Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-04T23:40:01.268243Z
Paper Citation Record · LEDGER
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences
As of 13 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 4 inbound Pith citation observations for arXiv:2509.06527.
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 2026-08-13T06:32:02.005865+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links, observed 2026-07-01T08:05:31.431306Z
A source-named dated measurement, never combined with another source.
Source: pith, observed 2026-07-01T08:15:32.483894Z
Reference resolution
38 of 38 outbound references displayed
- verified exact3
- verified fuzzy30
- unresolved5
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 73cbc026-1ae8-4cf1-b515-f90f7a4b7d53 · outbound
This paper cites André,Le lemme d’Abhyankar perfectoide, Publ.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences André,Le lemme d’Abhyankar perfectoide, Publ
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.828376Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 53e44470-a2f2-4802-93af-20a4e386e6eb · outbound
This paper cites André,La conjecture du facteur direct, Publ.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences André,La conjecture du facteur direct, Publ
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.818648Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation df4ccc0c-e9ee-4f4b-86c8-f82e57311008 · outbound
This paper cites Bhatt, M.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Bhatt, M
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.808565Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ea4514a8-032f-448f-9d93-a16e6ee3dc45 · outbound
This paper cites Bhatt, M.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Bhatt, M
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.798976Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 18ee4f1d-5922-4946-8eeb-380d37d6c661 · outbound
This paper cites Bhatt and P.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Bhatt and P
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.788862Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 87e9769d-2c79-4c80-b8e2-482798d22c89 · outbound
This paper cites Bhatt, L.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Bhatt, L
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.779714Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 843e5c77-f5c8-41d2-bcd7-1731a7ef428c · outbound
This paper cites Perfectoid pure singularities.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Perfectoid pure singularities
Reference 7
- Resolution
- unresolved
- no resolver link, observed 2026-08-04T23:40:00.014203Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 60a42c62-2110-48bf-9589-4ced39e0d4dc · outbound
This paper cites Bruns and A.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Bruns and A
Reference 8
- Resolution
- verified exact
- doi, observed 2026-08-04T23:40:01.297634Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation cc306bbd-e798-424e-aaeb-394f371c6c5d · outbound
This paper cites Bruns and J.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Bruns and J
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.770863Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation e4251b29-e15c-46e2-87a0-ac9a7cb1ddf4 · outbound
This paper cites Conca and J.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Conca and J
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.761830Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c457a85c-ab8c-49bb-ae6c-18c34e057ba4 · outbound
This paper cites Chiriacescu,On the theory of Japanese rings, Rev.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Chiriacescu,On the theory of Japanese rings, Rev
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.752707Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 241091f3-9e87-4062-83cf-dec52541c807 · outbound
This paper cites Dietz,Big Cohen-Macaulay algebras and seeds, Trans.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Dietz,Big Cohen-Macaulay algebras and seeds, Trans
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.743300Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ac3d0080-ccd0-4e55-8f9b-a7825975cd79 · outbound
This paper cites Gabber and L.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Gabber and L
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.733633Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d2839a9e-a48f-43bb-afee-5442b86cebd0 · outbound
This paper cites Gabber and L.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Gabber and L
