Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T15:04:19.071399Z
Paper Citation Record · LEDGER
As of 22 August 2026, this Paper Citation Record lists 56 of 56 outbound references and 1 inbound Pith citation observation for arXiv:2608.03178.
A citation records a reference. It does not transfer a finding from one paper to another.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-15T15:04:19.071399Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-08-16T00:32:12.296665Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-08-16T00:32:12.328838Z
56 of 56 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 78019bec-c3bc-4cc4-8114-e4ddab7841af · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Holonomy, the quantum adiabatic theorem, and berry’s phase,
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation b60d9e0e-ebcd-4d19-b461-711cbaf3c32e · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Quantal phase factors accompanying adiabatic changes,
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 0c483351-0935-405a-9817-a408c6ce9008 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Appearance of gauge structure in simple dynamical systems,
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation ebc01b69-b218-480c-8a5f-45715efbe362 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Berry’s phase for energy bands in solids,
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 46c595c8-4627-412e-8c13-0f3e3504f387 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Riemannian structure on manifolds of quantum states,
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 0752283a-5b5c-4e78-b26a-ae3d5f027031 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Theory of polariza- tion of crystalline solids,
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation b180d552-0743-4366-95f4-ce11bb4338cb · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Macroscopic polarization in crystalline di- electrics: the geometric phase approach,
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 0b6a24ca-1cbc-4860-b486-464ec7829203 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Orbital magnetization in periodic insulators,
Reference 8
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 1ec9dc44-12dd-4da0-9f44-a976b10f07cf · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Orbital magnetization in crystalline solids: Multi- band insulators, chern insulators, and metals,
Reference 9
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2429993c-6bbc-4968-ba62-e0f9c2bc0fcc · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Mag- netoelectric polarizability and axion electrodynamics in crys- talline insulators,
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation d55324f1-b410-4492-94f8-c2f69ee5f1d9 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Geometri- cal effects in orbital magnetic susceptibility,
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation f91a0eb7-c9d5-40f5-913a-c6d85bf1c433 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Field induced positional shift of bloch electrons and its dynamical implica- tions,
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 8b15f616-02f2-48e7-b722-1d19ea8b5fb2 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Quantum nonlinear hall effect induced by berry curvature dipole in time-reversal invariant ma- terials,
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation f9f22ffc-8f96-430a-a072-8cfeb2c2c364 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Intrinsic nonlinear conductivities induced by the quantum metric,
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 40a3ba26-c589-4335-b113-6089cc0d08e0 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Quantum-metric-induced nonlinear transport in a topological antiferromagnet,
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 0b41e0a7-e8f3-4a5c-95fb-455242b788f4 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Quantum metric nonlinear hall effect in a topological antiferromagnetic heterostructure,
Reference 16
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation bf741481-13d4-45b7-84e2-8b45d6b602d4 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Superfluidity in topo- logically nontrivial flat bands,
Reference 17
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d7a6797f-11a9-4a4d-ac4c-343717dfeeab · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Geometric origin of superfluidity in the lieb-lattice flat band,
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 13e3387d-b710-40c0-8a62-b58b0bb90979 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Band geometry, berry curvature, and super- fluid weight,
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation db10e155-fe4f-44ed-8293-6c63e7aa0728 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Quantum distance and anomalous landau levels of flat bands,
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation b1d8b6d7-55f2-4cda-8aec-55b3e03c7936 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Ge- ometric characterization of anomalous landau levels of isolated flat bands,
Reference 21
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 885a093b-0af9-46ce-90e5-eddfd0dd5762 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Quan- tum geometry and landau levels of quadratic band crossings,
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 4d5030c5-0b6f-4058-b67a-cbee0e778937 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Geo- metric stability of topological lattice phases,
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 84639d49-faa4-428f-9e83-ddd3df66490c · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Band geometry of fractional topological insula- tors,
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 66a34c0f-f2a4-4ad8-8b79-1eca5ef62d03 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Quantum geom- etry and stability of the fractional quantum hall effect in the hofstadter model,
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation bfcbab02-068b-4635-82cc-ce64b87a7aab · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Quantum geometry in quantum materials,
Reference 26
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 30c27c63-0c58-4191-90a1-6e5db8a5ffb4 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Measurements of the quantum geometric tensor in solids,
