top_quark_pred

formal source

 358  Constants.phi ^ (45 : ℕ) / 2000000
 359
 360/-- The top-quark structural mass (UpQuark sector, rung 21). -/
 361noncomputable def top_quark_pred : ℝ :=
 362  Constants.phi ^ (51 : ℕ) / 2000000
 363
 364/-- All structural quark mass predictions are positive. -/
 365theorem quark_preds_pos :
 366    0 < up_quark_pred ∧ 0 < charm_quark_pred ∧ 0 < top_quark_pred := by
 367  unfold up_quark_pred charm_quark_pred top_quark_pred
 368  refine ⟨div_pos (pow_pos Constants.phi_pos _) (by norm_num),
 369          div_pos (pow_pos Constants.phi_pos _) (by norm_num),
 370          div_pos (pow_pos Constants.phi_pos _) (by norm_num)⟩
 371
 372/-- The charm/up ratio equals φ^11 exactly (11-rung generation gap). -/
 373theorem charm_up_ratio : charm_quark_pred / up_quark_pred = Constants.phi ^ (11 : ℕ) := by
 374  unfold charm_quark_pred up_quark_pred
 375  have hpos : (0 : ℝ) < Constants.phi ^ (34 : ℕ) / 2000000 :=
 376    div_pos (pow_pos Constants.phi_pos _) (by norm_num)
 377  field_simp [ne_of_gt hpos]
 378
 379/-- The top/charm ratio equals φ^6 exactly (6-rung gap). -/
 380theorem top_charm_ratio : top_quark_pred / charm_quark_pred = Constants.phi ^ (6 : ℕ) := by
 381  unfold top_quark_pred charm_quark_pred
 382  have hpos : (0 : ℝ) < Constants.phi ^ (45 : ℕ) / 2000000 :=
 383    div_pos (pow_pos Constants.phi_pos _) (by norm_num)
 384  field_simp [ne_of_gt hpos]
 385
 386/-- Top quark structural prediction: φ^51/2000000 is in the multi-GeV range.
 387    This captures the scale correctly even without the full gap correction. -/
 388theorem top_quark_pred_order :
 389    (10000 : ℝ) < top_quark_pred ∧ top_quark_pred < 1000000 := by
 390  unfold top_quark_pred
 391  -- Use pre-computed bounds: phi^51 ∈ (45537548334, 45537549354)