Pith. sign in

Paper Citation Record · LEDGER

An Early History of Toric Ideals

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.

pith.paper-citation-record.v1
2505.18443 v1

Coverage vector

measured 54 of 54 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T14:41:36.540932Z

measured 55 of 55 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-20T17:20:29.589792Z

measured 1 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Reference resolution

54 of 54 outbound references displayed

  • verified exact0
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  • unresolved18
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External citation measurements

0
arxiv_reference, observed 2026-08-05T02:28:24.338817Z

Outbound references

Observation 788d089c-f10e-4133-8e13-93f106e974bd · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:46.738563Z

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.

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Observation 9ab33975-a0f7-4897-a0d7-82538c4a70bf · outbound

This paper cites Bigatti, and Lorenzo Robbiano, CoCoA: a system for doing Compu- tations in Commutative Algebra , Available at http://cocoa.dima.unige.it.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:46.508568Z

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.

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Observation 68587dcc-5ffb-4005-a57d-df22973a8f58 · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:46.318699Z

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.

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Observation e12e2f91-0e57-4435-99c5-5be09890a0ca · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 4

Resolution
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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.

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Observation 374b0cf3-56a1-4654-8572-a7bc0315d680 · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 5

Resolution
unresolved
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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.

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Observation b34cac0a-5c5f-482f-895e-3c26abb2b09f · outbound

This paper cites 4 (1970), 374–383.

An Early History of Toric Ideals 4 (1970), 374–383

Reference 6

Resolution
verified fuzzy
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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.

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Observation 2ae2f1a3-21a7-4b32-a05c-5eebf60f4d98 · outbound

This paper cites Sci., vol.

An Early History of Toric Ideals Sci., vol

Reference 7

Resolution
verified fuzzy
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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.

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Observation 4e34c6c5-4b57-45b2-aacd-eca75382e226 · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:45.499351Z

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.

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Observation 441c60c2-bb5d-48d9-8708-9e23d0d08643 · outbound

This paper cites Cox, John B.

An Early History of Toric Ideals Cox, John B

Reference 9

Resolution
unresolved
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Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T14:41:31.203849Z digest=sha256:777147d25f101df4f235706418625eaf709518654f10dfe5b0c3f39095620bdb

Observation cbd090a7-246c-41f3-b923-8e9461a127dd · outbound

This paper cites De Loera, Raymond Hemmecke, and Matthias K¨ oppe,Algebraic and geometric ideas in the theory of discrete optimization , MOS-SIAM Series on Optimization, vol.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:45.362474Z

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.

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Observation e011b0e8-2bc6-4c5d-a989-f1f8b72d0b41 · outbound

This paper cites De Loera, Raymond Hemmecke, Shmuel Onn, and Robert Weismantel,n-fold integer programming, Discrete Optim.

An Early History of Toric Ideals De Loera, Raymond Hemmecke, Shmuel Onn, and Robert Weismantel,n-fold integer programming, Discrete Optim

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:45.194760Z

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.

source=pdf_text observed=2026-08-07T14:41:31.476838Z digest=sha256:1da3b70bff60c5b0bac24e5be2ff4ef224f56cf00077a557c093c466a79f6847

Observation 0b71f4ed-d620-4cca-b5cc-7288d66dfcde · outbound

This paper cites De Loera, Raymond Hemmecke, Jeremiah Tauzer, and Ruriko Yoshida, Effective lattice point counting in rational convex polytopes , J.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:44.972782Z

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.

source=pdf_text observed=2026-08-07T14:41:31.594890Z digest=sha256:d3e8ad7fe662f6f58daa5b58ae42e16e0963d5823b50b516c5cbd0eafa2faf02

Observation 83af036d-068a-4946-b71e-301c5baefcb3 · outbound

This paper cites De Loera, J¨ org Rambau, and Francisco Santos, Triangulations, Algorithms and Computation in Mathematics, vol.

An Early History of Toric Ideals De Loera, J¨ org Rambau, and Francisco Santos, Triangulations, Algorithms and Computation in Mathematics, vol

Reference 13

Resolution
verified fuzzy
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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.

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Observation a523e72a-c652-4be2-9f87-36dd70f16758 · outbound

This paper cites De Loera, Bernd Sturmfels, and Rekha R.

An Early History of Toric Ideals De Loera, Bernd Sturmfels, and Rekha R

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:44.529179Z

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.

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Observation c4a1ca10-3058-4026-84f5-30b40679c28c · outbound

This paper cites de, 2024.

An Early History of Toric Ideals de, 2024

Reference 15

Resolution
verified fuzzy
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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.

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Observation 25a760ed-059d-47af-9752-7a68c17b9b77 · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:44.241009Z

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.

