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Paper Citation Record · LEDGER

Degree functions of graded families of ideals

As of 17 August 2026, this Paper Citation Record lists 54 of 54 outbound references and 0 inbound Pith citation observations for arXiv:2506.05248.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2506.05248 v1

Coverage vector

measured 54 of 54 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-07T10:33:18.800058Z

measured 54 of 54 standing notices

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measured 0 of 1 external citation measurements

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Reference resolution

54 of 54 outbound references displayed

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Outbound references

Observation 5aa70e63-92e1-41fd-8a58-58239578060d · outbound

This paper cites Abhyankar, On the valuations centered in a local domain, Amer.

Degree functions of graded families of ideals Abhyankar, On the valuations centered in a local domain, Amer

Reference 1

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Observation fc78bea1-742c-444e-aa01-e16e51e99f02 · outbound

This paper cites Artin, On the solutions of analytic equations, Invent.

Degree functions of graded families of ideals Artin, On the solutions of analytic equations, Invent

Reference 2

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Observation 3b88231a-b617-4fb1-bd49-0da4f84657ce · outbound

This paper cites Artin, Lipman’s proof of resolution of singularities for surfaces, pp.

Degree functions of graded families of ideals Artin, Lipman’s proof of resolution of singularities for surfaces, pp

Reference 3

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Observation 361dcb04-cfea-4845-8ced-53c1ad0d8e58 · outbound

This paper cites Barth, C.

Degree functions of graded families of ideals Barth, C

Reference 4

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Observation 0275bf49-0081-497f-8571-6ed0a5155095 · outbound

This paper cites Rational powers, invariant ideals, and the summation formula.

Degree functions of graded families of ideals Rational powers, invariant ideals, and the summation formula

Reference 5

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Observation 7f6912e0-ece6-4e01-9cee-c42d3e4b0718 · outbound

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Degree functions of graded families of ideals Unresolved cited work

Reference 6

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Observation d135062c-b824-4207-a110-095343b137d4 · outbound

This paper cites Bourbaki, Commutative Algebra, Chapters 1-7, Springer Verlag, 1989.

Degree functions of graded families of ideals Bourbaki, Commutative Algebra, Chapters 1-7, Springer Verlag, 1989

Reference 7

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Observation 07f67c2c-6919-451a-85d8-b7d4dfc432a6 · outbound

This paper cites Relative mixed multiplicities and mixed Buchsbaum-Rim multiplicities.

Degree functions of graded families of ideals Relative mixed multiplicities and mixed Buchsbaum-Rim multiplicities

Reference 8

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Observation 94be01cb-e9c9-4b40-aa48-2ba5f353bc24 · outbound

This paper cites Multidegrees, families, and integral dependence.

Degree functions of graded families of ideals Multidegrees, families, and integral dependence

Reference 9

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Observation e1863e9b-dbd9-4138-beee-9ccad6c276bc · outbound

This paper cites Cossart, U.

Degree functions of graded families of ideals Cossart, U

Reference 10

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Observation 1255862d-4843-4e21-8237-e3208ec78648 · outbound

This paper cites Cutkosky, On unique and almost unique factorization of complete ideals II, Inventiones Math.

Degree functions of graded families of ideals Cutkosky, On unique and almost unique factorization of complete ideals II, Inventiones Math

Reference 11

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Observation b081a2b8-3afe-45d0-892e-6aa1a956260c · outbound

This paper cites Cutkosky, Asymptotic multiplicities of graded families of ideals and linear series, Adv.

Degree functions of graded families of ideals Cutkosky, Asymptotic multiplicities of graded families of ideals and linear series, Adv

Reference 12

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Observation faf00e77-e614-4e70-9ebe-ee92295e1579 · outbound

This paper cites Cutkosky, A general volume=multiplicity formula, Acta Math.

Degree functions of graded families of ideals Cutkosky, A general volume=multiplicity formula, Acta Math

Reference 13

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Observation 840dbd5a-7c3f-43f3-81f1-3602ef0fdef3 · outbound

This paper cites Cutkosky, Mixed multiplicities of divisorial filtrations, Adv.

