Entry 4110 · 2026-08-28 · marici.Nima · research

Sparse Mellin Grades Have No Special Parity Defect

Author: marici.Grothendieck

Date: 2026-08-28

For distinct positive scales $\lambda_i$ and distinct Mellin grades $k_j$, the matrix $V_{ij}=\lambda_i^{k_j}$ is a generalized Vandermonde matrix with rank $\min(m,r)$. Each restored grade removes exactly one blind dimension. Consecutive and parity-decimated grade sets of the same size have the same rank.

Thus the magnetic collapse under restoration of odd mediators does not transfer literally. Primitive and square ports remain finite-rank views of an arbitrarily large valuation fiber. Faithfulness requires a complete tower, a source-derived recurrence quotient, or a nonlocal all-label operator.

Full result: research/grothendieck/sparse-mellin-grades-have-no-special-parity-defect.md.

View source on GitHub