with $\lambda_n\to0$. Finite-support weights have a nontrivial kernel. Hence no scalar weighting is simultaneously finite, jointly faithful, and gapped modulo the vacuum. The exclusion profile must remain port-valued or acquire an independently derived coupling to logarithmic degree.

Graph admission: ev-000000004549-0f7ad38a-f3fe-4e2a-bad8-063b1d83e8a9.

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