Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T11:04:16.100427Z
Paper Citation Record · LEDGER
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus
As of 17 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 0 inbound Pith citation observations for arXiv:1908.09861.
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 2026-08-17T06:30:58.91139+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
42 of 42 outbound references displayed
- verified exact10
- verified fuzzy29
- unresolved3
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 176c88f2-3c02-48b4-b4b1-4ab0f1cf051d · outbound
This paper cites The tropicalization of the moduli space of curves.Ann.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus The tropicalization of the moduli space of curves.Ann
Reference 1
- Resolution
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- raw_fallback, observed 2026-08-14T11:04:16.863297Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 9525cea7-1f48-4f95-a6bc-42c2ffd4cf10 · outbound
This paper cites Torification and factorization of birational maps.J.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Torification and factorization of birational maps.J
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.848130Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 0e141b8f-4552-4ed7-827d-2b88fb45496a · outbound
This paper cites Complete moduli in the presence of semiabelian group action.Ann.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Complete moduli in the presence of semiabelian group action.Ann
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.832330Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 5a898282-aa0d-410a-b55d-897e9ae51d99 · outbound
This paper cites Nonarchimedean geometry, tropicalization, and metrics on curves.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Nonarchimedean geometry, tropicalization, and metrics on curves
Reference 4
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:04:16.362662Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 34d0afdb-5d86-4499-9a11-d7cbcf1564f5 · outbound
This paper cites Cluster algebras.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Cluster algebras
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.815546Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 7278315a-d21b-4faf-8c6a-47c0f984a9bc · outbound
This paper cites Berkovich.Spectral theory and analytic geometry over non-Archimedean fields, volume 33 of Mathematical Surveys and Monographs.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Berkovich.Spectral theory and analytic geometry over non-Archimedean fields, volume 33 of Mathematical Surveys and Monographs
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.796608Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 91d210f1-02e4-4d40-8735-6757fbdbfcaf · outbound
This paper cites Berkovich.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Berkovich
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.779626Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 32e76442-c044-4b93-b286-d7572e126455 · outbound
This paper cites Bosch, U.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Bosch, U
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.763383Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation d3720446-c45c-4bd5-8abb-0fabab0a3f05 · outbound
This paper cites The Essential Skeleton of a product of degenerations.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus The Essential Skeleton of a product of degenerations
Reference 9
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:04:16.339515Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 4387b4cb-601d-4dd9-afa2-a2ba8a85b736 · outbound
This paper cites Fock and Alexander B.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Fock and Alexander B
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.747562Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 517d0b83-9492-41cd-ad85-a74a9e9a87be · outbound
This paper cites Introduction to toric varieties, volume 131 of Annals of Mathematics Studies.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Introduction to toric varieties, volume 131 of Annals of Mathematics Studies
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.730638Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation b6d70f4c-24ef-4729-8750-6fd98b20ce3a · outbound
This paper cites Intersection theory, volume 2 of Ergebnisse der Mathematik und ihrer Grenzgebiete.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Intersection theory, volume 2 of Ergebnisse der Mathematik und ihrer Grenzgebiete
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.713592Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation e1530761-0acf-4668-b179-705f12046913 · outbound
This paper cites Mirror symmetry for log Calabi-Yau surfaces I.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Mirror symmetry for log Calabi-Yau surfaces I
Reference 13
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:04:16.316488Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation c3dea33a-4590-4725-9095-cf06859eb227 · outbound
This paper cites Birational geometry of cluster algebras.Algebr.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Birational geometry of cluster algebras.Algebr
Reference 14
- Resolution
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- raw_fallback, observed 2026-08-14T11:04:16.696461Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 3a47a82e-cc89-4130-8d95-a2cef8627d63 · outbound
This paper cites Canonical bases for cluster algebras.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Canonical bases for cluster algebras
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.681183Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 009ad1e9-d867-446d-b245-0b2b3a3c78c6 · outbound
This paper cites From real affine geometry to complex geometry.Ann.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus From real affine geometry to complex geometry.Ann
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.666069Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 5e4c8627-e224-478f-a2e5-a746848ac55c · outbound
This paper cites Intrinsic mirror symmetry and punctured Gromov-Witten invariants.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Intrinsic mirror symmetry and punctured Gromov-Witten invariants
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.650861Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 57b90477-abdf-4914-8a2e-9ba630b7ca17 · outbound
This paper cites Skeletons and tropicalizations.Adv.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Skeletons and tropicalizations.Adv
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.633928Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation bd69b0fe-1389-41f1-8b05-27ea16e520e1 · outbound
This paper cites Theta functions and the secondary fan for Fano varieties.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Theta functions and the secondary fan for Fano varieties
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.617495Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 802e8533-f79b-4680-adbe-ecb66ed11ab1 · outbound
This paper cites Algebraic geometry.Springer-Verlag, NewYork-Heidelberg, 1977.Graduate Texts in Mathematics, No.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Algebraic geometry.Springer-Verlag, NewYork-Heidelberg, 1977.Graduate Texts in Mathematics, No
Reference 20
- Resolution
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- raw_fallback, observed 2026-08-14T11:04:16.600923Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 11f2b276-001f-408b-aa28-7c453b93d465 · outbound
