trureturingGitHub MATHEMATICAL ATLAS

Arith / CONCEPT

Horizontal Completeness Depth

Joint residues modulo an initial prime segment separate a bounded natural interval exactly when the segment's modulus product exceeds the interval, and the first such segment is its horizontal completeness depth.

Closed Authored exposition
DIRECT PREREQUISITES0
DIRECT CONSEQUENCES2
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THEOREM

Horizontal depth is the least faithful prime-residue depth

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Horizontal Completeness DepthHorizontal Completeness DepthPrimorial Witness BoundPrimorial Witness BoundPrime Observation Depth and GeometryPrime Observation Depth andGeometry
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Lean sourceResearch workspace
Status
Closed
Depth
0
Layer
D5/S3
Domain
Arith
Node ID
D5/S3/Arith/Coding/HorizontalCompletenessDepth
Repository path
D5/S3/Arith/Coding/HorizontalCompletenessDepth.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.