Truth boundary
Placement is not proof
This catalog is a textbook placement map. A listed source, upstream Lean cluster, or extended chapter is not a local ASPBE theorem unless an exact compiled declaration is linked separately.
OpenAI Math boundary. Audited clusters are pinned source or adapter inputs. Their upstream Lean 4.34.1 results are not local Lean 4.33.0 declarations until separately ported and compiled. Lean 4.33.0 is the migration target; this reader release preserves the published proof tree and records its actual version in the build evidence.
Graph-driven chapter map
Shared foundations first, source-specific consumers later
qit-states-measurements
States, density operators and measurements
Choose one canonical finite-dimensional state, positive-operator, Born-rule and POVM layer before importing downstream results.
Planned
Inspect pinned upstream memory (1 routes)
OpenAI Math snapshot adc7f1241b42 · upstream Lean 4.34.1 · local migration target 4.33.0.
Source placement does not certify an adapter, the whole chapter, or an SP/BE construction.
- oai-entanglement
InformationTheory/Entanglement
candidate foundational QIT spine; declaration-by-declaration admission only
Upstream evidence: lean-present-not-single-comparator-audited. adapter-backed. Not local admission.
Next boundary: A local semantic adapter and independent publication review are still required.
qit-composites
Composite systems, partial trace and purification
Freeze subsystem order and tensor conventions; purification and dilation remain non-unique representative constructions.
Planned
Inspect pinned upstream memory (1 routes)
OpenAI Math snapshot adc7f1241b42 · upstream Lean 4.34.1 · local migration target 4.33.0.
Source placement does not certify an adapter, the whole chapter, or an SP/BE construction.
- oai-entanglement
InformationTheory/Entanglement
candidate foundational QIT spine; declaration-by-declaration admission only
Upstream evidence: lean-present-not-single-comparator-audited. adapter-backed. Not local admission.
Next boundary: A local semantic adapter and independent publication review are still required.
qit-channels-distances
Channels, Choi maps, distances and operational tests
Completely positive maps, Kraus/Choi representations, trace/fidelity conventions and contractivity become shared nodes.
Planned
Inspect pinned upstream memory (3 routes)
OpenAI Math snapshot adc7f1241b42 · upstream Lean 4.34.1 · local migration target 4.33.0.
Source placement does not certify an adapter, the whole chapter, or an SP/BE construction.
- oai-amplitude-damping
InformationTheory/AmplitudeDamping
quantum channel, entropy, Holevo information, and operational capacity
Upstream evidence: comparator-backed. source-route. Not local admission.
Next boundary: A local semantic adapter and independent publication review are still required.
- oai-entanglement
InformationTheory/Entanglement
candidate foundational QIT spine; declaration-by-declaration admission only
Upstream evidence: lean-present-not-single-comparator-audited. adapter-backed. Not local admission.
Next boundary: A local semantic adapter and independent publication review are still required.
- oai-ppt-square
Analysis/Quantum/PPTSquare
CP/PPT/trace-preserving/entanglement-breaking channel geometry and an explicit PPT-square counterexample route
Upstream evidence: lean-present-not-comparator-audited. adapter-backed. Not local admission.
Next boundary: admit only after canonical CP, PPT, trace-preserving, Choi and entanglement-breaking adapters are fixed
qit-representation-foundations
Finite-group and unitary representation foundations
Group actions, representations, characters, averaging and fixed spaces are admitted only after manuscript-specific namespaces are purified.
Planned
Inspect pinned upstream memory (1 routes)
OpenAI Math snapshot adc7f1241b42 · upstream Lean 4.34.1 · local migration target 4.33.0.
Source placement does not certify an adapter, the whole chapter, or an SP/BE construction.
- oai-young-unitary-infrastructure
RepresentationTheory/Young · RepresentationTheory/YoungSymmetry · RepresentationTheory/FiniteUnitary
Young/Specht and finite-unitary representation ingredients relevant to Schur-Weyl prerequisites
Upstream evidence: lean-present-not-comparator-audited. adapter-backed. Not local admission.
Next boundary: purify manuscript-specific namespaces and assumptions, then admit only source-independent declarations with a real textbook consumer
qit-schur-weyl
Young diagrams, Specht modules and Schur–Weyl duality
Build the symmetric-group/unitary-group bridge needed by the quantum method of types; advanced Saxl and Foulkes–Howe results remain extensions, not prerequisites.
Planned
Inspect pinned upstream memory (3 routes)
OpenAI Math snapshot adc7f1241b42 · upstream Lean 4.34.1 · local migration target 4.33.0.
