Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T10:33:18.800058Z
Paper Citation Record · LEDGER
As of 8 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.
Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T10:33:18.800058Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+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
54 of 54 outbound references displayed
External citation measurements
No source-named external measurement is stored.
Observation 5aa70e63-92e1-41fd-8a58-58239578060d · outbound
Degree functions of graded families of ideals Abhyankar, On the valuations centered in a local domain, Amer
Reference 1
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation fc78bea1-742c-444e-aa01-e16e51e99f02 · outbound
Degree functions of graded families of ideals Artin, On the solutions of analytic equations, Invent
Reference 2
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 3b88231a-b617-4fb1-bd49-0da4f84657ce · outbound
Degree functions of graded families of ideals Artin, Lipman’s proof of resolution of singularities for surfaces, pp
Reference 3
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 361dcb04-cfea-4845-8ced-53c1ad0d8e58 · outbound
Reference 4
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 0275bf49-0081-497f-8571-6ed0a5155095 · outbound
Degree functions of graded families of ideals Rational powers, invariant ideals, and the summation formula
Reference 5
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7f6912e0-ece6-4e01-9cee-c42d3e4b0718 · outbound
Degree functions of graded families of ideals Unresolved cited work
Reference 6
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d135062c-b824-4207-a110-095343b137d4 · outbound
Degree functions of graded families of ideals Bourbaki, Commutative Algebra, Chapters 1-7, Springer Verlag, 1989
Reference 7
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 07f67c2c-6919-451a-85d8-b7d4dfc432a6 · outbound
Degree functions of graded families of ideals Relative mixed multiplicities and mixed Buchsbaum-Rim multiplicities
Reference 8
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 94be01cb-e9c9-4b40-aa48-2ba5f353bc24 · outbound
Degree functions of graded families of ideals Multidegrees, families, and integral dependence
Reference 9
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation e1863e9b-dbd9-4138-beee-9ccad6c276bc · outbound
Reference 10
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 1255862d-4843-4e21-8237-e3208ec78648 · outbound
Degree functions of graded families of ideals Cutkosky, On unique and almost unique factorization of complete ideals II, Inventiones Math
Reference 11
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b081a2b8-3afe-45d0-892e-6aa1a956260c · outbound
Degree functions of graded families of ideals Cutkosky, Asymptotic multiplicities of graded families of ideals and linear series, Adv
Reference 12
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation faf00e77-e614-4e70-9ebe-ee92295e1579 · outbound
Degree functions of graded families of ideals Cutkosky, A general volume=multiplicity formula, Acta Math
Reference 13
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 840dbd5a-7c3f-43f3-81f1-3602ef0fdef3 · outbound
Degree functions of graded families of ideals Cutkosky, Mixed multiplicities of divisorial filtrations, Adv
Reference 14
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d0b4880f-1c96-4785-ab01-60f39921dcb9 · outbound
Degree functions of graded families of ideals Cutkosky, Analytic Spread of filtrations on two dimensional normal local rings, Nagoya Math
Reference 15
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 225691fb-ff6f-4a1c-a918-cc3b82955c9c · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation cb80766c-341d-4e39-a21e-a117c6524e8a · outbound
Degree functions of graded families of ideals The Rees algebra and analytic spread of a divisorial filtration
Reference 17
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 0203fd76-b9e0-4c9d-8197-39260a4db2b9 · outbound
Degree functions of graded families of ideals Cutkosky and P
Reference 18
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b5a97b16-3c6d-4ccc-8811-01f986ff6674 · outbound
Degree functions of graded families of ideals Cutkosky and H
Reference 19
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4bd15f1d-6006-48ad-984f-71fd82f98991 · outbound
Degree functions of graded families of ideals Multiplicities and degree functions in local rings via intersection products
Reference 20
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b100cab4-d5e0-472d-b628-06d5606942cc · outbound
Degree functions of graded families of ideals Unresolved cited work
Reference 21
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e8ca2062-0e27-4294-8903-58fa371c0e27 · outbound
Degree functions of graded families of ideals Fulton, Intersection Theory, second edition, Springer, 1998
Reference 22
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c3aa43fb-5d5a-4840-8f03-01c848e4e890 · outbound
Reference 23
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5c7848da-9853-430c-8630-a7720761a033 · outbound
Degree functions of graded families of ideals Grauert, uber modifikationen und exceptilonelle analytischen mengen, Math
Reference 24
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 94f6539b-3868-4d02-844d-39f4e217420a · outbound
Degree functions of graded families of ideals Grothendieck, Éléments de géométrie algébrique II, Étude globale élémentaire de quelques classes de morphisms, Pub
Reference 25
