Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T14:41:36.540932Z
Paper Citation Record · LEDGER
As of 10 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 1 inbound Pith citation observation for arXiv:2505.18443.
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 2026-08-07T14:41:36.540932Z
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, observed 2026-05-20T17:20:29.589792Z
A source-named dated measurement, never combined with another source.
Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z
54 of 54 outbound references displayed
External citation measurements
0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z
Observation 788d089c-f10e-4133-8e13-93f106e974bd · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 1
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 9ab33975-a0f7-4897-a0d7-82538c4a70bf · outbound
An Early History of Toric Ideals Bigatti, and Lorenzo Robbiano, CoCoA: a system for doing Compu- tations in Commutative Algebra , Available at http://cocoa.dima.unige.it
Reference 2
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 68587dcc-5ffb-4005-a57d-df22973a8f58 · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 3
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 e12e2f91-0e57-4435-99c5-5be09890a0ca · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 4
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 374b0cf3-56a1-4654-8572-a7bc0315d680 · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 5
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 b34cac0a-5c5f-482f-895e-3c26abb2b09f · outbound
An Early History of Toric Ideals 4 (1970), 374–383
Reference 6
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 2ae2f1a3-21a7-4b32-a05c-5eebf60f4d98 · outbound
An Early History of Toric Ideals Sci., vol
Reference 7
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 4e34c6c5-4b57-45b2-aacd-eca75382e226 · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 8
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 441c60c2-bb5d-48d9-8708-9e23d0d08643 · outbound
An Early History of Toric Ideals Cox, John B
Reference 9
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation cbd090a7-246c-41f3-b923-8e9461a127dd · outbound
An Early History of Toric Ideals De Loera, Raymond Hemmecke, and Matthias K¨ oppe,Algebraic and geometric ideas in the theory of discrete optimization , MOS-SIAM Series on Optimization, vol
Reference 10
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 e011b0e8-2bc6-4c5d-a989-f1f8b72d0b41 · outbound
An Early History of Toric Ideals De Loera, Raymond Hemmecke, Shmuel Onn, and Robert Weismantel,n-fold integer programming, Discrete Optim
Reference 11
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 0b71f4ed-d620-4cca-b5cc-7288d66dfcde · outbound
An Early History of Toric Ideals De Loera, Raymond Hemmecke, Jeremiah Tauzer, and Ruriko Yoshida, Effective lattice point counting in rational convex polytopes , J
Reference 12
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 83af036d-068a-4946-b71e-301c5baefcb3 · outbound
An Early History of Toric Ideals De Loera, J¨ org Rambau, and Francisco Santos, Triangulations, Algorithms and Computation in Mathematics, vol
Reference 13
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 a523e72a-c652-4be2-9f87-36dd70f16758 · outbound
An Early History of Toric Ideals De Loera, Bernd Sturmfels, and Rekha R
Reference 14
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 c4a1ca10-3058-4026-84f5-30b40679c28c · outbound
An Early History of Toric Ideals de, 2024
Reference 15
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 25a760ed-059d-47af-9752-7a68c17b9b77 · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 16
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 895a94a6-5b6b-424b-b88e-0846464c76ae · outbound
An Early History of Toric Ideals Algebra 88 (1984), no
Reference 17
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 06b2f7b3-26e8-424c-93cc-bc465a0c8d5c · outbound
An Early History of Toric Ideals Jensen, Niels Lauritzen, and Rekha R
Reference 18
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 60d0c4ed-e472-4933-937d-0b83064175ef · outbound
An Early History of Toric Ideals Jensen, and Rekha R
Reference 19
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 881525b8-eda5-42df-b944-35d23e6a45b5 · outbound
An Early History of Toric Ideals Gomory, On the relation between integer and noninteger solutions to linear pro- grams, Proc
Reference 20
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 a7c59a7d-0ffc-43ed-8c5f-4a406f22e396 · outbound
An Early History of Toric Ideals Grayson and Michael E
Reference 21
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 028aa9f2-70b6-4c1b-96a2-1b81562ab7fd · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 22
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 fb67e19a-445c-40d7-82c7-5450c3aafae0 · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 23
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 c8da7028-a313-4343-880f-2eae43b1dd1a · outbound
An Early History of Toric Ideals 94, 2003, The Aussois 2000 Workshop in Combinatorial Optimization, pp
Reference 24
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 7ec8b38a-6e76-4ac2-94cb-4a34877c8e6e · outbound
An Early History of Toric Ideals thesis, Cornell University, 1997
Reference 25
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 120ab887-1715-440f-8ee0-68ddc59659ef · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 26