Source placement does not certify an adapter, the whole chapter, or an SP/BE construction.
- oai-young-unitary-infrastructure
RepresentationTheory/Young · RepresentationTheory/YoungSymmetry · RepresentationTheory/FiniteUnitary
Young/Specht and finite-unitary representation ingredients relevant to Schur-Weyl prerequisites
Upstream evidence: lean-present-not-comparator-audited. adapter-backed. Not local admission.
Next boundary: purify manuscript-specific namespaces and assumptions, then admit only source-independent declarations with a real textbook consumer
- oai-saxl
RepresentationTheory/Saxl
advanced symmetric-group and Specht-module route, not a prerequisite for Schur-Weyl
Upstream evidence: comparator-backed. source-route. Not local admission.
Next boundary: A local semantic adapter and independent publication review are still required.
- oai-foulkes-howe
RepresentationTheory/FoulkesHowe
advanced plethysm/Foulkes-Howe route, not a prerequisite for quantum representation theory
Upstream evidence: comparator-backed. source-route. Not local admission.
Next boundary: A local semantic adapter and independent publication review are still required.
qit-symmetry-applications
Invariant states, de Finetti, cloning and spectrum estimation
Consume the shared QIT and representation layers without turning conceptual symmetry correspondences into Lean dependencies.
Planned
qit-capacity-entanglement
Capacity, entanglement, secret key and games
Amplitude-damping capacity, entangled games and dimension-ten zero-key constructions are source routes above canonical state/channel adapters.
Planned
Inspect pinned upstream memory (5 routes)
OpenAI Math snapshot adc7f1241b42 · upstream Lean 4.34.1 · local migration target 4.33.0.
Source placement does not certify an adapter, the whole chapter, or an SP/BE construction.
- oai-amplitude-damping
InformationTheory/AmplitudeDamping
quantum channel, entropy, Holevo information, and operational capacity
Upstream evidence: comparator-backed. source-route. Not local admission.
Next boundary: A local semantic adapter and independent publication review are still required.
- oai-entangled-games
Probability/EntangledGames
finite-dimensional entangled-game, measurement, purification and repeated-game information route
Upstream evidence: comparator-backed. adapter-backed. Not local admission.
Next boundary: reuse only after state/measurement/trace-distance adapters are canonical
- oai-secret-key
InformationTheory/SecretKey
advanced QIT / private-key route after foundation adapters
Upstream evidence: lean-present-not-comparator-audited. source-route. Not local admission.
Next boundary: A local semantic adapter and independent publication review are still required.
- oai-dimension-ten-secret-key-bridge
InformationTheory/DimensionTen
companion density-state, entanglement, Choi-transfer and finite readout/key construction above the DimensionTen and SecretKey layers
Upstream evidence: lean-present-not-comparator-audited. source-route. Not local admission.
Next boundary: keep this as a downstream consumer; do not promote its local density or separability wrappers as the shared QIT foundation
- oai-soft-channel
InformationTheory/SoftChannel
classical information-theory candidate substrate, not quantum-labelled by default
Upstream evidence: comparator-backed. canonical-leaf. Not local admission.
Next boundary: A local semantic adapter and independent publication review are still required.
qit-optics-counterexamples
Extended chapter: quantum optics and channel counterexamples
Photon-number entropy, PPT-square phenomena and explicit channel geometry are advanced consumers, not foundational definitions.
Planned
Inspect pinned upstream memory (3 routes)
OpenAI Math snapshot adc7f1241b42 · upstream Lean 4.34.1 · local migration target 4.33.0.
Source placement does not certify an adapter, the whole chapter, or an SP/BE construction.
- oai-photon-number
InformationTheory/PhotonNumber
quantum optics and entropy photon-number route
Upstream evidence: comparator-backed. source-route. Not local admission.
Next boundary: A local semantic adapter and independent publication review are still required.
- oai-ppt-square
Analysis/Quantum/PPTSquare
CP/PPT/trace-preserving/entanglement-breaking channel geometry and an explicit PPT-square counterexample route
Upstream evidence: lean-present-not-comparator-audited. adapter-backed. Not local admission.
Next boundary: admit only after canonical CP, PPT, trace-preserving, Choi and entanglement-breaking adapters are fixed
- oai-dimension-ten-channel
Analysis/Quantum/DimensionTen
quantum-channel existence and geometry route
Upstream evidence: comparator-backed. source-route. Not local admission.
Next boundary: A local semantic adapter and independent publication review are still required.
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