THE HODGE COMPLEX - A Structural Origin for the Standard Model: From Discrete Substrate to Particle Physics
What if the Standard Model isn't fundamental, but the residue left over when a tiny lattice cancels against its own mirror?
The Hodge Complex: A Structural Origin for the Standard Model proposes that the Standard Model of particle physics can be derived from a single discrete object, the periodic 8 8 torus. Instead of adding extra dimensions, strings, or new fields, the Hodge Complex Standard Model (HCSM) starts with 64 lattice sites and asks what survives when the lattice's spectrum cancels against its mirror image. Fourteen modes survive. The book argues that those fourteen modes are exactly one generation of Standard Model particles.
From that starting point, the book develops, step by step and in theorem-and-proof form:
-The emergence of four-dimensional spacetime with Lorentzian signature, with no Wick rotation-The gauge algebra SU(3) SU(2) U(1)⁵, hypercharge quantization, and anomaly cancellation
-The CKM and PMNS mixing matrices, including a Cabibbo angle of π/14
-The Higgs sector, the top mass, the graviton, and the Newton constant
-Dark energy, the electroweak-Planck hierarchy, and vacuum stability
The book closes with a catalogue of falsifiable predictions, including no dark photon, no axion, no fourth generation, and a specific dark energy equation of state. It also states plainly what is derived, what is taken as input, and what remains open. Every chapter ends with exercises, and the numerical claims are checked in machine-precision arithmetic.
This is a formal, mathematical monograph. It is written for physicists, mathematicians, and advanced students who want to follow a complete derivation chain and test it, and who are curious about discrete and structural approaches to the foundations of physics. It is not a popular-science book.
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