Freiman marked initial bridges: word states

Proved

Freiman.lower_bridge_word_states

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

certificatesfreimanlower-construction

Finite safe word-extension checks for the 5/4/1 prescribed bridge words, with arbitrary repetitions handled by the existing core/ratio invariant.

Preamble

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

open Freiman

Formal statement

theorem Freiman.lower_bridge_word_states (c : LowerBridgeCase) (n : ℕ) (hc : lowerBridgeZero c = decide (n=0)) (hf : lowerBridgeFamily c ≠ .C) : ∀ d ∈ lowerBridgeLabels (lowerBridgeFamily c) n, lowerAdmissible (lowerPhysicalAdd (lowerFamilyPair (lowerBridgeFamily c) n 0 0) d) ∧ lowerParameterBox (lowerPhysicalAdd (lowerFamilyPair (lowerBridgeFamily c) n 0 0) d) := by
  sorry

Source

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

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