Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T12:35:12.153498Z
Paper Citation Record · LEDGER
Tropical geometry
As of 16 August 2026, this Paper Citation Record lists 53 of 53 outbound references and 0 inbound Pith citation observations for arXiv:1908.07012.
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 2026-08-16T06:30:59.297886+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
53 of 53 outbound references displayed
- verified exact1
- verified fuzzy33
- unresolved15
- parse uncertain0
- malformed identifier0
- metadata mismatch4
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 440e9a23-9d90-4854-a43e-7cdaacb8db56 · outbound
This paper cites A., Moll, V.
Tropical geometry A., Moll, V
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.589131Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 25d9cbaf-e101-4ea5-bfba-a0ccd66c0138 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 2
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.582269Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 56f3b213-cfb1-4405-a7a9-14e825959842 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.575437Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 219f12b8-2e26-4300-adb4-cb54b4437aac · outbound
This paper cites Chemical Applications of Graph Theory (A.T.
Tropical geometry Chemical Applications of Graph Theory (A.T
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.568433Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 20ff17c4-0ba1-4dbc-b605-049f93e192c8 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 5
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.560176Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 05524ebf-3b51-4217-a9f6-e0e6140b13e1 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 6
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.553376Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 91162b57-68a5-453c-8a1b-cc26f5ab8458 · outbound
This paper cites Sturmfels, B.: Moduli of tropical plane curves.
Tropical geometry Sturmfels, B.: Moduli of tropical plane curves
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.546689Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 192eb884-f3bc-486b-8cf2-01fc0f1913fe · outbound
This paper cites Springer Monographs in Mathemat- ics.
Tropical geometry Springer Monographs in Mathemat- ics
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.539223Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d2ece9b4-3bef-4057-956a-fd7947753041 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.532479Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7b4b3de6-403e-4c8b-97db-24d8efe327b6 · outbound
This paper cites Discrete and Computational Geom- etry 47, no.
Tropical geometry Discrete and Computational Geom- etry 47, no
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.525744Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5398beb6-7976-4f0c-a3e8-b0d17022f9e2 · outbound
This paper cites Algebra and Number Theory3 (2009).
Tropical geometry Algebra and Number Theory3 (2009)
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.517767Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 640f65e7-1a26-45a1-9571-37b1cca2ad73 · outbound
This paper cites Algebra Number Theory, 6(6) (2012).
Tropical geometry Algebra Number Theory, 6(6) (2012)
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.510486Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 5c55d719-2d07-4497-8e8e-0ef85c7a51a7 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 13
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.503268Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ea2b41a3-18e1-4aca-9198-ce6de23f47ad · outbound
This paper cites Combinatorial algebraic geometry, 65–86, Fields Inst.
Tropical geometry Combinatorial algebraic geometry, 65–86, Fields Inst
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.495628Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ab55ac0c-4d31-43f6-b2e0-29042966f4c5 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.488625Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 402de6c5-3ec7-4ee5-a5f7-dd9da072dd7e · outbound
This paper cites An introduction to chip-firing.
Tropical geometry An introduction to chip-firing
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.481580Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b13ec5f8-8968-4512-978f-1a50b220b553 · outbound
This paper cites A., Little, J., O’Shea, D.: Ideals, varieties, and algorithms.
Tropical geometry A., Little, J., O’Shea, D.: Ideals, varieties, and algorithms
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.474935Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e5579b11-5d6e-4cfc-8ef3-5eddc8bc4ee7 · outbound
This paper cites G., Erds, P: On a combinatorial problem.
Tropical geometry G., Erds, P: On a combinatorial problem
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.467783Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 00042041-6d08-4438-9b8e-807711b17399 · outbound
This paper cites Structures for algorithms and applica- tions.
Tropical geometry Structures for algorithms and applica- tions
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.460432Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 04aa8d07-ae95-4584-b657-1ab875cedd8b · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 20
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.453480Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 8f56f4a3-d842-4d94-98df-11ab35e4de0b · outbound
This paper cites ACM Transactions on Graphics (TOG) 8, No.
Tropical geometry ACM Transactions on Graphics (TOG) 8, No
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.446110Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7f7ff746-255e-4315-9598-9e46c749a915 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.438703Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 24be0412-4c40-43e1-bb95-9cc9ae3244b6 · outbound
This paper cites Polytopes- combinatorics and computation (Oberwolfach, 1997), 43?73, DMV Sem., 29, Birkhuser, Basel (2000).
Tropical geometry Polytopes- combinatorics and computation (Oberwolfach, 1997), 43?73, DMV Sem., 29, Birkhuser, Basel (2000)
Reference 23
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.431228Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation cb1ede14-b7db-413e-a9fe-07b3c46b51c2 · outbound
This paper cites Duke Math.
Tropical geometry Duke Math
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.423386Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7c9584db-5c0d-4fc9-8267-904d984f8eac · outbound
This paper cites E.: Macaulay2, a software system for research in algebraic geome- try.
Tropical geometry E.: Macaulay2, a software system for research in algebraic geome- try
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.415364Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b0a432ad-bace-4963-abec-2f3dba420a79 · outbound
This paper cites Tropicalized quartics and canonical embeddings for tropical curves of genus 3.
Tropical geometry Tropicalized quartics and canonical embeddings for tropical curves of genus 3
Reference 26
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-14T12:35:12.219345Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6c89ddac-4efb-4a9d-8b32-ec5d08a70969 · outbound
This paper cites Graduate Texts in Mathematics, No.
Tropical geometry Graduate Texts in Mathematics, No
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.407260Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3653a7c4-e2a6-4a3c-a566-9a49ac0a5c07 · outbound
This paper cites (German) Math.
