trureturingGitHub MATHEMATICAL ATLAS

Tower / CONCEPT

Bounded Forces Periodic

A bounded orbit under an expanding multiplier is zero, so periodic digits make the remainders repeat with the same period.

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THEOREM

Periodic digits force a periodic orbit

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Bounded Forces PeriodicBounded Forces PeriodicCollapse Is ExpandingCollapse Is ExpandingNot Eventually PeriodicNot Eventually Periodic
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Status
Closed
Depth
0
Layer
D5/S0
Domain
Tower
Node ID
D5/S0/Tower/NonPisotFrontier/BoundedForcesPeriodic
Repository path
D5/S0/Tower/NonPisotFrontier/BoundedForcesPeriodic.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
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745bf90812f7175f83e1235688249f9495f23bfc
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143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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Dependency edges, status, and source coordinates come from the verified release and certified topology. Blueprint exposition is labeled separately. A fallback title carries no additional mathematical authority.