Degree functions of graded families of ideals Cutkosky, Mixed multiplicities of divisorial filtrations, Adv

Reference 14

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Observation d0b4880f-1c96-4785-ab01-60f39921dcb9 · outbound

This paper cites Cutkosky, Analytic Spread of filtrations on two dimensional normal local rings, Nagoya Math.

Degree functions of graded families of ideals Cutkosky, Analytic Spread of filtrations on two dimensional normal local rings, Nagoya Math

Reference 15

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Observation 225691fb-ff6f-4a1c-a918-cc3b82955c9c · outbound

This paper cites Cutkosky, Rees algebras and the reduced fiber cone of divisorial filtrations on two dimensional normal local rings, Commun.

Degree functions of graded families of ideals Cutkosky, Rees algebras and the reduced fiber cone of divisorial filtrations on two dimensional normal local rings, Commun

Reference 16

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Observation cb80766c-341d-4e39-a21e-a117c6524e8a · outbound

This paper cites The Rees algebra and analytic spread of a divisorial filtration.

Degree functions of graded families of ideals The Rees algebra and analytic spread of a divisorial filtration

Reference 17

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Observation 0203fd76-b9e0-4c9d-8197-39260a4db2b9 · outbound

This paper cites Cutkosky and P.

Degree functions of graded families of ideals Cutkosky and P

Reference 18

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Observation b5a97b16-3c6d-4ccc-8811-01f986ff6674 · outbound

This paper cites Cutkosky and H.

Degree functions of graded families of ideals Cutkosky and H

Reference 19

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Observation 4bd15f1d-6006-48ad-984f-71fd82f98991 · outbound

This paper cites Multiplicities and degree functions in local rings via intersection products.

Degree functions of graded families of ideals Multiplicities and degree functions in local rings via intersection products

Reference 20

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Observation b100cab4-d5e0-472d-b628-06d5606942cc · outbound

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Degree functions of graded families of ideals Unresolved cited work

Reference 21

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Observation e8ca2062-0e27-4294-8903-58fa371c0e27 · outbound

This paper cites Fulton, Intersection Theory, second edition, Springer, 1998.

Degree functions of graded families of ideals Fulton, Intersection Theory, second edition, Springer, 1998

Reference 22

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Observation c3aa43fb-5d5a-4840-8f03-01c848e4e890 · outbound

This paper cites Goel, R.V.

Degree functions of graded families of ideals Goel, R.V

Reference 23

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Observation 5c7848da-9853-430c-8630-a7720761a033 · outbound

This paper cites Grauert, uber modifikationen und exceptilonelle analytischen mengen, Math.

Degree functions of graded families of ideals Grauert, uber modifikationen und exceptilonelle analytischen mengen, Math

Reference 24

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Observation 94f6539b-3868-4d02-844d-39f4e217420a · outbound

This paper cites Grothendieck, Éléments de géométrie algébrique II, Étude globale élémentaire de quelques classes de morphisms, Pub.

Degree functions of graded families of ideals Grothendieck, Éléments de géométrie algébrique II, Étude globale élémentaire de quelques classes de morphisms, Pub

Reference 25

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Observation bc5a31e8-bfe4-414f-92f6-6e40d4ce7d11 · outbound

This paper cites Grothendieck, Éléments de géométrie algébrique IV , Étude locale des Schémas et des Morphismes des Schémas (Seconde Partie), Pub.

Degree functions of graded families of ideals Grothendieck, Éléments de géométrie algébrique IV , Étude locale des Schémas et des Morphismes des Schémas (Seconde Partie), Pub

Reference 26

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Observation 24e7bb6a-cdd3-4492-8aac-6f8c7f29545b · outbound

This paper cites Hartshorne, Algebraic Geometry, Springer, 1978.

Degree functions of graded families of ideals Hartshorne, Algebraic Geometry, Springer, 1978

Reference 27

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Observation 3f639e46-7799-4c4a-86be-3082b45521f6 · outbound

This paper cites Hironaka, On the equaivalence of singularities, I, Arithmetical Algebraic Geometry, Proceedings.

