Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-03T15:42:19.588551Z
Paper Citation Record · LEDGER
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces
As of 10 August 2026, this Paper Citation Record lists 37 of 37 outbound references and 0 inbound Pith citation observations for arXiv:2512.16267.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
37 of 37 outbound references displayed
- verified exact2
- verified fuzzy0
- unresolved35
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 714b9a3d-e7b4-416d-bc39-1ff72d077d10 · outbound
This paper cites an unresolved cited work.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Unresolved cited work
Reference 1
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:15.252235Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bf4f95bd-6385-47be-989a-ccfc119ba4c0 · outbound
This paper cites Schambergeret al., Advanced Materials35, e2206110 (2023).
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Schambergeret al., Advanced Materials35, e2206110 (2023)
Reference 2
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:15.400970Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 7bac4935-f8fd-401f-841e-3aea1dba8a17 · outbound
This paper cites Vikran and T.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Vikran and T
Reference 3
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:15.470466Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 14498c47-5ff1-47de-933a-308796ae7d80 · outbound
This paper cites Arnold, I.
Reference 4
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:15.657720Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 70fb2a4d-96b9-4433-8799-f3f90cbc15db · outbound
This paper cites an unresolved cited work.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Unresolved cited work
Reference 5
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:15.742384Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 6b4dd8e5-8a55-478e-8c28-29e186cb8a2c · outbound
This paper cites Topology and Dynamics of Active Nematic Vesicles.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Topology and Dynamics of Active Nematic Vesicles
Reference 6
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:15.900950Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0c7e547f-1ca0-4a58-8a5d-f5978dd5dde4 · outbound
This paper cites an unresolved cited work.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Unresolved cited work
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:16.074433Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ff2ec25d-386e-45ef-b387-70e15e2593d0 · outbound
This paper cites Clairand, A.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Clairand, A
Reference 8
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:16.188041Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 75873dfc-10d5-4e5f-ab18-6ffa43f2dac7 · outbound
This paper cites Nishiyama, T.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Nishiyama, T
Reference 9
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:16.360552Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 44d436c9-1454-48e3-b0fd-b8fab510b68f · outbound
This paper cites P´ erez-Gonz´ alez, G.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces P´ erez-Gonz´ alez, G
Reference 10
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:16.489024Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 3b1fdd21-6b60-4f18-bdf6-ac463cf65901 · outbound
This paper cites an unresolved cited work.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Unresolved cited work
Reference 11
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:16.553280Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5705a860-4e3f-4422-9612-eb779f031dc1 · outbound
This paper cites Glentis, C.
Reference 12
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:16.693881Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9e795bf7-0ddc-42dc-8cd8-fc7d22d3cc5a · outbound
This paper cites an unresolved cited work.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Unresolved cited work
Reference 13
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:16.827590Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cc959661-3514-478d-8fd9-288f72ce8e22 · outbound
This paper cites Pieuchot, J.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Pieuchot, J
Reference 14
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:17.027703Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 0686adf9-0bee-497f-aa51-09352ccf2dbf · outbound
This paper cites Brandst¨ atter, D.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Brandst¨ atter, D
Reference 15
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:17.214512Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation bce0844c-2286-44b5-81fa-cc54016e9e1e · outbound
This paper cites Mechanics of active surfaces.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Mechanics of active surfaces
Reference 16
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:17.348638Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c5d50eb6-d3eb-4c09-b1e3-2295066ff96f · outbound
This paper cites an unresolved cited work.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Unresolved cited work
Reference 17
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:17.532445Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cc8e995d-3917-4f41-8a82-9c79e5a8e4bc · outbound
This paper cites Torres-S´ anchez, M.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Torres-S´ anchez, M
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:17.691121Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 32898f49-a0a3-4545-8c0c-267eae112277 · outbound
This paper cites Theory of nematic and polar active fluid surfaces.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Theory of nematic and polar active fluid surfaces
Reference 19
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:17.860005Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c4601aa8-f8c0-4bb6-81d7-808871b43aa0 · outbound
This paper cites Active nematic flows on curved surfaces.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Active nematic flows on curved surfaces
Reference 20
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:17.975094Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ce26b3a0-b308-4430-8d25-74dffe2ad163 · outbound
This paper cites Active swarms on a sphere.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Active swarms on a sphere
Reference 21
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:18.058555Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation d39b7cb5-d7bd-4149-b62c-3128acff081a · outbound
This paper cites Curvature-controlled defect dynamics in active systems.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Curvature-controlled defect dynamics in active systems
Reference 22
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:18.133221Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ed610d46-e572-4d03-b1ab-0ea7be5ea2cc · outbound
This paper cites Alaimo, C.
