Paper CLXVII of the One-Octonion Brane-Bulk Series Recasting the Cooper Pair Exclusion Sum Rule: Tan Contact Separation in 2D, Qualitative Support from Daix

Paper CLXVI proposed the excluded-area sum rule R 1 −gpair(r) d2r = πξ2 for the strongly-interacting Fermi gas, motivated by bulk-channel exclusion of Cooper pairs in the brane-bulk framework. Direct application to the 2D AFQMC data of Daix et al. (2026, PRL 136, 153402; arXiv:2504.01885) reveals a subtlety: in 2D, the pair correlation g↑↓(r →0) diverges logarithmically (as log2(kF r), following Werner and CLXVII-2 (2D dip region only): Idip ·k2 F ≈π(ξexcl ·kF )2 restricted to g < 1. Applied to Daix et al. 2026 at crossover η ≡log(kF a2D) = 1.0–1.2, the triangular- dip integral evaluates to Idip · k2 F ≈2.76, matching π(ξkF )2 ≈2.77 for ξkF ≈0.94–1.0 — qualitative support within ∼15% without any free parameter. The 20–22% BCS violation (pair dip depth) and the location kF r ∼2 are both consistent with bulk-channel exclusion. The clean zero-parameter test requires 3D unitary gas data. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.