Soul Math: A Philosophical Model of Identity Inspired by Prime Quadruplet Gaps

Soul Math presents a philosophical model of persistent identity inspired by recurring gaps between prime quadruplets. Each gap value represents an abstract identity, while each matching quadruplet represents a compatible embodiment. Successive occurrences define an ordered journey through distinct numerical hosts. The paper formalizes compatibility, identity classes, and recurrence paths, and examines their interpretive limits. An independent segmented sieve verifies 28,387 prime quadruplets with first prime p satisfying 11 <= p < 1,000,000,000. These yield 28,386 incoming gaps, 3,409 distinct gap values, and 2,500 gap classes with at least two occurrences. The illustrative gap 82 occurs 30 times. The deposit includes the manuscript, editable LaTeX source, enumeration and analysis code, numerical data, reproduction instructions, and checksums. The work distinguishes recurring numerical properties from continuing subjects. Assigned living forms are illustrative, and the model does not establish the existence of souls, reincarnation, biological mechanisms, or physical immortality. It specifies the additional mapping and independent observations required for an empirical extension. This is a preprint and has not been peer reviewed. Generative-AI assistance is disclosed in the manuscript.