A Numerical Grammar of the Periodic Table: Deriving 118 Elements from Ten Ontological Constants via N=Z+2

We present a systematic grammatical framework for interpreting the periodic table of elements through a reindexing scheme N = Z + 2, where Z denotes standard atomic number and N represents an ontological position incorporating the photon (N=1) and neutron (N=2) as precursors to hydrogen (N=3). This shift reveals that all 118 known elements derive compositionally from precisely ten indecomposable ontological constants (Unity, Structure, Motion, Stability, Expression, Connection, Force, Enclosure, Blueprint, Agency), partitioned into Energetic and Structural categories. We establish three deterministic rules governing element derivation: (I) prime number decomposition via hierarchical Agency addition, (II) composite factorization following closest-factor and category-dependent modification syntax, and (III) reflexive self-referential structures in the 11-series (11, 22, 33, ..., 110). The framework demonstrates complete coverage of the periodic table with inherent termination at N=120 (oganesson), while N=121 proves logically impossible due to an irreducible Agency-Unity paradox. This grammar suggests the periodic table encodes a formal linguistic structure with philosophical implications for the intelligibility of matter.