A Brief Theory of Almost Everything with Examples of Its Use

This work introduces the mathematical formalism of constraint geometry: a framework in which dynamics is not postulated through equations of motion, but emerges as the projection of a natural tendency onto a set of admissible variations.

The core objects — state S, constraint functional C, admissible directions A(S), and induced bilinear form g_S — are defined and their properties investigated:

• Non-integrability — explicit curvature formula through third derivatives of C (Theorem 4.3, verified symbolically)
• Dynamic constraint — evolution of C via accumulated structural difference Q(t)
• Bifurcations — splitting of admissible directions into incompatible components
• Non-Markovianity — path dependence derived from differential geometry
• Spectral saturation — three active constraint channels as the natural saturation point

A concrete realization through elliptic functions (Lamé equation) and a Python library implementing the core objects are included.

The title “A Brief Theory of Almost Everything” is deliberately chosen: this formalism applies to any science that possesses structure — from physics and cosmology through biology and economics to artificial intelligence. It does not claim to explain everything — it offers a unified mathematical language in which constraints in each of these fields can be formulated as the geometry of admissible variations.

Languages: English (29 pp.) and Bulgarian (29 pp.)

Acknowledgments: This work is the result of collaboration between the author and generative language models (DeepSeek, ChatGPT, Claude, Gemini, Copilot), used for technical verification, symbolic checks, and code generation. Responsibility for the formulation, definitions, and final text rests with the author.