trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Total spectral rows and direct concatenation

A given complex encoder supported on legal direct concatenations obeys every total-row rank bound.

Closed Authored exposition
DIRECT PREREQUISITES3
DIRECT CONSEQUENCES1
PROOF DEPTH6
DOCUMENT LINKS1
THEOREM

The necessary spectral and threshold bounds

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Direct concatenation without a separatorDirect concatenation without aseparatorUniversal Replacement Capacity GrowthUniversal Replacement CapacityGrowthPartial Trace and Quantum Mutual InformationPartial Trace and QuantumMutual InformationTotal spectral rows and direct concatenationTotal spectral rows and directconcatenationExact ranks and entropy for direct concatenationExact ranks and entropy fordirect concatenation
Proof dependencyStructural affinityDocument link

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Lean sourceResearch workspace
Status
Closed
Depth
6
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/Entanglement/KBonacciDirectSupportObstruction
Repository path
D5/S3/Quantum/Entanglement/KBonacciDirectSupportObstruction.lean
Truth release
sha256:76a8db6a0f78609b1b9d4a959c8392f2752f2daaddc1930e046e34ce07d0f608
Source commit
b52262a023c4db9bb30a128ebfd80ea4ef4c1a53
Source tree
37a24ddf3b9983bdabf0acbfd9b32b06c35c28d3

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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.