trureturingGitHub MATHEMATICAL ATLAS

Arith / CONCEPT

Ramified Five Matrix Reduction

An integral matrix that squares to five times the identity is nonnilpotent over the integers and invertible over the rationals, but its reduction at the ramified prime five is square-zero.

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DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH1
DOCUMENT LINKS1
THEOREM

Reduction at five turns an integral square root of five nilpotent

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Exact Dual-Lattice FormulaExact Dual-Lattice FormulaRamified Five Matrix ReductionRamified Five Matrix Reduction
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Lean sourceResearch workspace
Status
Closed
Depth
1
Layer
D5/S3
Domain
Arith
Node ID
D5/S3/Arith/Lattices/RamifiedFiveMatrixReduction
Repository path
D5/S3/Arith/Lattices/RamifiedFiveMatrixReduction.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.