Tropical geometry (German) Math
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.399159Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 258f307d-aab1-44ac-8d76-d38e52ce807a · outbound
This paper cites Available at http://home.imf.au.dk/jensen/software/gfan/gfan.html.
Tropical geometry Available at http://home.imf.au.dk/jensen/software/gfan/gfan.html
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.391832Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d4c5acd0-cb64-4b34-b214-ec704416298c · outbound
This paper cites Surveys in combinatorics, 2003 (Bangor), 277–307, London Math.
Tropical geometry Surveys in combinatorics, 2003 (Bangor), 277–307, London Math
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.384609Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d4f23994-ebb6-4a87-a929-09031e8ea450 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 31
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.376026Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 84f33554-1ca9-4bc7-89d2-371d59304dd1 · outbound
This paper cites Canadian J.
Tropical geometry Canadian J
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.367911Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 08c17ad1-fc55-4d71-a970-6e96503e9b01 · outbound
This paper cites Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (ISSAC 2014).
Tropical geometry Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (ISSAC 2014)
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.359343Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation efac671f-7e83-4369-82c8-0dabafb69bdf · outbound
This paper cites Lifting tropical bitangents.
Reference 34
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-14T12:35:12.209028Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 49ca03e6-a37a-496f-a515-261a036016c8 · outbound
This paper cites Lifting tropical self intersections.
Reference 35
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-14T12:35:12.198850Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation fc61ec63-d1c9-40e8-bb42-78f4536b815f · outbound
This paper cites Fibonacci Quart.
Tropical geometry Fibonacci Quart
Reference 36
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.350983Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation c234dd76-f014-4120-a094-5d76f2e78c30 · outbound
This paper cites Linear and Rational Factorization of Tropical Polynomials.
Tropical geometry Linear and Rational Factorization of Tropical Polynomials
Reference 37
- Resolution
- verified exact
- local_arxiv, observed 2026-08-14T12:35:12.188796Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f190c937-3cce-4a5b-868a-039d758c5546 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 38
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.342306Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 9861737a-1ba8-4023-bbb6-01e4314c1cf2 · outbound
This paper cites Graduate Studies in Mathe- matics, 161.
Tropical geometry Graduate Studies in Mathe- matics, 161
Reference 39
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.333535Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 579849c3-52f0-4f5f-b045-80538411e0f9 · outbound
This paper cites A., Rowland, E.: p-regularity of the p-adic valuation of the Fibonacci sequence.
Tropical geometry A., Rowland, E.: p-regularity of the p-adic valuation of the Fibonacci sequence
Reference 40
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.325753Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation b1c72940-78b5-4ec2-8831-faf6526dc34d · outbound
This paper cites Curves and abelian varieties, 203–230, Contemp.
Tropical geometry Curves and abelian varieties, 203–230, Contemp
Reference 41
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.317876Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 110014d9-9c60-4029-8be5-b2ac43a2a6cf · outbound
This paper cites Tropical hyperelliptic curves in the plane.
Tropical geometry Tropical hyperelliptic curves in the plane
Reference 42
- Resolution
- metadata mismatch
- local_arxiv, observed 2026-08-14T12:35:12.178175Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 039fff52-9af5-4e33-9300-676c60e917a1 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 43
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.310873Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d294d0c3-aaf7-4140-8317-406a885e7cf7 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 44
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.303756Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d0bb37b2-5363-4f82-b507-2fd0116b6158 · outbound
This paper cites Tropical and non- Archimedean geometry, 15–44, Contemp.
Tropical geometry Tropical and non- Archimedean geometry, 15–44, Contemp
Reference 45
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.295256Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 693699c0-d0c6-477c-8271-7e56864dbb85 · outbound
This paper cites A.: Geometrisches zur Zahlenlehre, Sitzenber.
Tropical geometry A.: Geometrisches zur Zahlenlehre, Sitzenber
Reference 46
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.287192Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2e9e7112-e779-4e50-9437-3f2a0139200d · outbound
This paper cites Idempotency (Bristol, 1994), 50–69, Publ.
Tropical geometry Idempotency (Bristol, 1994), 50–69, Publ
Reference 47
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.279926Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ca4f8e20-7673-4750-92ae-b71cfc956eca · outbound
This paper cites (French) J.
Tropical geometry (French) J
Reference 48
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.272054Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4c5deb10-0976-4641-8768-3b4fa47d3ce7 · outbound
This paper cites Idempotent mathematics and mathematical physics, 289–317, Contemp.
Tropical geometry Idempotent mathematics and mathematical physics, 289–317, Contemp
Reference 49
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.263549Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3fcb14b3-f9c6-43aa-a686-736f513ed17a · outbound
This paper cites and Gao, Xiao-Shan and Takayama, Nobuki, eds.), World Scientific, pp.
Tropical geometry and Gao, Xiao-Shan and Takayama, Nobuki, eds.), World Scientific, pp
Reference 50
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.255303Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ced98fbc-9112-43d6-b723-618858166914 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 51
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.245895Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4958039e-1f51-41d2-8b21-4e531266f549 · outbound
This paper cites Mathematical foun- dations of computer science, 1988 (Carlsbad, 1988), 107–120, Lecture Notes in Comput.
Tropical geometry Mathematical foun- dations of computer science, 1988 (Carlsbad, 1988), 107–120, Lecture Notes in Comput
Reference 52
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:35:12.236931Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d7143cdb-fbec-4ce0-a993-d07973d23196 · outbound
This paper cites an unresolved cited work.
Tropical geometry Unresolved cited work
Reference 53
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:35:12.227650Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.