Quantum / CONCEPT
SpectralTransposeRecovery
The existing finite-matrix functional calculus constructs a support projection and spectral inverse square root. The shared decoder normalization lemma is the existing proof extracted once and consumed by both the original candidate and the reference completion; it claims no independent mathematical gain. Explicit Kraus completion gives a canonical CPTP candidate even for a zero CP branch. Exact recoverability and smoothness are separate conclusions.
Closed
DIRECT PREREQUISITES1
DIRECT CONSEQUENCES7
PROOF DEPTH3
DOCUMENT LINKS0
spectral support on kraus
RELATIONSHIP ATLAS
Every connection, in context.
Direct recorded relationships
Proof dependencyStructural affinityDocument link
Certified topology / UPSTREAM
Prerequisites
Certified topology / DOWNSTREAM
Consequences
- A reference-preserving full-space Petz channeltruth-dependency · Closed
- Actual spectral whiteningtruth-dependency · Closed
- GeometricTraceConvexitytruth-dependency · Closed
- Schwarz and trace rigidity give actual Petz recoverytruth-dependency · Closed
- SpectralRecoveryCorrectnesstruth-dependency · Closed
- SupportPerspectiveTransporttruth-dependency · Closed
- The Eventual-Click Doob Instrumenttruth-dependency · Closed
RELATED KNOWLEDGE
Structural connections
- A reference-preserving full-space Petz channelstructural-affinity · Closed
- Actual spectral whiteningstructural-affinity · Closed
- Constructive transport of moving logical matrix unitsstructural-affinity · Closed
- FiniteKrausReversibilitystructural-affinity · Closed
- GeometricTraceConvexitystructural-affinity · Closed
- KrausCompletionstructural-affinity · Closed
- MatrixUnitDecoderstructural-affinity · Closed
- MatrixUnitGeneratorstructural-affinity · Closed
- OrthogonalSyndromeChannelstructural-affinity · Closed
- OrthogonalSyndromeDecodingstructural-affinity · Closed
- PointwiseTensorGeometrystructural-affinity · Closed
- Schwarz and trace rigidity give actual Petz recoverystructural-affinity · Closed
- SpectralRecoveryCorrectnessstructural-affinity · Closed
- SupportPerspectiveTransportstructural-affinity · Closed
- The Eventual-Click Doob Instrumentstructural-affinity · Closed
Documents & exposition
None recorded in this release.
Other authored & advisory relationships
None recorded in this release.
LIBRARY / RELEASE VERSIONS
Content history
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