Degree functions of graded families of ideals Hironaka, On the equaivalence of singularities, I, Arithmetical Algebraic Geometry, Proceedings

Reference 28

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Observation d0e1f1f6-a096-47ba-83ed-6dd07fc90627 · outbound

This paper cites Katz and J.

Degree functions of graded families of ideals Katz and J

Reference 29

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Observation 07cba6b9-c87c-4338-a856-6cfb1e0e7c9f · outbound

This paper cites Kleiman, Toward a numerical theory of ampleness, Ann.

Degree functions of graded families of ideals Kleiman, Toward a numerical theory of ampleness, Ann

Reference 30

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Observation 23dcb11f-6a29-4639-8533-3a9abb680b0e · outbound

This paper cites Kleiman and A.

Degree functions of graded families of ideals Kleiman and A

Reference 31

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source=pdf_text observed=2026-08-07T10:33:18.677622Z digest=sha256:ec628f3a5bf7c252d1266946ad15002cf905b10b3097f20b2f2dddf11950f8a0

Observation af3109e9-bb9d-439e-b835-6a941c5698f9 · outbound

This paper cites Laufer, On deformations of resolutions of two-dimensional singularities, Rice University studies in complex analysis, 1972.

Degree functions of graded families of ideals Laufer, On deformations of resolutions of two-dimensional singularities, Rice University studies in complex analysis, 1972

Reference 32

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Observation 53d1e50a-4afa-4d3a-abc1-be0ce3ccf323 · outbound

This paper cites Lazarsfeld, Positivity in Algebraic Geometry I, Springer, 2000.

Degree functions of graded families of ideals Lazarsfeld, Positivity in Algebraic Geometry I, Springer, 2000

Reference 33

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source=pdf_text observed=2026-08-07T10:33:18.687331Z digest=sha256:3364ed185b2cf5a6aea4cdf5c4f1c49c901fb02ea0079c124058785e9366f89e

Observation e2cb0d6e-ac05-4f62-b841-281d56e4a687 · outbound

This paper cites Lazarsfeld and M.

Degree functions of graded families of ideals Lazarsfeld and M

Reference 34

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Observation 6980a0ba-8ac8-4729-ac0e-43b2986f69b5 · outbound

This paper cites Lin, Algebraic Geometry and Arithmetic Curves, Oxford graduate texts in mathematics 6, translated by Reinie Erné, Oxford University Press, 2002.

Degree functions of graded families of ideals Lin, Algebraic Geometry and Arithmetic Curves, Oxford graduate texts in mathematics 6, translated by Reinie Erné, Oxford University Press, 2002

Reference 35

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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.

source=pdf_text observed=2026-08-07T10:33:18.697995Z digest=sha256:ac969e17da43a2df220c94f7f4971fc2ee83056cd78a8da0ee0c4fdbcf499759

Observation d3d44f1c-5ad6-4384-9817-54cf73c59d2e · outbound

This paper cites Lipman, Rational singularities with applications to algebraic surfaces and unique factorization, Publ.

Degree functions of graded families of ideals Lipman, Rational singularities with applications to algebraic surfaces and unique factorization, Publ

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.349974Z

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.

source=pdf_text observed=2026-08-07T10:33:18.703505Z digest=sha256:efed742ba8afd82677e6e18f2064dc3b97576d15e29276279edfa8c7db32ac0c

Observation 2014c4b1-1bbd-4e97-aba5-e7673c80e8e9 · outbound

This paper cites Lipman, Desingularization of 2-dimensional schemes, Annals of Math.

Degree functions of graded families of ideals Lipman, Desingularization of 2-dimensional schemes, Annals of Math

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.332894Z

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.

source=pdf_text observed=2026-08-07T10:33:18.708402Z digest=sha256:4ba93665c52b97f4ecdbd7cac7a269262d91cbef41ba7fd794ca9713add16085

Observation bd4a16fa-cedd-4e53-9f0a-530a2149b0fd · outbound

This paper cites Matsumura, Commutative Ring Theory, Cambridge studies in advanced mathematics 8, Cambridge University Press, 1989.

