trureturingGitHub MATHEMATICAL ATLAS

Combinatorics / CONCEPT

Nonsingularity of actual uniform reflection cross-Grams

Fix one indexed array of 2n permutation rows on n symbols. Its indicator matrices, fibres and joint counts all use the same rows. Pairwise commutation is an explicit additional hypothesis. No distinct-row or reduced-array hypothesis is imposed.

Closed Authored exposition
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES0
PROOF DEPTH1
DOCUMENT LINKS1
THEOREM

Every actual off-diagonal cross-Gram has trivial real kernel

RELATIONSHIP ATLAS

Every connection, in context.

Explore in 3D
Direct recorded relationships
Component parity of uniform reflection arraysComponent parity of uniformreflection arraysNonsingularity of actual uniform reflection cross-GramsNonsingularity of actualuniform reflection cross-Grams
Proof dependencyStructural affinityDocument link

Certified topology / UPSTREAM

Prerequisites

Certified topology / DOWNSTREAM

Consequences

None recorded in this release.

RELATED KNOWLEDGE

Structural connections

Documents & exposition

Other authored & advisory relationships

None recorded in this release.

LIBRARY / RELEASE VERSIONS

Content history

Loading release versions...
Browse the archive

Certified provenance

Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
1
Layer
D5/S3
Domain
Combinatorics
Node ID
D5/S3/Combinatorics/Graph/URSActualNonsingularity
Repository path
D5/S3/Combinatorics/Graph/URSActualNonsingularity.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

Authority boundary

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.