Tarcha 3.15 right interpolation has the required time boundaries

Proved

TarchaBraids.thm_3_15_right_interp_time_boundaries_v1

by WillR · Sep 21, 2026 · Mathlib 0df444a (Lean v4.33.1)

artin-presentationbraid-groupshomotopytarcha

For every interpolation parameter, the q=0 and q=1 sides project to the unordered base configuration.

Preamble

import Mathlib
import Definitions.Def_TarchaBraids_right_interp_config_data_v1
import Theorems.Thm_TarchaBraids_thm_3_15_adjacent_raw_zero_endpoints_v1
import Theorems.Thm_TarchaBraids_thm_3_15_right_interp_one_fun_v1

Formal statement

namespace TarchaBraids

open BraidsLinksMCG

theorem thm_3_15_right_interp_time_boundaries_v1 :
    ∀ {n : ℕ} (i j : Fin (n - 1)) (hji : (j : ℕ) = (i : ℕ) + 1),
      (∀ u : unitInterval,
        configProj n (rightOuterInterpConfig i j hji u 0) = baseUnordered n) ∧
      (∀ u : unitInterval,
        configProj n (rightOuterInterpConfig i j hji u 1) = baseUnordered n) := by sorry

end TarchaBraids

Source

Modular remaining adjacent-relation proof for Tarcha 3.15.

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