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theorem proved term proof

spectral_emergence

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formal statement (Lean)

 495theorem spectral_emergence : SpectralEmergenceCert where
 496  vertices_8 := Q3_vertices

proof body

Term-mode proof.

 497  edges_12 := Q3_edges
 498  faces_6 := Q3_faces
 499  euler_2 := Q3_euler_characteristic
 500  aut_48 := Q3_aut_order
 501  sector_sum_8 := sector_dim_sum
 502  generators_12 := gauge_generators_eq_edges
 503  three_gen := three_generations
 504  flavors_24 := fermion_count_24
 505  flavors_DV := fermions_eq_D_times_V
 506  states_aut := fermion_states_eq_aut
 507  quark_lepton_3to1 := quark_lepton_ratio
 508  mass_positive := mass_rung_pos
 509  mass_scaling := mass_rung_step
 510  ground_zero_cost := consciousness_zero_cost
 511  ground_unique := zero_defect_unique
 512  deviation_costs := any_deviation_costs
 513  D3_viability := D3_viable
 514  D3_only := D3_unique_viable
 515
 516/-! ## Part 9: The Spectral Self-Consistency Identity
 517
 518The ultimate closure: the structures derived FROM Q₃ (gauge group, mass
 519hierarchy, consciousness) are EXACTLY the structures needed to CONSTRUCT
 520the recognition operator R̂ that acts ON Q₃.
 521
 522  T0-T8 → R̂ on Q₃ → spectral analysis → {gauge, mass, consciousness, D=3}
 523    ↑                                                    |
 524    └────────────────────────────────────────────────────┘
 525
 526This is a FIXED POINT, not a circle. The framework is the unique
 527self-consistent solution to: "construct an operator whose spectral
 528analysis reproduces its own construction axioms." -/
 529
 530/-- Self-consistency as a proposition: the outputs of spectral analysis
 531    match the inputs to the construction. -/

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