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May 6, 20260 citationsOpen Access

Substrate-Framework Particle Equations

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EGEliot Gable

Key Points

  • This research aims to describe the substrate framework's complete particle catalogue within the Standard Model.
  • Developed a closed-form equation parameterized by an identity vector.
  • Classified particles into groups based on their properties within the framework.
  • Utilized a tuple of integer-valued slots to represent per-particle data.
  • Introduced a single equation that captures data on every Standard Model mode and dark-sector mode.
  • Established seven particle groups, each defined by one identity-vector schema.

Abstract

The substrate framework’s complete particle catalogue — chain position and mass for every Standard Model mode and every predicted dark-sector mode — reduces to a single closed-form equation parameterized by a small per-group identity vector. The Standard Model + framework dark sector partition into seven particle groups, and each group has one identity-vector schema. Per-particle data within a group is a finite tuple of integer-valued slots.

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Cite This Study

Eliot Gable (2026) studied this question.

synapsesocial.com/papers/69fa8eac04f884e66b5310e1https://doi.org/10.5281/zenodo.20028868
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