This paper cites Rational curves on quasi-projective surfaces.Mem.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Rational curves on quasi-projective surfaces.Mem
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.586280Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 02235b40-a0ef-4685-9782-0d184895daef · outbound
This paper cites Equations forM 0,n.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Equations forM 0,n
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.570891Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 4eba41b7-3d97-40cf-bb8f-8294f4bb6132 · outbound
This paper cites an unresolved cited work.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:04:16.555299Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 3feb733c-5f09-40fb-b8bf-c4a34b13af3b · outbound
This paper cites Princeton University Press, Princeton, NJ, 2007.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Princeton University Press, Princeton, NJ, 2007
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.540152Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 149216b4-44d0-4ba4-8b57-c47ac35fc5d5 · outbound
This paper cites Cambridge University Press, Cambridge, 2013.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Cambridge University Press, Cambridge, 2013
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.524107Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation b5bc1300-5639-4952-bc8e-fe2969da7a04 · outbound
This paper cites Homological mirror symmetry and torus fibrations.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Homological mirror symmetry and torus fibrations
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.506769Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 6f0b2a1d-93c0-4234-88cf-b8c83fbd2db4 · outbound
This paper cites Affine structures and non-Archimedean analytic spaces.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Affine structures and non-Archimedean analytic spaces
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.491731Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation fd5fe2a8-06cd-433f-b520-52935cf3a510 · outbound
This paper cites Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and mirror symmetry.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and mirror symmetry
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.476672Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 83ab3126-0170-446d-9fac-01a4f18b4fa2 · outbound
This paper cites Theta bases and log Gromov-Witten invariants of cluster varieties.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Theta bases and log Gromov-Witten invariants of cluster varieties
Reference 29
- Resolution
- unresolved
- no resolver link, observed 2026-08-14T11:04:16.036802Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation c4d88f3e-ba5f-4391-8ca1-9839e5063c85 · outbound
This paper cites On the geometric P=W conjecture.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus On the geometric P=W conjecture
Reference 30
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:04:16.278043Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation ebf53ff3-f69e-4828-b1fd-6e72b74d1f5a · outbound
This paper cites Weight functions on non-archimedean analytic spaces and the Kontsevich-Soibelman skeleton.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Weight functions on non-archimedean analytic spaces and the Kontsevich-Soibelman skeleton
Reference 31
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:04:16.256434Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation d6054898-2331-41c8-9795-58b037760240 · outbound
This paper cites The essential skeleton of a degeneration of algebraic varieties.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus The essential skeleton of a degeneration of algebraic varieties
Reference 32
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:04:16.232986Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 9bef2aee-d89d-4281-926b-b0ed915fc8f1 · outbound
This paper cites The non-archimedean SYZ fibration.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus The non-archimedean SYZ fibration
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.461803Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation d8149c35-28fc-494a-b499-a5ce9d86dadd · outbound
This paper cites Skeletons of stable maps I: Rational curves in toric varieties.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Skeletons of stable maps I: Rational curves in toric varieties
Reference 34
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:04:16.210530Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation dc94ca7a-3169-4982-ac17-770f83926134 · outbound
This paper cites Metrization of differential pluriforms on Berkovich analytic spaces.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Metrization of differential pluriforms on Berkovich analytic spaces
Reference 35
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:04:16.189145Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 0e4c5d23-fb5b-4214-bdbd-55a4713563cd · outbound
This paper cites Géométrie toroïdale et géométrie analytique non archimédienne.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Géométrie toroïdale et géométrie analytique non archimédienne
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.445498Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 21afbb98-67f4-4be4-9663-3136f49ecf31 · outbound
This paper cites an unresolved cited work.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Unresolved cited work
Reference 37
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T11:04:16.429104Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 05500ffe-fba9-4db9-bec4-b4dd092f4556 · outbound
This paper cites Tropicalization of the moduli space of stable maps.Mathematische Zeitschrift, 281(3):1035–1059, 2015.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Tropicalization of the moduli space of stable maps.Mathematische Zeitschrift, 281(3):1035–1059, 2015
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.410675Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation e4644f27-c735-4e25-be97-7a283823eaf3 · outbound
This paper cites Enumeration of holomorphic cylinders in log Calabi–Yau surfaces.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Enumeration of holomorphic cylinders in log Calabi–Yau surfaces
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.395107Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation afe908d2-7e82-473c-b22e-5c4dabe3f64c · outbound
This paper cites Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. II. Positivity, integrality and the gluing formula.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Enumeration of holomorphic cylinders in log Calabi-Yau surfaces. II. Positivity, integrality and the gluing formula
Reference 40
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:04:16.168114Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation f54e5a43-f99f-4070-a0c2-ba1a962ebcb8 · outbound
This paper cites Gromov compactness in non-archimedean analytic geometry.J.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Gromov compactness in non-archimedean analytic geometry.J
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T11:04:16.379019Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Observation 607122dd-a4ea-4e4b-a2d1-1437cfda31b3 · outbound
This paper cites Cluster structures and subfans in scattering diagrams.
The Frobenius structure theorem for affine log Calabi-Yau varieties containing a torus Cluster structures and subfans in scattering diagrams
Reference 42
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T11:04:16.146196Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.
Pith citing papers
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