Computer science01
Database theory
Relational Normalization and Lossless Join as Admissible Forgetting
Decomposition forgets structure only when dependencies permit exact reconstruction without spurious tuples. Lossless join becomes a precise reconstruction obligation rather than a loose analogy.
STAGE AREADINESS 4
NormalizationLossless joinSource-read priority
PUBLICATION_GRAPH.json#cs_database_normalizationComputer science02
Automata / formal languages
Myhill–Nerode as Admissible Forgetting
State distinctions may be forgotten exactly when no admissible future observation distinguishes them. Minimal DFA construction becomes an exact observational quotient preserving language behavior.
STAGE AREADINESS 3
AutomataState quotientFuture observation
PUBLICATION_GRAPH.json#cs_myhill_nerodeComputer science03
Algorithms / optimization
Dynamic Programming as Sufficient State Retention
History may be forgotten only when the retained state preserves every distinction relevant to future optimal continuation. DP state design is therefore a concrete sufficiency problem.
STAGE AREADINESS 3
StateSufficiencyBellman principle
PUBLICATION_GRAPH.json#cs_dynamic_programmingComputer science04
Compilers / programming languages
Compiler Pipelines as Representation-Preserving Transport
Each intermediate representation is a representation boundary; compiler passes transport state while preserving declared semantics and forgetting only distinctions irrelevant to the target obligation.
STAGE AREADINESS 3
IRTransportSemantics preservation
PUBLICATION_GRAPH.json#cs_compilersComputer science05
Distributed data processing
MapReduce as Boundary Formation, Equivalence, and Closure
Shuffle forms intermediate equivalence classes, reduce closes each class, and combiner legality depends on composable local closure. Key design determines what the computation preserves or forgets.
STAGE AREADINESS 3
Distributed systemsEquivalence classesClosure
PUBLICATION_GRAPH.json#cs_mapreduceComputer science06
Graph algorithms
Dijkstra’s Algorithm as a Moving Closure Frontier
A settled vertex crosses a frontier when no remaining admissible path can improve its distance. Nonnegative weights are the condition that makes this finalization monotone and lawful.
STAGE AREADINESS 3
Graph algorithmsInvariantClosure frontier
PUBLICATION_GRAPH.json#cs_dijkstraComputer science07
Formal methods / verification
Abstract Interpretation and CEGAR as Distinction Forgetting and Repair
Abstraction forgets distinctions; spurious counterexamples witness harmful forgetting; refinement restores what the proof obligation requires.
STAGE AREADINESS 3
AbstractionWitnessRepair loop
PUBLICATION_GRAPH.json#cs_cegarMathematics08
Linear algebra / numerical analysis / PDE
Schur Complements, Static Condensation, and Dirichlet-to-Neumann Reduction
Interior degrees of freedom may be eliminated while retaining the response required at an exposed boundary. Schur reduction becomes an exact calibration of obligation-relative forgetting.
STAGE AREADINESS 5
Exact reductionBoundary responseSource-read priority
PUBLICATION_GRAPH.json#math_schur_dtnPhysics09
Quantum information / operator algebras
Petz Recovery: Recovery Is Not Inversion
Recovery depends on the channel, reference state, and sufficient family. Successful recovery is conditional and typed; it does not make coarse-graining globally invertible.
STAGE AREADINESS 5
RecoverySufficiencySource-read priority
PUBLICATION_GRAPH.json#phys_petzMathematics10
Geometric topology / geometric analysis
Poincaré–Perelman as a Boundary Repair Architecture
Ricci flow exposes continuation defects while surgery performs controlled local repair under global proof obligations, without altering the status or content of Perelman’s theorem.
STAGE AREADINESS 5
RepairMonotone witnessProof-status firewall
PUBLICATION_GRAPH.json#math_poincare_perelmanMathematics11
Numerical analysis / PDE
Galerkin Projection as Obligation-Preserving Reduction
Projection may forget degrees of freedom only relative to the quantity, norm, or proof obligation that must survive. Later obligations can require reopening the representation.