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.724235Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation d962e0f9-3b94-4b83-b076-d12ab80e80d2 · outbound
This paper cites Grothendieck,Élements de Géométrie Algébrique III, Publications Math.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Grothendieck,Élements de Géométrie Algébrique III, Publications Math
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.713630Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 3682ce24-1244-4358-a461-ffc1662a292a · outbound
This paper cites an unresolved cited work.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Unresolved cited work
Reference 16
- Resolution
- unresolved
- raw_fallback, observed 2026-08-04T23:40:01.702037Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 6b43f575-6c1d-48f2-8581-ddea8e79fcac · outbound
This paper cites Illusie,Grothendieck’s existence theorem in formal geometry, Fundamental Algebraic Geometry, Mathematical Surveys and Monographs123AMS 2005.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Illusie,Grothendieck’s existence theorem in formal geometry, Fundamental Algebraic Geometry, Mathematical Surveys and Monographs123AMS 2005
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.692525Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 63ab7125-0bc1-4844-a62e-91069dd227ec · outbound
This paper cites Ishiro, K.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Ishiro, K
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.682605Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 62701050-e556-4d52-b1dd-3580d3f8b6e8 · outbound
This paper cites Ishizuka,Perfectoid towers generated from prisms,https://arxiv.org/abs/2409.15785v2.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Ishizuka,Perfectoid towers generated from prisms,https://arxiv.org/abs/2409.15785v2
Reference 19
- Resolution
- verified exact
- raw_fallback, observed 2026-08-04T23:40:01.478335Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 98d171dd-0ffd-4ffc-9ff3-78b59001ada2 · outbound
This paper cites Ishizuka and K.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Ishizuka and K
Reference 20
- Resolution
- unresolved
- no resolver link, observed 2026-08-04T23:40:00.538773Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation 5efd0165-6f55-4eee-bbeb-1fe1e5bc92e5 · outbound
This paper cites Ishizuka and K.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Ishizuka and K
Reference 21
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.672897Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 4cbf111f-bbea-45a0-8dbc-aa3ad7867bcd · outbound
This paper cites Kawakami and T.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Kawakami and T
Reference 22
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.662540Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 6121d7cc-2af0-4fd5-beb9-0c3fbd60032b · outbound
This paper cites Quasi-canonical lifting of projective varieties in positive characteristic.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Quasi-canonical lifting of projective varieties in positive characteristic
Reference 23
- Resolution
- verified exact
- local_arxiv, observed 2026-08-04T23:40:01.313315Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 5767a183-cbc0-47fc-8b38-4963ccec12ad · outbound
This paper cites Kollár,Singularities of the minimal model program, With a collaboration of Sándor Kovács, Cambridge Uni- versity Press, Cambridge (2013).
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Kollár,Singularities of the minimal model program, With a collaboration of Sándor Kovács, Cambridge Uni- versity Press, Cambridge (2013)
Reference 24
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.652667Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 82bc56aa-19ba-4384-9a2d-5fbbf7cb448a · outbound
This paper cites Kollár and S.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Kollár and S
Reference 25
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.641561Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 044987be-68a5-4ee8-9b41-e28667295a47 · outbound
This paper cites Ma,Lim Ulrich sequences and Lech’s conjecture, Invent.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Ma,Lim Ulrich sequences and Lech’s conjecture, Invent
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.631032Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c1ef97bf-bfd9-48a6-abaf-30a4866211f6 · outbound
This paper cites Matsumura,Commutative ring theory, Cambridge University Press.8(1986).