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 74e53e75-589d-4277-8b0a-14b8d7049019 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Direct measurement of the quantum metric tensor in solids,
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 821b734f-9e8a-40b5-87be-284b345d3e32 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals From berry curvature to quantum metric: a new era of quantum geometry metrology for bloch electrons in solids,
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation ccbd226f-9c17-4be5-8e65-f1539c05d411 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals K ¨ahler geometry and chern insulators: Relations between topology and the quantum met- ric,
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 9aae7031-52f6-47b8-b7f2-79cf346c3ef9 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Engineering geometrically flat chern bands with fubini–study k¨ahler structure,
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 6eb87fac-1d5c-4daa-8fa0-38f0a88525fe · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Fractional chern insulator states in twisted bilayer graphene: An analytical approach,
Reference 32
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 7eb0d3f9-3a97-453e-8d5a-a733b3c2c0d3 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Symmetry-protectedZ 2-quantization and quaternionic berry connection with kramers degeneracy,
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 917be202-d19a-4202-bf59-73398076c22b · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Hyper k ¨ahler and quaternionic k¨ahler geome- try
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 57f7b1be-69a6-492b-ac0f-98431fda1059 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Unresolved cited work
Reference 35
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 97002894-d893-4eb0-9fe8-0b36e7d215c4 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals A four-dimensional generalization of the quantum hall effect,
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 153d7549-5c37-4853-9627-c462d2ffaff5 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals The quantum hall ef- fect on r4,
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation bdd0f1a6-0fe5-44fc-97a9-fd61ec1156f2 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals High-dimensional topological insula- tors with quaternionic analytic landau levels,
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation a80ac2de-ca8c-4ed4-bd93-0f44f380166b · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Topological in- sulators with su(2) landau levels,
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 2586bcb3-d00a-4421-9010-5c6161d1f9f4 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Band structure engineering of ideal fractional chern insulators,
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 26d1cbfa-dec9-4e76-b9bb-345256bfb2be · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Relating the topology of dirac hamiltonians to quantum geometry: When the quantum metric dictates chern numbers and winding num- bers,
Reference 41
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 81c58495-edda-4f94-b345-ad7d31526cd5 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals V ortexability: A unifying criterion for ideal fractional chern insulators,
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation e909d31e-4ef5-475f-ab42-498f482821a0 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Quantum spin hall effect,
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 73ce6195-b9f8-43c4-91a8-ea7bd6ffda54 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Fractional topological insula- tors,
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 7630a912-1a04-4f10-805e-8d7ad2fd1bc0 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Fractional topological liquids with time- reversal symmetry and their lattice realization,
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 4d426829-7df8-4b48-9384-db831f26102e · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals SU(2)non-abelian holonomy and dissipationless spin current in semiconductors,
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 41c1cdae-1911-4421-90d8-36fcca77813f · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Universal wilson loop bound of quantum geometry,
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation dfb8c944-3779-4c94-bc02-d2313762a074 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Fractional topological insulators in three di- mensions,
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 79a9da02-150c-4283-aabb-04817b51673e · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Quaternionic analysis,
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 0c776987-6b0b-4fb7-8c03-c5a411558c2a · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Calibrated geome- tries,
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 93c1bc7a-8bb8-477a-9be7-1fcc5ad7cf12 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Quaternionic k ¨ahler manifolds,
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 3a983029-5990-45fa-bcd7-145e863d575c · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Non-commutative linear algebra and plurisubharmonic functions of quaternionic variables,
Reference 52
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation ac526a9f-5b01-4c97-8939-71ec308887f7 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Z 2 topological order and the quan- tum spin hall effect,
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 390e6a5e-496e-441b-b0fb-d81ca31f05b5 · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Topological insulators in three dimensions,
Reference 54
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 59c3e60a-6705-4570-a0fb-9a2b9b10a12b · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals Topological field theory of time-reversal invariant insulators,
Reference 55
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation bc16fd63-33ae-4dd1-b124-e256f190834a · outbound
Quaternion-Kahler geometry of time reversal symmetric crystals pullback
Reference 56
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.
Observation 22234671-2d57-4cf1-9d27-b0a027525019 · inbound
Second-Chern Bounds in Non-Abelian Quantum Geometry Quaternion-Kahler geometry of time reversal symmetric crystals
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.