STAGE AREADINESS 5
ProjectionError obligationSource-read priority
PUBLICATION_GRAPH.json#math_galerkinPhysics12
Celestial mechanics / dynamical systems
CR3BP: Hill Regions and Transport Boundaries
Integrals and invariant structures define admissible regions and transport channels in phase space, making boundary language concrete as reachable dynamical geometry.
STAGE AREADINESS 5
TransportReachabilityPhase space
PUBLICATION_GRAPH.json#phys_cr3bpPhysics13
Classical / quantum gauge theory
Gauge Symmetry: Redundant Representation versus Physical Distinction
Different mathematical descriptions may encode the same physical state. Representational difference must not be promoted to physical difference without gauge-invariant content.
STAGE AREADINESS 4
GaugeEquivalenceInvariant content
PUBLICATION_GRAPH.json#phys_gaugeMathematics14
Topology / algebraic geometry
Sheaves and Gluing as Local-to-Global Closure
Local representations form a global object only when overlap and compatibility obligations close; failed gluing makes the local-to-global defect explicit.
STAGE AREADINESS 4
GluingCompatibilityLocal → global
PUBLICATION_GRAPH.json#math_sheavesComputer science01
Database theory
Relational Normalization and Lossless Join as Admissible Forgetting
Decomposition forgets structure only when dependencies permit exact reconstruction without spurious tuples. Lossless join becomes a precise reconstruction obligation rather than a loose analogy.
STAGE AREADINESS 4
NormalizationLossless joinSource-read priority
PUBLICATION_GRAPH.json#cs_database_normalizationComputer science02
Automata / formal languages
Myhill–Nerode as Admissible Forgetting
State distinctions may be forgotten exactly when no admissible future observation distinguishes them. Minimal DFA construction becomes an exact observational quotient preserving language behavior.
STAGE AREADINESS 3
AutomataState quotientFuture observation
PUBLICATION_GRAPH.json#cs_myhill_nerodeComputer science03
Algorithms / optimization
Dynamic Programming as Sufficient State Retention
History may be forgotten only when the retained state preserves every distinction relevant to future optimal continuation. DP state design is therefore a concrete sufficiency problem.
STAGE AREADINESS 3
StateSufficiencyBellman principle
PUBLICATION_GRAPH.json#cs_dynamic_programmingComputer science04
Compilers / programming languages
Compiler Pipelines as Representation-Preserving Transport
Each intermediate representation is a representation boundary; compiler passes transport state while preserving declared semantics and forgetting only distinctions irrelevant to the target obligation.
STAGE AREADINESS 3
IRTransportSemantics preservation
PUBLICATION_GRAPH.json#cs_compilersComputer science05
Distributed data processing
MapReduce as Boundary Formation, Equivalence, and Closure
Shuffle forms intermediate equivalence classes, reduce closes each class, and combiner legality depends on composable local closure. Key design determines what the computation preserves or forgets.
STAGE AREADINESS 3
Distributed systemsEquivalence classesClosure
PUBLICATION_GRAPH.json#cs_mapreduceComputer science06
Graph algorithms
Dijkstra’s Algorithm as a Moving Closure Frontier
A settled vertex crosses a frontier when no remaining admissible path can improve its distance. Nonnegative weights are the condition that makes this finalization monotone and lawful.
STAGE AREADINESS 3
Graph algorithmsInvariantClosure frontier
PUBLICATION_GRAPH.json#cs_dijkstraComputer science07
Formal methods / verification
Abstract Interpretation and CEGAR as Distinction Forgetting and Repair
Abstraction forgets distinctions; spurious counterexamples witness harmful forgetting; refinement restores what the proof obligation requires.