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Observation 895a94a6-5b6b-424b-b88e-0846464c76ae · outbound

This paper cites Algebra 88 (1984), no.

An Early History of Toric Ideals Algebra 88 (1984), no

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:44.070047Z

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.

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Observation 06b2f7b3-26e8-424c-93cc-bc465a0c8d5c · outbound

This paper cites Jensen, Niels Lauritzen, and Rekha R.

An Early History of Toric Ideals Jensen, Niels Lauritzen, and Rekha R

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:43.950713Z

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.

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Observation 60d0c4ed-e472-4933-937d-0b83064175ef · outbound

This paper cites Jensen, and Rekha R.

An Early History of Toric Ideals Jensen, and Rekha R

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:43.798172Z

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.

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Observation 881525b8-eda5-42df-b944-35d23e6a45b5 · outbound

This paper cites Gomory, On the relation between integer and noninteger solutions to linear pro- grams, Proc.

An Early History of Toric Ideals Gomory, On the relation between integer and noninteger solutions to linear pro- grams, Proc

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:43.643733Z

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.

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Observation a7c59a7d-0ffc-43ed-8c5f-4a406f22e396 · outbound

This paper cites Grayson and Michael E.

An Early History of Toric Ideals Grayson and Michael E

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:43.483477Z

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.

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Observation 028aa9f2-70b6-4c1b-96a2-1b81562ab7fd · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:43.292313Z

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.

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Observation fb67e19a-445c-40d7-82c7-5450c3aafae0 · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:43.135652Z

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.

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Observation c8da7028-a313-4343-880f-2eae43b1dd1a · outbound

This paper cites 94, 2003, The Aussois 2000 Workshop in Combinatorial Optimization, pp.

An Early History of Toric Ideals 94, 2003, The Aussois 2000 Workshop in Combinatorial Optimization, pp

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:43.011005Z

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.

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Observation 7ec8b38a-6e76-4ac2-94cb-4a34877c8e6e · outbound

This paper cites thesis, Cornell University, 1997.

An Early History of Toric Ideals thesis, Cornell University, 1997

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:42.839965Z

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.

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Observation 120ab887-1715-440f-8ee0-68ddc59659ef · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:42.662912Z

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.

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Observation c1984906-3ab5-425f-b395-e9497c5ff58b · outbound

This paper cites Algebraic Combin.

An Early History of Toric Ideals Algebraic Combin

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:42.484478Z

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.

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Observation b1f84c80-e852-47c4-a62e-5d8a4e2b4477 · outbound

This paper cites Sci., vol.

An Early History of Toric Ideals Sci., vol

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:42.274949Z

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.

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Observation 82616312-8cb9-40c2-8300-262cc137d86d · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:42.040719Z

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.

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Observation c778e7a5-f296-415a-b829-221ebbd26267 · outbound

This paper cites Thomas,The associated primes of initial ideals of lattice ideals , Math.

An Early History of Toric Ideals Thomas,The associated primes of initial ideals of lattice ideals , Math

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:41.847805Z

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.

source=pdf_text observed=2026-08-07T14:41:34.284140Z digest=sha256:b8f1d2bfcdcb8e601b8e9076cc3a9332290cd4fd5f2b3865f64a4294a4acc456

Observation 5adeeae7-0128-429b-acc9-0188c34aba10 · outbound

This paper cites 139, 1999, Effective methods in algebraic geometry (Saint-Malo, 1998), pp.

An Early History of Toric Ideals 139, 1999, Effective methods in algebraic geometry (Saint-Malo, 1998), pp

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:41.654717Z

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.

source=pdf_text observed=2026-08-07T14:41:34.405850Z digest=sha256:43fca487dea11d3ce2520cb91bd029294c30855182f3c02ce5bb16461cd193c2

Observation 273c9195-b7db-4e4e-bc15-c7d0bfdd1e17 · outbound

This paper cites 96, 2003, Algebraic and geometric methods in discrete optimization, pp.

An Early History of Toric Ideals 96, 2003, Algebraic and geometric methods in discrete optimization, pp

Reference 32

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:41.483937Z

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.

source=pdf_text observed=2026-08-07T14:41:34.520110Z digest=sha256:8b74e568b2e28778fc7323290d8f086066c382e5ba255e7d335c6eaa9df6762e

Observation 78f400e8-fb4e-4852-96c1-d9c9b8f5f608 · outbound

This paper cites Thomas, Computing Gr¨ obner fans of toric ideals, Experiment.

