The Sedenion Triangular Root: A Child-Originated Partial Desimplicialization Operator on Cayley–Dickson Bitmasks

This preprint formalizes a symbolic operator originally proposed by Pedro Barone Agourakis at age 7, called the triangular root, and develops a sedenion-bitmask version as a partial desimplicialization operator on Cayley–Dickson support masks. The paper defines a geometric triangular root as a partial inverse to XOR/projective closure in PG(3,2), and then introduces a zero-divisor-filtered version using the Cayley–Dickson decomposition S = O ⊕ O. The finite classification obtained is 66 = 30 + 36: 66 geometrically rooted masks, of which 30 survive the zero-divisor filter and 36 become ghost roots. This record includes the PDF/A manuscript, LaTeX source package, bibliography, XMP metadata, and a verification script for the finite classification.