Reference 23
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:18.216373Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 887f0f53-92f9-4934-a3fc-0e34aa35ddc7 · outbound
This paper cites Dynamical patterns in active nematics on a sphere.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Dynamical patterns in active nematics on a sphere
Reference 24
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:18.304348Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c526fdce-6a04-4c9d-9801-96ed44560b5e · outbound
This paper cites Ai, B.-y.
Reference 25
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:18.388155Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 9e3d8270-d3fa-4a49-ba13-56a83932d554 · outbound
This paper cites Stability of milling patterns in self-propelled swarms on surfaces.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Stability of milling patterns in self-propelled swarms on surfaces
Reference 26
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:18.445022Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 334b1747-83c9-45c0-869d-cef158a97d24 · outbound
This paper cites Omori,Mechanics and Geometry of Fields (Japanese) (Shokabo, Tokyo, 1991).
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Omori,Mechanics and Geometry of Fields (Japanese) (Shokabo, Tokyo, 1991)
Reference 27
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:18.589740Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 79aa2942-149e-4203-ad81-e2e25bec4378 · outbound
This paper cites Frankel,The Geometry of Physics(Cambridge Uni- versity Press, 2011).
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Frankel,The Geometry of Physics(Cambridge Uni- versity Press, 2011)
Reference 28
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:18.734962Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation ab7b43b9-25b0-4892-8dd1-f61d97e1d4ef · outbound
This paper cites Active Particles on Curved Surfaces.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Active Particles on Curved Surfaces
Reference 29
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:18.856795Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation a3a7cd30-c336-4540-a82c-6fa2b463ee09 · outbound
This paper cites an unresolved cited work.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Unresolved cited work
Reference 30
- Resolution
- verified exact
- arxiv_id, observed 2026-08-03T15:43:21.435932Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 1105f49a-12fd-487c-bd25-12f1fa4deaa8 · outbound
This paper cites Janzen, E.
Reference 31
- Resolution
- verified exact
- arxiv_id, observed 2026-08-03T15:43:21.112956Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.
Observation 2a013ef2-89fc-4f14-8e44-100399543043 · outbound
This paper cites Schweitzer, W.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Schweitzer, W
Reference 32
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:19.074091Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 4a9e8945-228f-4c37-8d6e-f5851fff81cc · outbound
This paper cites Ohta and T.
Reference 33
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:19.140762Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 71ce662b-95b2-4a44-944e-0c5843af2456 · outbound
This paper cites Hiraiwa, A.
Reference 34
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:19.284419Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5d31cf82-adaa-4be5-87e6-a82985be1372 · outbound
This paper cites Hiraiwa, Physical Review E99, 012614 (2019).
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Hiraiwa, Physical Review E99, 012614 (2019)
Reference 35
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:19.392004Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 1e19f3c5-e338-4e56-b57c-05df19f03ed2 · outbound
This paper cites Modify the Improved Euler scheme to integrate stochastic differential equations.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Modify the Improved Euler scheme to integrate stochastic differential equations
Reference 36
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:19.481083Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 2f6753f9-eab1-4ef6-a807-6fd25a4c7ddb · outbound
This paper cites Riemann Normal Coordinate expansions using Cadabra.
A geometric framework for curvature-dependent collective behavior of polar active agents on curved surfaces Riemann Normal Coordinate expansions using Cadabra
Reference 37
- Resolution
- unresolved
- no resolver link, observed 2026-08-03T15:42:19.588551Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Pith citing papers
No inbound Pith citation observations are available.