STAGE AREADINESS 3
AbstractionWitnessRepair loop
PUBLICATION_GRAPH.json#cs_cegarMathematics08
Linear algebra / numerical analysis / PDE
Schur Complements, Static Condensation, and Dirichlet-to-Neumann Reduction
Interior degrees of freedom may be eliminated while retaining the response required at an exposed boundary. Schur reduction becomes an exact calibration of obligation-relative forgetting.
STAGE AREADINESS 5
Exact reductionBoundary responseSource-read priority
PUBLICATION_GRAPH.json#math_schur_dtnPhysics09
Quantum information / operator algebras
Petz Recovery: Recovery Is Not Inversion
Recovery depends on the channel, reference state, and sufficient family. Successful recovery is conditional and typed; it does not make coarse-graining globally invertible.
STAGE AREADINESS 5
RecoverySufficiencySource-read priority
PUBLICATION_GRAPH.json#phys_petzMathematics10
Geometric topology / geometric analysis
Poincaré–Perelman as a Boundary Repair Architecture
Ricci flow exposes continuation defects while surgery performs controlled local repair under global proof obligations, without altering the status or content of Perelman’s theorem.
STAGE AREADINESS 5
RepairMonotone witnessProof-status firewall
PUBLICATION_GRAPH.json#math_poincare_perelmanMathematics11
Numerical analysis / PDE
Galerkin Projection as Obligation-Preserving Reduction
Projection may forget degrees of freedom only relative to the quantity, norm, or proof obligation that must survive. Later obligations can require reopening the representation.
STAGE AREADINESS 5
ProjectionError obligationSource-read priority
PUBLICATION_GRAPH.json#math_galerkinPhysics12
Celestial mechanics / dynamical systems
CR3BP: Hill Regions and Transport Boundaries
Integrals and invariant structures define admissible regions and transport channels in phase space, making boundary language concrete as reachable dynamical geometry.
STAGE AREADINESS 5
TransportReachabilityPhase space
PUBLICATION_GRAPH.json#phys_cr3bpPhysics13
Classical / quantum gauge theory
Gauge Symmetry: Redundant Representation versus Physical Distinction
Different mathematical descriptions may encode the same physical state. Representational difference must not be promoted to physical difference without gauge-invariant content.
STAGE AREADINESS 4
GaugeEquivalenceInvariant content
PUBLICATION_GRAPH.json#phys_gaugeMathematics14
Topology / algebraic geometry
Sheaves and Gluing as Local-to-Global Closure
Local representations form a global object only when overlap and compatibility obligations close; failed gluing makes the local-to-global defect explicit.
STAGE AREADINESS 4
GluingCompatibilityLocal → global
PUBLICATION_GRAPH.json#math_sheavesComputer science01
Database theory
Relational Normalization and Lossless Join as Admissible Forgetting
Decomposition forgets structure only when dependencies permit exact reconstruction without spurious tuples. Lossless join becomes a precise reconstruction obligation rather than a loose analogy.
STAGE AREADINESS 4
NormalizationLossless joinSource-read priority
PUBLICATION_GRAPH.json#cs_database_normalizationComputer science02
Automata / formal languages
Myhill–Nerode as Admissible Forgetting
State distinctions may be forgotten exactly when no admissible future observation distinguishes them. Minimal DFA construction becomes an exact observational quotient preserving language behavior.
STAGE AREADINESS 3
AutomataState quotientFuture observation
PUBLICATION_GRAPH.json#cs_myhill_nerodeComputer science03
Algorithms / optimization
Dynamic Programming as Sufficient State Retention
History may be forgotten only when the retained state preserves every distinction relevant to future optimal continuation. DP state design is therefore a concrete sufficiency problem.
STAGE AREADINESS 3
StateSufficiencyBellman principle
PUBLICATION_GRAPH.json#cs_dynamic_programmingComputer science04
Compilers / programming languages
Compiler Pipelines as Representation-Preserving Transport
Each intermediate representation is a representation boundary; compiler passes transport state while preserving declared semantics and forgetting only distinctions irrelevant to the target obligation.
