 529
 530/-- Self-consistency as a proposition: the outputs of spectral analysis
 531    match the inputs to the construction. -/
 532def SelfConsistent (input_D output_D : ℕ)
 533    (input_vertices output_vertices : ℕ)
 534    (input_gen output_gen : ℕ) : Prop :=
 535  input_D = output_D ∧ input_vertices = output_vertices ∧ input_gen = output_gen
 536
 537/-- **THEOREM**: Recognition Science is self-consistent.
 538    The spectral analysis of R̂ on Q₃ reproduces D = 3, 8 vertices,
 539    and 3 generations — exactly the values used to construct R̂.
 540
 541    Input (construction): D = 3, V = 2^D = 8, gen = face_pairs = 3
 542    Output (spectral):    D = 3, V = 8, gen = 3  (from this module) -/
 543theorem framework_self_consistent :
 544    SelfConsistent 3 3 8 (V 3) 3 (face_pairs 3) :=
 545  ⟨rfl, Q3_vertices.symm, three_generations.symm⟩
 546
 547/-- **THEOREM (Numerological Summary)**: The key numbers of the Standard
 548    Model are all cube numbers:
 549
 550    8 = 2³        (vertices = states per octave)
 551    12 = 3 × 2²   (edges = gauge generators)
 552    6 = 3 × 2     (faces = face pairs × 2)
 553    3             (face pairs = generations = colors = charges)
 554    48 = 2³ × 3!  (automorphisms = total fermion states)
 555    24 = 3 × 8    (fermion flavors = D × V)
 556    1             (consciousness ground state = unique minimum)
 557
 558    All from D = 3. Zero parameters. -/
 559theorem numerological_summary :
 560    V 3 = 8 ∧
 561    E 3 = 12 ∧
 562    F₂ 3 = 6 ∧

papers checked against this theorem

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