trureturingGitHub MATHEMATICAL ATLAS

Quantum / CONCEPT

Future Statistics and the Infinite Operator System

Future operator statistics are exactly the annihilator of the generated system.

Closed Authored exposition
DIRECT PREREQUISITES2
DIRECT CONSEQUENCES3
PROOF DEPTH6
DOCUMENT LINKS1
THEOREM

Future statistics characterize the infinite-system annihilator

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Quantum Relative-Entropy Defect CompositionQuantum Relative-Entropy DefectCompositionPermanent Stability of the Operator-System TowerPermanent Stability of theOperator-System TowerFuture Statistics and the Infinite Operator SystemFuture Statistics and theInfinite Operator SystemOperational Readout Quotient RepresentationOperational Readout QuotientRepresentationObserver Pullback Trace IdentityObserver Pullback TraceIdentityVisible State-Space DimensionVisible State-Space Dimension
Proof dependencyStructural affinityDocument link

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Certified provenance

Exact release coordinate

Lean sourceResearch workspace
Status
Closed
Depth
6
Layer
D5/S3
Domain
Quantum
Node ID
D5/S3/Quantum/Fibers/FutureStatisticsEquivalence
Repository path
D5/S3/Quantum/Fibers/FutureStatisticsEquivalence.lean
Truth release
sha256:c0d04258d27972c1cf58485e21d64dbcbe336405346ba95133913c64ba2856aa
Source commit
745bf90812f7175f83e1235688249f9495f23bfc
Source tree
143bc6c9ab9054c406f0cdd7f3b296eb38768b5c

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.