STAGE AREADINESS 3
IRTransportSemantics preservation
PUBLICATION_GRAPH.json#cs_compilersComputer science05
Distributed data processing
MapReduce as Boundary Formation, Equivalence, and Closure
Shuffle forms intermediate equivalence classes, reduce closes each class, and combiner legality depends on composable local closure. Key design determines what the computation preserves or forgets.
STAGE AREADINESS 3
Distributed systemsEquivalence classesClosure
PUBLICATION_GRAPH.json#cs_mapreduceComputer science06
Graph algorithms
Dijkstra’s Algorithm as a Moving Closure Frontier
A settled vertex crosses a frontier when no remaining admissible path can improve its distance. Nonnegative weights are the condition that makes this finalization monotone and lawful.
STAGE AREADINESS 3
Graph algorithmsInvariantClosure frontier
PUBLICATION_GRAPH.json#cs_dijkstraComputer science07
Formal methods / verification
Abstract Interpretation and CEGAR as Distinction Forgetting and Repair
Abstraction forgets distinctions; spurious counterexamples witness harmful forgetting; refinement restores what the proof obligation requires.
STAGE AREADINESS 3
AbstractionWitnessRepair loop
PUBLICATION_GRAPH.json#cs_cegarMathematics08
Linear algebra / numerical analysis / PDE
Schur Complements, Static Condensation, and Dirichlet-to-Neumann Reduction
Interior degrees of freedom may be eliminated while retaining the response required at an exposed boundary. Schur reduction becomes an exact calibration of obligation-relative forgetting.
STAGE AREADINESS 5
Exact reductionBoundary responseSource-read priority
PUBLICATION_GRAPH.json#math_schur_dtnPhysics09
Quantum information / operator algebras
Petz Recovery: Recovery Is Not Inversion
Recovery depends on the channel, reference state, and sufficient family. Successful recovery is conditional and typed; it does not make coarse-graining globally invertible.
STAGE AREADINESS 5
RecoverySufficiencySource-read priority
PUBLICATION_GRAPH.json#phys_petzMathematics10
Geometric topology / geometric analysis
Poincaré–Perelman as a Boundary Repair Architecture
Ricci flow exposes continuation defects while surgery performs controlled local repair under global proof obligations, without altering the status or content of Perelman’s theorem.
STAGE AREADINESS 5
RepairMonotone witnessProof-status firewall
PUBLICATION_GRAPH.json#math_poincare_perelmanMathematics11
Numerical analysis / PDE
Galerkin Projection as Obligation-Preserving Reduction
Projection may forget degrees of freedom only relative to the quantity, norm, or proof obligation that must survive. Later obligations can require reopening the representation.
STAGE AREADINESS 5
ProjectionError obligationSource-read priority
PUBLICATION_GRAPH.json#math_galerkinPhysics12
Celestial mechanics / dynamical systems
CR3BP: Hill Regions and Transport Boundaries
Integrals and invariant structures define admissible regions and transport channels in phase space, making boundary language concrete as reachable dynamical geometry.
STAGE AREADINESS 5
TransportReachabilityPhase space
PUBLICATION_GRAPH.json#phys_cr3bpPhysics13
Classical / quantum gauge theory
Gauge Symmetry: Redundant Representation versus Physical Distinction
Different mathematical descriptions may encode the same physical state. Representational difference must not be promoted to physical difference without gauge-invariant content.
STAGE AREADINESS 4
GaugeEquivalenceInvariant content
PUBLICATION_GRAPH.json#phys_gaugeMathematics14
Topology / algebraic geometry
Sheaves and Gluing as Local-to-Global Closure
Local representations form a global object only when overlap and compatibility obligations close; failed gluing makes the local-to-global defect explicit.
STAGE AREADINESS 4
GluingCompatibilityLocal → global
PUBLICATION_GRAPH.json#math_sheaves