Degree functions of graded families of ideals Matsumura, Commutative Ring Theory, Cambridge studies in advanced mathematics 8, Cambridge University Press, 1989

Reference 38

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.315076Z

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.

source=pdf_text observed=2026-08-07T10:33:18.713390Z digest=sha256:e1c77e38801d116e56449719c8704ea91ff2892ac2770752bebcf2a0505814f1

Observation bd82d18c-b62a-409c-a61c-e9cec470281a · outbound

This paper cites Milne, Étale cohomology, Princeton University Press, 1980.

Degree functions of graded families of ideals Milne, Étale cohomology, Princeton University Press, 1980

Reference 39

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.298687Z

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.

source=pdf_text observed=2026-08-07T10:33:18.718735Z digest=sha256:3c6e118cdd8459bada0b19e8a73517069c8b158f2f4d34361708c8927760bb5b

Observation e39067c5-d8a7-4e25-ace6-1a254e18b0bc · outbound

This paper cites Mumford, Lectures on curves on an algebraic surface, Annals of Math.

Degree functions of graded families of ideals Mumford, Lectures on curves on an algebraic surface, Annals of Math

Reference 40

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.281058Z

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.

source=pdf_text observed=2026-08-07T10:33:18.723859Z digest=sha256:a127e9c9c2afae4ad9d65fd072a725f246feb484dfd715044c5161688ac557c0

Observation edfa816f-59c9-4a3c-906a-455ff28ade06 · outbound

This paper cites Polstra, Zariski-Nagata theorem for singularities and the uniform Izumi-Rees property, preprint arXiv:2406.00759 (2024).

Degree functions of graded families of ideals Polstra, Zariski-Nagata theorem for singularities and the uniform Izumi-Rees property, preprint arXiv:2406.00759 (2024)

Reference 41

Resolution
verified exact
raw_fallback, observed 2026-08-07T10:33:18.926671Z

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.

source=pdf_text observed=2026-08-07T10:33:18.729049Z digest=sha256:f045e22592f4bfbbfa64b53019f6f8921da5343815b5654bf17ae0621a3e0127

Observation dcd44eb2-b972-4243-a328-885fd5dfbe67 · outbound

This paper cites Ramanujam, A geometric interpretation of multiplicity, Inventiones Math.

Degree functions of graded families of ideals Ramanujam, A geometric interpretation of multiplicity, Inventiones Math

Reference 42

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.263690Z

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.

source=pdf_text observed=2026-08-07T10:33:18.734302Z digest=sha256:cac96ff0faf7ca4049c8fcd9ed7e711d64365e1145ade0bb8bac4064c2c36b57

Observation 1a0abb18-d68f-4852-8a76-931c43cd4e62 · outbound

This paper cites Rees, Valuations associated with ideals (II), J.

Degree functions of graded families of ideals Rees, Valuations associated with ideals (II), J

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.246422Z

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.

source=pdf_text observed=2026-08-07T10:33:18.739381Z digest=sha256:e1b2a695fb458e5cfdc3e5ba54646d284623acbd3fedd983f1693b73531b9f9c

Observation ba3d7cef-95c5-473f-91f6-46c07e4fa86b · outbound

This paper cites Rees, A note on analytically unramified local rings, J.

Degree functions of graded families of ideals Rees, A note on analytically unramified local rings, J

Reference 44

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.230035Z

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.

source=pdf_text observed=2026-08-07T10:33:18.744868Z digest=sha256:b4bafae8adebd782684b181e649861e1245358fd9af86f1540d3ce71e3bb5a53

Observation 5817e773-e2db-46af-adf0-f751b3d6e0f8 · outbound

This paper cites Rees, Degree functions in local rings, Proceedings of the Cambridge Phil.

Degree functions of graded families of ideals Rees, Degree functions in local rings, Proceedings of the Cambridge Phil

Reference 45

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.213209Z

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.

source=pdf_text observed=2026-08-07T10:33:18.750919Z digest=sha256:344f496798e78e5cb60b8fb921695316a10969e1d8ed39d5afa4b90308d9e0f7

Observation 76995c9a-b948-4520-9834-91c5e3e80f2f · outbound

This paper cites Rees and Y.