An Early History of Toric Ideals Thomas, Computing Gr¨ obner fans of toric ideals, Experiment

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:41.332066Z

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.

source=pdf_text observed=2026-08-07T14:41:34.621527Z digest=sha256:6d158e7ceb45402d5f278f7d6e4215ff116b929a198f9eec2a80acc4526d17b7

Observation 299a124a-0c76-44f1-a6b2-b3765a59f1c3 · outbound

This paper cites Jensen, Gfan, a software system for Gr¨ obner fans and tropical varieties, Available at http://home.imf.au.dk/jensen/software/gfan/gfan.html.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:41.106300Z

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.

source=pdf_text observed=2026-08-07T14:41:34.716775Z digest=sha256:639d8171d85be9f1ddceb71dac11550f5994912b6e1addeba17020c0c661b679

Observation 6cef84e3-cfc5-4b57-b1a4-8d0ed0783998 · outbound

This paper cites Lenstra, Jr., Integer programming with a fixed number of variables , Math.

An Early History of Toric Ideals Lenstra, Jr., Integer programming with a fixed number of variables , Math

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:40.896869Z

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.

source=pdf_text observed=2026-08-07T14:41:34.806102Z digest=sha256:514eec7386c7d4e695ace9adb264de6eaabd022b7b02c6d664492562951ea56e

Observation 351031d8-7f04-4606-b39d-bbafe0c539dc · outbound

This paper cites 50, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1986.

An Early History of Toric Ideals 50, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1986

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:40.748576Z

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.

source=pdf_text observed=2026-08-07T14:41:34.898325Z digest=sha256:d36500f722dd03e3e7c677864bdb912b0849845f389c81baa1998b700ce0291b

Observation 20858ee0-22fd-4a1f-96fb-f6e40fcc0654 · outbound

This paper cites Mayr and Albert R.

An Early History of Toric Ideals Mayr and Albert R

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:40.518049Z

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.

source=pdf_text observed=2026-08-07T14:41:35.005409Z digest=sha256:b587b372d260501a4aec540191a07ae2e093f3b36b59ae2d9fc46563c5e861bb

Observation 294f6258-90e5-4e4c-b30a-e3834c93bb67 · outbound

This paper cites 6, 1988, Computational aspects of commutative algebra, pp.

An Early History of Toric Ideals 6, 1988, Computational aspects of commutative algebra, pp

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:40.336863Z

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.

source=pdf_text observed=2026-08-07T14:41:35.100564Z digest=sha256:c033a98eab6ee4094a68451e6c517a26dc91100f17f5abffcd1c08c4f38c4905

Observation 09728352-12c0-4cda-9b4e-acd61f399b71 · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:40.106564Z

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.

source=pdf_text observed=2026-08-07T14:41:35.210294Z digest=sha256:1a1c77928bcdabc4f723b5da16096f9115f4852984e4fa83e9ad5cec0e63298c

Observation 3e891b2d-cc0a-4c1c-9bcd-60576dc95ac4 · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 40

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:39.818714Z

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.

source=pdf_text observed=2026-08-07T14:41:35.303025Z digest=sha256:10bc88def011185e0111eecda4be8b9d11389d4d63609fa8c5ada0afb95b365f

Observation c7a92fdd-999e-4c34-9f30-21dcbe2adb96 · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:39.564999Z

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.

source=pdf_text observed=2026-08-07T14:41:35.389368Z digest=sha256:316e5d7862064d11731cd819d2f16d1334e74e5c33102a3565ed61bf411d183c

Observation 30b5856f-fa30-4ed8-8ef6-8b33c4ad78c3 · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:39.281742Z

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.

source=pdf_text observed=2026-08-07T14:41:35.476810Z digest=sha256:b1cb2bea0dfb8babd62f4469357bf463865dce0d03563213f0ef07bbb11dd5a7

Observation b966886e-4b86-4fe6-97c8-e0232ed94cf8 · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 43

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:39.026553Z

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.

source=pdf_text observed=2026-08-07T14:41:35.571101Z digest=sha256:3f0456262514019c8c9bd990f61953d06b175cca995d908b34ffc89bb452ae8f

Observation f8933061-b338-42f3-aa8f-84ccb464296e · outbound

This paper cites 8, American Mathematical Society, Providence, RI, 1996.

An Early History of Toric Ideals 8, American Mathematical Society, Providence, RI, 1996

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:38.798149Z

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.

source=pdf_text observed=2026-08-07T14:41:35.660268Z digest=sha256:2319132a8ad760e59ddbb719fe7fd9b6f43a3d3a8f02ed2363b0075b4dbf739b

Observation 087a415a-cc65-44a8-859a-76d8489f11e3 · outbound

This paper cites Sym- pos.

