Hi everyone in the Wolfram Physics / Fundamental Physics Project community, I’ve just finished a 29-page cumulative working document that takes a strictly graph-first approach to electromagnetism, charge, chirality, and family replication. The core is built on a finite oriented graph with compact U(1) links — very much in the spirit of causal graphs and hypergraph models. Quick summary of what’s in the paper:
Charge is literally an integer-valued flux-divergence defect on the graph. Exact regional Gauss law, topological quantization from link compactness, exact lattice continuity, Coulomb law from graph-Laplacian minimization, and full Maxwell dynamics emerging in the aligned deconfined phase — all proved cleanly. A common topological language (cellular gauge data + relative current classes + twisted Spinc index theory) unifies charge, chirality, and three-family replication. Explicit finite toy model: product graph $ G = \Lambda_4 \times I_s \times T^2_F $ with domain-wall/overlap fermions and internal flux index 3 gives minimal charge + chirality + three replicated families from one parent generation. Preferred strong ontology (the part I’m most excited about): charged particles are reinterpreted as self-bound local causal shells. A charged lepton is a trapped spinor core coupled to a bosonic shell-deformation sector on a closed 2D simplicial surface. The minimal regular shell is naturally tetrahedral; the leading deformation multiplet is a geometric triplet whose microscopic anisotropy + holonomy collapse to a single-vector operator that automatically produces the exact cosine spectrum used in Koide-type charged-lepton relations. Strong coefficient locking and a codimension-one dynamical balance surface emerge from identical-link tetrahedral geometry and radial-wall tension.
The paper is deliberately layered: theorems vs. constructions vs. strong-but-incomplete branches vs. ruled-out ideas. It overlaps structurally with tetrahedral A₄ flavor models but supplies a concrete geometric engine inside the shell rather than abstract flavons. Full PDF (masterworkingdocument_v8.pdf) is attached. Transparency note: I used Grok (xAI) heavily to help me refine the writing, tighten the LaTeX, organize the sections, and make the ideas as clear as possible. The core physics ideas, and ontology are my own — but the AI was instrumental for making this possible. I’d love honest feedback from this community, especially on:
how the compact-graph U(1) core and causal-shell picture might connect to hypergraph / causal-graph dynamics, any overlaps or tensions with the Wolfram Physics framework, suggestions for next steps or things I should stress/test.
Happy to discuss any part of it. Thanks in advance!
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