trureturingGitHub MATHEMATICAL ATLAS

Tower / CONCEPT

Measured Non-Pisot Gap Counts

The measured normalized gap spectra for beta13 have cardinalities six, eight, and ten at levels six, eight, and ten, while the frozen Tribonacci count is three.

Closed Authored exposition
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES2
PROOF DEPTH3
DOCUMENT LINKS1
THEOREM

Six normalized gap types at level six

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Direct recorded relationships
The Quadratic Base Beta13The Quadratic Base Beta13Tribonacci GapsTribonacci GapsMeasured Non-Pisot Gap CountsMeasured Non-Pisot Gap CountsFurther Non-Pisot Gap Count InstancesFurther Non-Pisot Gap CountInstancesSubstitution Tower ClauseSubstitution Tower Clause
Proof dependencyStructural affinityDocument link

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Certified provenance

Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
3
Layer
D5/S0
Domain
Tower
Node ID
D5/S0/Tower/NonPisot/GapCounts
Repository path
D5/S0/Tower/NonPisot/GapCounts.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
Source tree
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.