Gauge Fields, Fermions, and Self-Gravitating Matter on the Golden Cone (INDYNA Research Note 18)

This companion note to the Shift Law (Note 17) equips the golden cone with physics. A Peierls magnetic field leaves the golden level crossing exactly intact when aligned with a two-fold axis — a symmetry-protected crossing drifting linearly, g*(B)=φ-2-0.1716 B — and opens it quadratically for generic orientation: an orientable experimental signature. A Dirac monopole switches the network between worlds: for odd charge all multiplicities become even and the spectrum lives on half-integer golden powers, -51/4φ1/2, +51/4φ-3/2, +53/4φ1/2, while the golden crossing is flux-periodic mod 2. The lattice Dirac operator satisfies the index theorem ind = V-E exactly and carries the golden fermion mass ratio m(3')/m(3)=√((5+√5)/(5-√5))=φ. The calorimetric machinery yields Tpeak≃ 0.44 Δ, a third experimental channel. Coupling matter self-consistently to the geometry produces attraction, curvature, a Fermi-pinning law κpint02≈ 0.31, and a single collapse mechanism — exhaustion of the angular budget |δ|≤ 3π (visible) or ≤π (shadow, nearly incompressible, threshold 4.6× higher) — realized in two ways: the scalar sea reconstructs (Fermi pinning) on the way, while the Dirac sea, pinning-free with topologically rigid index, gravitates several times more strongly and reaches the same bound already at κc=0.872, with the approach law Δ r∝(κc-κ)2 predicted from the square-root behaviour of the deficit at the degeneracy. The Fermi-gap alternation gapped–gapless–gapped for monopole charge Q=0,1,2 survives unchanged inside the gravitating loop. Outlook: the Penrose programme announced here is treated in Note 22; Note 19 is "Time as the Irrational Part". Part of the INDYNA Notes series (Notes 16–34). All numbers reproduce from the INDYNA law register (master data record, doi:10.5281/zenodo.21891088). Licence CC-BY-4.0.