An obsolete or dialectal superlative form meaning 'most beat' or most defeated/exhausted; archaic beat poetry slang.
From 'beat' (worn out, exhausted) + '-inest' (superlative suffix, archaic). This formation is characteristic of pre-modern English superlatives before standardization.
This looks like a word from 1950s Beat Generation slang trying to say 'most exhausted,' but the grammar is wrong for modern English—we'd say 'most beat' now, showing how language standardizes over decades.
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