 446    - **Mass**: φ-ladder with rung ratio = φ
 447    - **Consciousness**: unique zero-defect ground state
 448    - **Uniqueness**: D = 3 is the only viable dimension -/
 449structure SpectralEmergenceCert where
 450  -- Geometry
 451  vertices_8 : V 3 = 8
 452  edges_12 : E 3 = 12
 453  faces_6 : F₂ 3 = 6
 454  euler_2 : V 3 + F₂ 3 = E 3 + 2
 455  aut_48 : aut_order 3 = 48
 456  -- Gauge content
 457  sector_sum_8 :
 458    SpectralSector.dim .color + SpectralSector.dim .weak +
 459    SpectralSector.dim .hypercharge + SpectralSector.dim .conjugate = V 3
 460  generators_12 :
 461    SpectralSector.gauge_rank .color + SpectralSector.gauge_rank .weak +
 462    SpectralSector.gauge_rank .hypercharge = E 3
 463  -- Generations
 464  three_gen : face_pairs 3 = 3
 465  -- Fermion census
 466  flavors_24 : fermion_flavors = 24
 467  flavors_DV : fermion_flavors = 3 * V 3
 468  states_aut : total_fermion_states = aut_order 3
 469  quark_lepton_3to1 :
 470    SpectralSector.dim .color * face_pairs 3 * 2 =
 471    3 * (SpectralSector.dim .hypercharge * face_pairs 3 * 2)
 472  -- Mass hierarchy
 473  mass_positive :
 474    ∀ (ys : ℝ) (_ : 0 < ys) (n : ℤ), 0 < mass_rung ys n
 475  mass_scaling :
 476    ∀ (ys : ℝ) (n : ℤ), mass_rung ys (n + 1) = phi * mass_rung ys n
 477  -- Consciousness
 478  ground_zero_cost : consciousness_ground.total_cost = 0
 479  ground_unique :

papers checked against this theorem

No papers in the current corpus map onto this theorem yet.