unchallengeably

un·chal·lenge·a·ble

 (ŭn-chăl′ən-jə-bəl)
adj.
Not open to challenge: unchallengeable facts.

un·chal′lenge·a·bly adv.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

unchallengeably

(ʌnˈtʃælɪndʒəblɪ)
adv
in a way that cannot be challenged; in an unchallengeable manner
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
References in periodicals archive
This is so because the time 'long ago' when things came into being is both indefinite and 'still part of the present' and has 'an unchallengeably sacred authority' (1979:24)--hence its sense being translatable as 'The Law'.
United Europe; a wider Holy Roman Empire; a New Order without the Nazis; a federation of European nations with a place for England, France, Spain, Wales, Brittany, Lithuania, Flanders, the Grand Duchy of Muscovy and all the rest; a forest of ancient flags on a green ground; an empire of extreme diversity, prosperous but aware that prosperity is not all; peaceable but unchallengeably strong in its own defence; a Europe taking its place once more as the natural centre and summit of the world.
(28) He had prestige which was close to being unchallengeably high.
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