Paper Citation Record · LEDGER

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data

As of 8 August 2026, this Paper Citation Record lists 40 of 40 outbound references and 0 inbound Pith citation observations for arXiv:2601.13467.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2601.13467 v2

Coverage vector

measured 40 of 40 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-03T09:46:26.853616Z

measured 40 of 40 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

40 of 40 outbound references displayed

verified exact1
verified fuzzy0
unresolved39
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f57c0298-6504-4729-9c33-25dc96258191 · outbound

This paper cites Since∥P ⊥S′P ⊥∥op ≤ ∥S′∥op ≤1, the Cauchy-Schwarz relation in (30) gives Q(S) ij ≤ ∥S′∥op √gii gjj ≤ √gii gjj.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Since∥P ⊥S′P ⊥∥op ≤ ∥S′∥op ≤1, the Cauchy-Schwarz relation in (30) gives Q(S) ij ≤ ∥S′∥op √gii gjj ≤ √gii gjj

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:23.827059Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 59c58a80-36b8-4afd-ae60-464afe7feb81 · outbound

This paper cites Then |η(k)|= 2 Re eiθvAv∗ B ≤C(k)≤1, with equality|η|=Cwhen the witness phase is aligned with the A/B coherence.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Then |η(k)|= 2 Re eiθvAv∗ B ≤C(k)≤1, with equality|η|=Cwhen the witness phase is aligned with the A/B coherence

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:23.914769Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7f495f35-343f-4069-967f-f9549b2669cd · outbound

This paper cites an unresolved cited work.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Unresolved cited work

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:24.025495Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eb998d84-4a92-4daa-87a8-04986efd41eb · outbound

This paper cites Quantum Entanglement as a Cohomological Obstruction,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Quantum Entanglement as a Cohomological Obstruction,

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:24.145984Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 278c7afd-c669-435a-838e-f71902788f7f · outbound

This paper cites Berry phase effects on electronic properties,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Berry phase effects on electronic properties,

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:24.225415Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 805e5347-913d-4fdc-8c2c-343628bbbf6a · outbound

This paper cites Hyperbolic band theory through Higgs bundles,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Hyperbolic band theory through Higgs bundles,

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:24.559282Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5aaf336d-ddf1-4a36-a743-ff956bb333a2 · outbound

This paper cites Colloquium: Topological insulators,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Colloquium: Topological insulators,

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:24.370653Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8e6b489e-6cd2-49fa-9d45-3736c0ec13e1 · outbound

This paper cites Topological insulators and superconductors,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Topological insulators and superconductors,

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:24.455494Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 720ba568-6460-4e0f-990b-1001320fca33 · outbound

This paper cites Hyperbolic band theory.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Hyperbolic band theory

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:24.507326Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 79fcf4d0-4eb1-42ab-b077-0a57f3add6e4 · outbound

This paper cites Crystallography of Hyperbolic Lattices.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Crystallography of Hyperbolic Lattices

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:24.999632Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fca3bbf8-1818-41a7-98c2-3dff39d14ce2 · outbound

This paper cites Automorphic Bloch theorems for hyperbolic lattices.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Automorphic Bloch theorems for hyperbolic lattices

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:24.669344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3cca2eb2-c3d0-443a-8092-e1d191a298c9 · outbound

This paper cites Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Hyperbolic Band Theory under Magnetic Field and Dirac Cones on a Higher Genus Surface

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:24.771295Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 72b84942-bff7-41b3-874d-dd20fe5fcf13 · outbound

This paper cites Algebra of hyperbolic band theory under magnetic field,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Algebra of hyperbolic band theory under magnetic field,

Reference 13

Resolution: verified exact; doi, observed 2026-08-03T09:49:25.241831Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.

Observation dcb74b1f-7de3-42ce-866b-e833aa6435b0 · outbound

This paper cites The Sheaf-Theoretic Structure Of Non-Locality and Contextuality.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data The Sheaf-Theoretic Structure Of Non-Locality and Contextuality

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.269364Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 76c1bec4-2ad2-441a-91dc-e288e12b1468 · outbound

This paper cites On the hyperbolic Bloch transform.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data On the hyperbolic Bloch transform

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.050381Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4487453e-6055-4f6b-b43a-7abcd45c6873 · outbound

This paper cites Hyperbolic Lattices in Circuit Quantum Electrodynamics.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Hyperbolic Lattices in Circuit Quantum Electrodynamics

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.125677Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8b6db8ec-7b92-4aba-804c-e177a041ec03 · outbound

This paper cites A scalable superconducting circuit framework for emulating physics in hyperbolic space,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data A scalable superconducting circuit framework for emulating physics in hyperbolic space,

Reference 17

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.215590Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3ff858d8-856a-44ff-89b3-832aeea852eb · outbound

This paper cites Separability criterion for density matrices,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Separability criterion for density matrices,

Reference 18

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.438346Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e4f7ae20-f04f-422a-b826-7ca1d2adf901 · outbound

This paper cites Detecting Quantum Entanglement.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Detecting Quantum Entanglement