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Matsumura,Commutative ring theory, Cambridge University Press.8(1986)
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.621080Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation af52a104-0c11-47e2-a836-90b3eddc6f5b · outbound
This paper cites Mumford,Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics 5, Oxford University Press, London, 1970.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Mumford,Abelian varieties, Tata Institute of Fundamental Research Studies in Mathematics 5, Oxford University Press, London, 1970
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.610598Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation be4b0a44-aed5-41f5-aa75-a259ec573571 · outbound
This paper cites Murayama,A uniform treatment of Grothendieck’s localization problem, Compositio Math.158(2022), 57–88.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Murayama,A uniform treatment of Grothendieck’s localization problem, Compositio Math.158(2022), 57–88
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.599886Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 984721cf-65ec-4f07-882c-4b7ff6093b9c · outbound
This paper cites Narasimhan,The irreducibility of ladder determinantal varieties, Journal of Algebra102(1986), 162–185.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Narasimhan,The irreducibility of ladder determinantal varieties, Journal of Algebra102(1986), 162–185
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.589235Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation c80565e6-fd92-4cd6-9423-2a5d2d35bbe9 · outbound
This paper cites Rezk,Étale extensions ofλ-rings,https://rezk.web.illinois.edu/etale-lambda.pdf.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Rezk,Étale extensions ofλ-rings,https://rezk.web.illinois.edu/etale-lambda.pdf
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.577476Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b66c601f-39f4-461a-9e4b-793f4ccc5742 · outbound
This paper cites Shimomoto,On the Witt vectors of perfect rings in positive characteristic, Communications in Algebra43 (2015), 5328–5342.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Shimomoto,On the Witt vectors of perfect rings in positive characteristic, Communications in Algebra43 (2015), 5328–5342
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.566360Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 79c04bf3-57f6-4de6-a649-8c622847dcfe · outbound
This paper cites Shimomoto,On the semicontinuity problem of fibers and globalF-regularity, Communications in Algebra45 (2017), 1057–1075.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Shimomoto,On the semicontinuity problem of fibers and globalF-regularity, Communications in Algebra45 (2017), 1057–1075
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.555895Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 13be9d16-c1a8-4eb8-a5b7-05a824288154 · outbound
This paper cites Shimomoto and E.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Shimomoto and E
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.544264Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation ecbc3b85-068f-4d4f-b192-52563cc7ff76 · outbound
This paper cites an unresolved cited work.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-08-04T23:40:01.533996Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation b55d3df8-9f85-48e7-a915-e92fa444db06 · outbound
This paper cites an unresolved cited work.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Unresolved cited work
Reference 36
- Resolution
- unresolved
- raw_fallback, observed 2026-08-04T23:40:01.523783Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0d3b4bbf-def1-48b8-95c6-04bdbf26d8e0 · outbound
This paper cites Strahan,Content and Q-sequences in mixed characteristic local rings, Journal of Algebra666(2025), 633–656.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Strahan,Content and Q-sequences in mixed characteristic local rings, Journal of Algebra666(2025), 633–656
Reference 37
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.512952Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation f4d187a2-ff58-4c9f-9e6d-a9418b96302c · outbound
This paper cites Zdanowicz,Liftability of singularities and their Frobenius morphism modulop2, International Mathematics Research Notices2018(2017), 4513–4577.
{\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences Zdanowicz,Liftability of singularities and their Frobenius morphism modulop2, International Mathematics Research Notices2018(2017), 4513–4577
Reference 38
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-04T23:40:01.501350Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Pith citing papers
Observation 983d5ff8-129e-4cbe-b602-095c33a38b2d · inbound
A characterization of perfectoid towers in terms of conormal cones cites this paper.
A characterization of perfectoid towers in terms of conormal cones {\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences
Reference 10
- Resolution
- verified exact
- local_arxiv, observed 2026-06-29T14:33:30.833051Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 18b2d8e7-a02c-4d82-8d0e-66000e1e243c · inbound
Structural properties and tilting correspondences of perfectoid towers cites this paper.
Structural properties and tilting correspondences of perfectoid towers {\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences
Reference 19
- Resolution
- verified exact
- local_arxiv, observed 2026-06-29T14:23:30.578698Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 0ecd3a35-5aff-4a9a-90d3-4e3155469267 · inbound
Structural properties and tilting correspondences of perfectoid towers cites this paper.
Structural properties and tilting correspondences of perfectoid towers {\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences
Reference 19
- Resolution
- verified exact
- local_arxiv, observed 2026-07-01T08:15:32.486014Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.
Observation 6190bb3e-dca3-4b54-84db-24fdc826e2b1 · inbound
Regular rings and perfectoid towers cites this paper.
Regular rings and perfectoid towers {\delta}-rings, perfectoid towers, and lim Cohen-Macaulay sequences
Reference 16
- Resolution
- verified exact
- local_arxiv, observed 2026-06-29T14:23:30.726585Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-13T06:32:02.005865+00:00.