An Early History of Toric Ideals Sym- pos

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:38.580834Z

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.

source=pdf_text observed=2026-08-07T14:41:35.788040Z digest=sha256:9110498f88f078bede47e8d52a3f7aa14793d2f7e63ec12e3c0744db506f6955

Observation 15d18c2e-c569-4f0c-bf27-5dcc521ef2e7 · outbound

This paper cites Thomas, Variation of cost functions in integer programming , Math.

An Early History of Toric Ideals Thomas, Variation of cost functions in integer programming , Math

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:38.325977Z

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.

source=pdf_text observed=2026-08-07T14:41:35.864965Z digest=sha256:ecbe37bd6ad3f473ea153a3902684da02737cc2f989a1ea7671f0dab144fe7fb

Observation 07cb53e1-5aae-4f08-89a1-7742997dcee7 · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 47

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:38.114369Z

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.

source=pdf_text observed=2026-08-07T14:41:35.961777Z digest=sha256:a9165ae1f85afcd85a9555cd6b1808bab81b5da7c2af598cde34604ebae963d9

Observation 16a6a79f-4747-438d-88d4-e248416e3964 · outbound

This paper cites an unresolved cited work.

An Early History of Toric Ideals Unresolved cited work

Reference 48

Resolution
unresolved
raw_fallback, observed 2026-08-07T14:41:37.931984Z

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.

source=pdf_text observed=2026-08-07T14:41:36.035830Z digest=sha256:8ad7463005fb54f9ec9d0d9afcf14fb3c6898135f3314892ae1e395b2c1e1492

Observation e14a12ca-b5bd-49b0-97f1-5fc002555594 · outbound

This paper cites Pure Appl.

An Early History of Toric Ideals Pure Appl

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:37.742319Z

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.

source=pdf_text observed=2026-08-07T14:41:36.142597Z digest=sha256:1677527948e66a71c9a6b486aa362652783c99dd10fbf387d761d8aefbd89ade

Observation 69935075-493b-4ec1-8a1f-65ee73aaf965 · outbound

This paper cites Tayur, Rekha R.

An Early History of Toric Ideals Tayur, Rekha R

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:37.554149Z

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.

source=pdf_text observed=2026-08-07T14:41:36.226069Z digest=sha256:cb452e35be5c6c7827dda4184bbbe082eaeb07fecb1d7d2ff143f1623ec3470c

Observation cec28b07-457a-4378-9df2-d3ea9edc3d8b · outbound

This paper cites Thomas, A geometric Buchberger algorithm for integer programming , Math.

An Early History of Toric Ideals Thomas, A geometric Buchberger algorithm for integer programming , Math

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:37.343855Z

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.

source=pdf_text observed=2026-08-07T14:41:36.304290Z digest=sha256:8d1e0127f8d1f9d8336423c43fd06f0912b487e6a8d2b802628ab233a937b496

Observation e187ecd1-c7fe-4f4d-902d-2073d8b44ed5 · outbound

This paper cites Thomas and Robert Weismantel, Test sets and inequalities for integer programs , Integer programming and combinatorial optimization (Vancouver, BC, 1996), Lecture Notes in Comput.

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

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:37.171151Z

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.

source=pdf_text observed=2026-08-07T14:41:36.373658Z digest=sha256:2f1e5532b556df3530ed80d1c1f094f5e975b45ca8bac9e889666eead5ad8653

Observation 02ca1d43-b1cb-41ce-ba94-53ddebdc93ec · outbound

This paper cites Algebra Engrg.

An Early History of Toric Ideals Algebra Engrg

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:36.978886Z

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.

source=pdf_text observed=2026-08-07T14:41:36.476904Z digest=sha256:5ad33727904638c86ba2273fd6613822fc87452d35164e289c833fd1b2cbeb9d

Observation 50021680-5988-49f7-a385-0f7a39de20f4 · outbound

This paper cites Villarreal, Rees algebras of edge ideals, Comm.

An Early History of Toric Ideals Villarreal, Rees algebras of edge ideals, Comm

Reference 54

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T14:41:36.769142Z

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.

source=pdf_text observed=2026-08-07T14:41:36.540932Z digest=sha256:024e6ebd8615d9cdcf810cfab4eca7da38562164c4e24159eeb51e80515a91c8

Pith citing papers

Observation a35292d0-5715-4c49-a908-8a7290c97b84 · inbound

Copositive Matrices with Ordered Off-Diagonal Entries cites this paper.

Copositive Matrices with Ordered Off-Diagonal Entries An Early History of Toric Ideals

Reference 193

Resolution
verified exact
arxiv_id, observed 2026-05-20T17:23:36.364462Z

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.

source=arxiv_source observed=2026-05-20T17:20:29.589792Z digest=sha256:fca49b61ebefcda1e2aab77ac0ae514061d8ceeb9c5e71b209ef35c4654ae929