Reference 19

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.315114Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4f3abdee-a709-49dc-8362-d6683a1d2eaf · outbound

This paper cites Entanglement detection.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Entanglement detection

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.368187Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0555b3b1-027e-4b9d-80c2-bf0cac3b8140 · outbound

This paper cites Computable measure of entanglement,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Computable measure of entanglement,

Reference 21

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.407793Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 9b1b7dc2-fbcd-4ee8-86c3-7033bf659a16 · outbound

This paper cites Quantum Hall Effect and Langlands Program.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Quantum Hall Effect and Langlands Program

Reference 22

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.627401Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bebaec0b-1a20-4d64-bdc6-c9d82fa7f248 · outbound

This paper cites Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances

Reference 23

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.505032Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation bb697c4d-a77d-4ad5-8a78-9e299c74ccf1 · outbound

This paper cites Parallel transport and “quantum holonomy.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Parallel transport and “quantum holonomy

Reference 24

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.539662Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 18c2165b-4e3f-4592-8efb-9d644272fa64 · outbound

This paper cites An extension of kakutani’s theorem on infinite product measures to the tensor product of semifinite w*-algebras,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data An extension of kakutani’s theorem on infinite product measures to the tensor product of semifinite w*-algebras,

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.592005Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation acdcb67d-b71a-4f51-bb9f-f202e9971832 · outbound

This paper cites Statistical distance and hilbert space,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Statistical distance and hilbert space,

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.889273Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation c94dc388-86ec-4819-b494-8bf2ccdc4771 · outbound

This paper cites Topological Aspects of Matters and Langlands Program.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Topological Aspects of Matters and Langlands Program

Reference 27

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.663623Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb5ebef1-e328-45d9-9692-aa79e22a4bc0 · outbound

This paper cites Model for a quantum hall effect without landau levels: Condensed-matter realization of the.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Model for a quantum hall effect without landau levels: Condensed-matter realization of the

Reference 28

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.724568Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f784bfa7-5d08-4e56-92cf-0910eb0f530a · outbound

This paper cites Riemannian structure on manifolds of quantum states,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Riemannian structure on manifolds of quantum states,

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.789543Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0cadf2df-0cee-4fc7-b2d4-c31881f7faec · outbound

This paper cites Computation of Uhlmann’s parallel transport for density matrices and the Bures metric on three-dimensional Hilbert space,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Computation of Uhlmann’s parallel transport for density matrices and the Bures metric on three-dimensional Hilbert space,

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:26.272708Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e1a9064a-7bea-4e1c-ba33-8aca3c5f92be · outbound

This paper cites Statistical distance and the geometry of quantum states,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Statistical distance and the geometry of quantum states,

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:25.987330Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7a18d364-86de-412b-89a3-b3f529f00d2e · outbound

This paper cites Topological indices for open and thermal systems via uhlmann’s phase,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Topological indices for open and thermal systems via uhlmann’s phase,

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:26.080612Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3d44cd96-5057-4a58-a911-63cfef11e071 · outbound

This paper cites Uhlmann phase as a topological measure for one-dimensional fermion systems,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Uhlmann phase as a topological measure for one-dimensional fermion systems,

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:26.178583Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fef28ac1-bb33-4e13-8eed-b08bd418e597 · outbound

This paper cites Proof of the geometric Langlands conjecture IV: ambidexterity.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Proof of the geometric Langlands conjecture IV: ambidexterity

Reference 34

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:26.651084Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d038742e-a2ed-4cca-a2a9-fd94462222dc · outbound

This paper cites Proof of the geometric langlands conjecture i: construction of the functor,.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Proof of the geometric langlands conjecture i: construction of the functor,

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:26.371531Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 44c515f7-3ea9-4237-9797-910d97aa8d36 · outbound

This paper cites Proof of the geometric Langlands conjecture II: Kac-Moody localization and the FLE.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Proof of the geometric Langlands conjecture II: Kac-Moody localization and the FLE

Reference 36

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:26.468130Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ee1e8fea-e2ad-4f83-a94b-e583b0963a90 · outbound

This paper cites Proof of the geometric Langlands conjecture III: compatibility with parabolic induction.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Proof of the geometric Langlands conjecture III: compatibility with parabolic induction

Reference 37

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:26.554725Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 601fc044-368b-43f0-8e35-b7b7cd7e9e51 · outbound

This paper cites Electric-Magnetic Duality And The Geometric Langlands Program.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Electric-Magnetic Duality And The Geometric Langlands Program

Reference 39

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:26.755593Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 68276942-a237-4465-b287-a8d06fce83f4 · outbound

This paper cites Lectures on the Langlands Program and Conformal Field Theory.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Lectures on the Langlands Program and Conformal Field Theory

Reference 40

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:26.853616Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6159ebea-4ac8-4ebb-9679-24c5eb99c625 · outbound

This paper cites an unresolved cited work.

Quantum Entanglement, Stratified Spaces, and Topological Matter: Towards Entanglement-Sensitive Langlands Data Unresolved cited work

Reference 2010

Resolution: unresolved; no resolver link, observed 2026-08-03T09:46:24.289449Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.