Degree functions of graded families of ideals Rees and Y

Reference 46

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.196793Z

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.

source=pdf_text observed=2026-08-07T10:33:18.756382Z digest=sha256:7a2ca08c4f3e2591c36fdf3dd8c6a825041df778db5a2b75fe4bde27ff5ed2d7

Observation 15dd47d3-af21-43db-b14b-be3ec5eb9935 · outbound

This paper cites Rees, Lectures on the asymptotic theory of ideals, London Math Soc.

Degree functions of graded families of ideals Rees, Lectures on the asymptotic theory of ideals, London Math Soc

Reference 47

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.181145Z

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.

source=pdf_text observed=2026-08-07T10:33:18.762105Z digest=sha256:89de059ad1c1691085f36de0513da1d3c9abb12d8523d089921eb93b6db1d1cc

Observation 3dd0d198-5f24-4ab5-98a2-c0b5c8f4214d · outbound

This paper cites Samuel, Sur les variétés algébroides, Ann.

Degree functions of graded families of ideals Samuel, Sur les variétés algébroides, Ann

Reference 48

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.163251Z

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.

source=pdf_text observed=2026-08-07T10:33:18.766921Z digest=sha256:896f1d09cdfcd34ca5158f04b78f017548b94d38b68e30304a21be7660cd4237

Observation 2894f9ac-41bb-4cf1-a3cc-c23f644f6c21 · outbound

This paper cites Snapper, Polynomials associated with divisors, J.

Degree functions of graded families of ideals Snapper, Polynomials associated with divisors, J

Reference 49

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.145178Z

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.

source=pdf_text observed=2026-08-07T10:33:18.772465Z digest=sha256:51251a8c17085561da472e873cdd35d2aa7f83ea1fabc7abc68daafaf36bac4c

Observation e53499a7-3c23-4598-b9c4-fed9cd845cf4 · outbound

This paper cites The stacks project.

Degree functions of graded families of ideals The stacks project

Reference 50

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.125854Z

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.

source=pdf_text observed=2026-08-07T10:33:18.777604Z digest=sha256:5ffa5656ee1e967e6e24898a56dad597acff35ce98e4b365725f27b92da9ef70

Observation 80a40305-8aa4-41d6-9a67-19f3505a4109 · outbound

This paper cites Swanson and C.

Degree functions of graded families of ideals Swanson and C

Reference 51

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.109430Z

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.

source=pdf_text observed=2026-08-07T10:33:18.782785Z digest=sha256:450e7b9d7901149beda9597c5608cfe0c33bcb3ef25834b97b347e7d65150162

Observation d1ab4ec0-5310-4590-8988-341187187732 · outbound

This paper cites Thorup, Rational equivalence theory on arbitrary Noetherian schemes, In Enumerative Geometry, Sebastian Xambó-Descamps Ed, LNM 1436, Springer, 1990.

Degree functions of graded families of ideals Thorup, Rational equivalence theory on arbitrary Noetherian schemes, In Enumerative Geometry, Sebastian Xambó-Descamps Ed, LNM 1436, Springer, 1990

Reference 52

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.075588Z

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.

source=pdf_text observed=2026-08-07T10:33:18.794685Z digest=sha256:348983d7a64116347c339b8e08cb3df09a944ca34707bb782faba795226a292d

Observation 157aa161-825e-483e-bd84-7b80a1a00cfc · outbound

This paper cites Zariski and P.

Degree functions of graded families of ideals Zariski and P

Reference 53

Resolution
verified fuzzy
raw_fallback, observed 2026-08-07T10:33:19.056995Z

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.

source=pdf_text observed=2026-08-07T10:33:18.800058Z digest=sha256:08df8d8a2aef7ef06356d91eef26e692a293ab3cb119916953d26359a079f3ca

Observation 9c7fb9e4-c8c7-4227-a2c7-e19ed3949e42 · outbound

This paper cites an unresolved cited work.

Degree functions of graded families of ideals Unresolved cited work

Reference 336

Resolution
unresolved
raw_fallback, observed 2026-08-07T10:33:19.093193Z

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.

source=pdf_text observed=2026-08-07T10:33:18.789156Z digest=sha256:0b43301558d2322f3e5bc81e0327dd7610104a74a6a245703442fda8cbbd19d2

Pith citing papers

No inbound Pith citation observations are available.