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation bc5a31e8-bfe4-414f-92f6-6e40d4ce7d11 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 24e7bb6a-cdd3-4492-8aac-6f8c7f29545b · outbound
Degree functions of graded families of ideals Hartshorne, Algebraic Geometry, Springer, 1978
Reference 27
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 3f639e46-7799-4c4a-86be-3082b45521f6 · outbound
Degree functions of graded families of ideals Hironaka, On the equaivalence of singularities, I, Arithmetical Algebraic Geometry, Proceedings
Reference 28
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d0e1f1f6-a096-47ba-83ed-6dd07fc90627 · outbound
Reference 29
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 07cba6b9-c87c-4338-a856-6cfb1e0e7c9f · outbound
Degree functions of graded families of ideals Kleiman, Toward a numerical theory of ampleness, Ann
Reference 30
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 23dcb11f-6a29-4639-8533-3a9abb680b0e · outbound
Degree functions of graded families of ideals Kleiman and A
Reference 31
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation af3109e9-bb9d-439e-b835-6a941c5698f9 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 53d1e50a-4afa-4d3a-abc1-be0ce3ccf323 · outbound
Degree functions of graded families of ideals Lazarsfeld, Positivity in Algebraic Geometry I, Springer, 2000
Reference 33
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e2cb0d6e-ac05-4f62-b841-281d56e4a687 · outbound
Degree functions of graded families of ideals Lazarsfeld and M
Reference 34
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 6980a0ba-8ac8-4729-ac0e-43b2986f69b5 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d3d44f1c-5ad6-4384-9817-54cf73c59d2e · outbound
Degree functions of graded families of ideals Lipman, Rational singularities with applications to algebraic surfaces and unique factorization, Publ
Reference 36
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2014c4b1-1bbd-4e97-aba5-e7673c80e8e9 · outbound
Degree functions of graded families of ideals Lipman, Desingularization of 2-dimensional schemes, Annals of Math
Reference 37
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation bd4a16fa-cedd-4e53-9f0a-530a2149b0fd · outbound
Degree functions of graded families of ideals Matsumura, Commutative Ring Theory, Cambridge studies in advanced mathematics 8, Cambridge University Press, 1989
Reference 38
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation bd82d18c-b62a-409c-a61c-e9cec470281a · outbound
Degree functions of graded families of ideals Milne, Étale cohomology, Princeton University Press, 1980
Reference 39
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e39067c5-d8a7-4e25-ace6-1a254e18b0bc · outbound
Degree functions of graded families of ideals Mumford, Lectures on curves on an algebraic surface, Annals of Math
Reference 40
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation edfa816f-59c9-4a3c-906a-455ff28ade06 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation dcd44eb2-b972-4243-a328-885fd5dfbe67 · outbound
Degree functions of graded families of ideals Ramanujam, A geometric interpretation of multiplicity, Inventiones Math
Reference 42
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 1a0abb18-d68f-4852-8a76-931c43cd4e62 · outbound
Degree functions of graded families of ideals Rees, Valuations associated with ideals (II), J
Reference 43
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ba3d7cef-95c5-473f-91f6-46c07e4fa86b · outbound
Degree functions of graded families of ideals Rees, A note on analytically unramified local rings, J
Reference 44
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5817e773-e2db-46af-adf0-f751b3d6e0f8 · outbound
Degree functions of graded families of ideals Rees, Degree functions in local rings, Proceedings of the Cambridge Phil
Reference 45
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 76995c9a-b948-4520-9834-91c5e3e80f2f · outbound
Reference 46
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 15dd47d3-af21-43db-b14b-be3ec5eb9935 · outbound
Degree functions of graded families of ideals Rees, Lectures on the asymptotic theory of ideals, London Math Soc
Reference 47
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 3dd0d198-5f24-4ab5-98a2-c0b5c8f4214d · outbound
Degree functions of graded families of ideals Samuel, Sur les variétés algébroides, Ann
Reference 48
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2894f9ac-41bb-4cf1-a3cc-c23f644f6c21 · outbound
Degree functions of graded families of ideals Snapper, Polynomials associated with divisors, J
Reference 49
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e53499a7-3c23-4598-b9c4-fed9cd845cf4 · outbound
Degree functions of graded families of ideals The stacks project
Reference 50
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 80a40305-8aa4-41d6-9a67-19f3505a4109 · outbound
Degree functions of graded families of ideals Swanson and C
Reference 51
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation d1ab4ec0-5310-4590-8988-341187187732 · outbound
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
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 157aa161-825e-483e-bd84-7b80a1a00cfc · outbound
Degree functions of graded families of ideals Zariski and P
Reference 53
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 9c7fb9e4-c8c7-4227-a2c7-e19ed3949e42 · outbound
Degree functions of graded families of ideals Unresolved cited work
Reference 336
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
No inbound Pith citation observations are available.