Freiman marked initial bridges: survivor endpoint

Proved

Freiman.lower_bridge_survivor_endpoint

by tp · Sep 9, 2026 · Mathlib 0df444a (Lean v4.33.1)

certificatesfreimanlower-construction

The marked-family case split maps the safe J12,12 target bound to the actual normalized S/C22 lower endpoint using its source-certified large branch.

Preamble

import Definitions.Def_Freiman_lowerBridgeCatalog
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Push

open Freiman

Formal statement

theorem Freiman.lower_bridge_survivor_endpoint (hlarge : ∀ c n k, lowerBridgeZero c = decide (n=0) → lowerBridgeSurvivorLarge c n k) (t : ℝ) (f : LowerInitialFamily) (n k p : ℕ)
    (hmarked : (f = .A ∧ k = 0) ∨ (f = .B ∧ k = 0) ∨ (f = .C ∧ p = 0))
    (hsafe : lowerInitialSafeBound t f n k p) (s : LowerPair)
    (hnorm : lowerNormalize s =
      ((lowerNormalize (lowerFamilyPair f n k p)).1 ++ [1],
       (lowerNormalize (lowerFamilyPair f n k p)).2 ++ [1])) :
    lowerLocalLower s ([2],[2]) ≤ lowerLocalCoordinate s t := by
  sorry

Source

Freiman report, initial_bridges.tex, corrected marked H entries; H_entry_bridges.json 185 exact polynomial records.

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