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 c1984906-3ab5-425f-b395-e9497c5ff58b · outbound
An Early History of Toric Ideals Algebraic Combin
Reference 27
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 b1f84c80-e852-47c4-a62e-5d8a4e2b4477 · outbound
An Early History of Toric Ideals Sci., vol
Reference 28
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 82616312-8cb9-40c2-8300-262cc137d86d · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 29
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 c778e7a5-f296-415a-b829-221ebbd26267 · outbound
An Early History of Toric Ideals Thomas,The associated primes of initial ideals of lattice ideals , Math
Reference 30
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 5adeeae7-0128-429b-acc9-0188c34aba10 · outbound
An Early History of Toric Ideals 139, 1999, Effective methods in algebraic geometry (Saint-Malo, 1998), pp
Reference 31
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 273c9195-b7db-4e4e-bc15-c7d0bfdd1e17 · outbound
An Early History of Toric Ideals 96, 2003, Algebraic and geometric methods in discrete optimization, pp
Reference 32
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 78f400e8-fb4e-4852-96c1-d9c9b8f5f608 · outbound
An Early History of Toric Ideals Thomas, Computing Gr¨ obner fans of toric ideals, Experiment
Reference 33
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 299a124a-0c76-44f1-a6b2-b3765a59f1c3 · outbound
An Early History of Toric Ideals Jensen, Gfan, a software system for Gr¨ obner fans and tropical varieties, Available at http://home.imf.au.dk/jensen/software/gfan/gfan.html
Reference 34
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 6cef84e3-cfc5-4b57-b1a4-8d0ed0783998 · outbound
An Early History of Toric Ideals Lenstra, Jr., Integer programming with a fixed number of variables , Math
Reference 35
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 351031d8-7f04-4606-b39d-bbafe0c539dc · outbound
An Early History of Toric Ideals 50, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1986
Reference 36
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 20858ee0-22fd-4a1f-96fb-f6e40fcc0654 · outbound
An Early History of Toric Ideals Mayr and Albert R
Reference 37
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 294f6258-90e5-4e4c-b30a-e3834c93bb67 · outbound
An Early History of Toric Ideals 6, 1988, Computational aspects of commutative algebra, pp
Reference 38
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 09728352-12c0-4cda-9b4e-acd61f399b71 · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 39
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 3e891b2d-cc0a-4c1c-9bcd-60576dc95ac4 · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 40
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 c7a92fdd-999e-4c34-9f30-21dcbe2adb96 · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 41
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 30b5856f-fa30-4ed8-8ef6-8b33c4ad78c3 · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 42
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 b966886e-4b86-4fe6-97c8-e0232ed94cf8 · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 43
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 f8933061-b338-42f3-aa8f-84ccb464296e · outbound
An Early History of Toric Ideals 8, American Mathematical Society, Providence, RI, 1996
Reference 44
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 087a415a-cc65-44a8-859a-76d8489f11e3 · outbound
An Early History of Toric Ideals Sym- pos
Reference 45
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 15d18c2e-c569-4f0c-bf27-5dcc521ef2e7 · outbound
An Early History of Toric Ideals Thomas, Variation of cost functions in integer programming , Math
Reference 46
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 07cb53e1-5aae-4f08-89a1-7742997dcee7 · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 47
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 16a6a79f-4747-438d-88d4-e248416e3964 · outbound
An Early History of Toric Ideals Unresolved cited work
Reference 48
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 e14a12ca-b5bd-49b0-97f1-5fc002555594 · outbound
An Early History of Toric Ideals Pure Appl
Reference 49
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 69935075-493b-4ec1-8a1f-65ee73aaf965 · outbound
An Early History of Toric Ideals Tayur, Rekha R
Reference 50
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 cec28b07-457a-4378-9df2-d3ea9edc3d8b · outbound
An Early History of Toric Ideals Thomas, A geometric Buchberger algorithm for integer programming , Math
Reference 51
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 e187ecd1-c7fe-4f4d-902d-2073d8b44ed5 · outbound
An Early History of Toric Ideals Thomas and Robert Weismantel, Test sets and inequalities for integer programs , Integer programming and combinatorial optimization (Vancouver, BC, 1996), Lecture Notes in Comput
Reference 52
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 02ca1d43-b1cb-41ce-ba94-53ddebdc93ec · outbound
An Early History of Toric Ideals Algebra Engrg
Reference 53
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 50021680-5988-49f7-a385-0f7a39de20f4 · outbound
An Early History of Toric Ideals Villarreal, Rees algebras of edge ideals, Comm
Reference 54
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 a35292d0-5715-4c49-a908-8a7290c97b84 · inbound
Copositive Matrices with Ordered Off-Diagonal Entries An Early History of Toric Ideals
Reference 193
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.