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Paper Citation Record · LEDGER

The two extremal rays of some Hyper-K\"ahler fourfolds

As of 20 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2501.09578.

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

pith.paper-citation-record.v1
2501.09578 v2

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T20:00:51.399985Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-20T06:33:59.587034+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

29 of 29 outbound references displayed

  • verified exact1
  • verified fuzzy5
  • unresolved23
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation db1e46f9-5f30-4fb4-8e62-395f2b130ba8 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:52.149501Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.201351Z digest=sha256:360160a8c47f0b791ca44e06b4d00a042b611a59a61fe0229156f850f90c2dba

Observation 19fb4809-6c2e-488a-9514-85145f2cc80a · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:52.132428Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.209289Z digest=sha256:63f530632f7024938fce65b29bf375455a94248a05c034478edea75ffe0582e0

Observation 6ecb2b00-ef7c-4236-9413-a25bb3116f86 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:52.115571Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.217429Z digest=sha256:c0bcc5c54976979f9244782c79d51b5680d1e6c1dceae1f9d638b79c92b5b73d

Observation f828a7aa-6ad4-496a-9f77-9e129127fee2 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:52.093927Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.227120Z digest=sha256:0e2ba426f0b0bcc5e3ea67689c15dc434713ffebd87db65dddf397246b132672

Observation d4376655-25c6-4c08-b1b2-e2d1ceaacb86 · outbound

This paper cites Mukai models of Fano varieties.

The two extremal rays of some Hyper-K\"ahler fourfolds Mukai models of Fano varieties

Reference 5

Resolution
unresolved
no resolver link, observed 2026-08-10T20:00:51.237245Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-10T20:00:51.237245Z digest=sha256:6bbaf109516f618745870541085608cc019211245f1aed67546a79917593fe99

Observation b8fdcd72-4fc1-4a63-8486-a8d80919af9e · outbound

This paper cites MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations , Invent.\ Math.\ 198 (2014) 505--590.

The two extremal rays of some Hyper-K\"ahler fourfolds MMP for moduli of sheaves on K3s via wall-crossing: nef and movable cones, Lagrangian fibrations , Invent.\ Math.\ 198 (2014) 505--590

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:00:52.074053Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.243530Z digest=sha256:a8dfb75ed8e67afde3f9da5d59fa81da790624000453924bf2e386fe8a53be36

Observation 8c4fbc70-5df1-48e8-9d7c-d94a4018f5be · outbound

This paper cites I Math.\ 301 (1985), no.

The two extremal rays of some Hyper-K\"ahler fourfolds I Math.\ 301 (1985), no

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:00:52.050978Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.249881Z digest=sha256:4d0efcc79d0f310da9471ad5f93597ff48a6b32eabc51d6085ee4993e6f3d9fa

Observation 573f7afd-d922-4652-b22f-af7837ce03a3 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:52.031252Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.256552Z digest=sha256:16c6d87ceed18c881415c8e157dfb6ac1f9da6155db64a10fd97607f44ea7fe8

Observation b4a63bff-9049-475e-98e2-12c09a38b7f7 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:52.012095Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.263499Z digest=sha256:97b01344f0252d02991d5933f61cc57ca46cebb750c5c119498e960a84817033

Observation c898a748-e5d7-46b5-a485-b735058b95a6 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.989380Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.270297Z digest=sha256:28cb2d1f12199ac1d041863ca97cf54cafe65b014460662b63590c564781c5a6

Observation c64aefe0-1143-4b87-99ac-01ffcb2e3341 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.970931Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.275839Z digest=sha256:f2d5beea2304a49c2d84f5b4ad724f762717f7d0edd391301e9ab675876e22a9

Observation 35726528-f9b8-40b5-b890-f2d2e84fdb0d · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.952722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.281323Z digest=sha256:07cd41c4f89eedc8ba1151bae0b6e73f4f3169ef3fdaec4cb32a08acaa2267f9

Observation 0c2d7474-6555-45de-82a3-c0542ed8163b · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.933104Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.287532Z digest=sha256:c21ad98206a2f7e1cfe681fe97e811f62242a93e141b01c4b56c9cb6b0521bfd

Observation 8f753d75-9106-44b9-858b-7069512cfa26 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.911077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.293436Z digest=sha256:7120cea2b4310ae35c0bc8eda1aefe6017c39bcf83b64e07f2a04e553caa56df

Observation 25917679-ef86-4793-952d-75c5612b1b93 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.884883Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.298823Z digest=sha256:30fa5734e69ee3ace65c167555b1253c3af29f456e5a144bcef2eb588247398b

Observation 90134272-8f89-4cfb-af45-2770c0b1d809 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.862528Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.304360Z digest=sha256:4fa9cce78faf29998a8cdcee3affc0ac0a86482c289234a9b7034cd46966bfd8

Observation 1da2e080-9204-4932-a80a-e132b9e6868d · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 17

Resolution
verified exact
raw_fallback, observed 2026-08-10T20:00:51.549334Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.310504Z digest=sha256:a921e68ba6a899e653bd5224d8741c1f7c62980651d392f85da7cc66a06b9779

Observation 7563dae6-8ee0-4a6f-ad6d-47117ef886b8 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.840761Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.316396Z digest=sha256:160044256362fbf64aa50b30ee267dad3eed1a503b6ae380b98124d8c718f83d

Observation f3f61885-7d66-435a-9cbe-bfd9a5187387 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.818972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.322286Z digest=sha256:61aa740023b22d3243556b85ca59b1fa92122c48af75b8d53b654c9ce0edf6d5

Observation 8d2fe4da-c714-4d83-9c61-df7a12f7495f · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.798369Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.327829Z digest=sha256:931b3445b2d3eb70f959ebf0dfa4b2b429b2d6497d13bf2748ad7576e0d30167

Observation fc3c4804-cbe5-4bbe-b658-df319b996034 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.773986Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.334486Z digest=sha256:ce99c1dc4aa885add3b0ef166fa56d88795ed5adb3695824162f38e91e1c4084

Observation b6658572-545e-478e-8093-f265cda728b8 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.751824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.339997Z digest=sha256:ef19a94c53810e8c81e37c353eb0236892527eb58d20ef3494f8388f816fb9ca

Observation 4a431a06-e578-4b27-b2f1-8d84bdca33be · outbound

This paper cites In: Complex and differential geometry, Springer Proc.\ Math.\ 8, 257–-322, 2011.

The two extremal rays of some Hyper-K\"ahler fourfolds In: Complex and differential geometry, Springer Proc.\ Math.\ 8, 257–-322, 2011

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:00:51.733462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.346128Z digest=sha256:01a0add25b4fdba453f7895ff6c4209862eab2ba9f571e9391c4278ef9261b42

Observation 7a3b76f7-bf7e-4945-9e21-9b195202d620 · outbound

This paper cites Springer, Cham, 2014.

The two extremal rays of some Hyper-K\"ahler fourfolds Springer, Cham, 2014

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:00:51.713791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.355273Z digest=sha256:3c1f86714eee0df2aa451dd07c989e9c60f2711585a2ca27e1f26f77bcc32841

Observation d0e8f22e-834a-4a90-b23e-bc0c8047f550 · outbound

This paper cites I, Kinokuniya Company Ltd., Tokyo, 1988, 357–377.

The two extremal rays of some Hyper-K\"ahler fourfolds I, Kinokuniya Company Ltd., Tokyo, 1988, 357–377

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T20:00:51.690397Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.366084Z digest=sha256:ed8b6de3ad413d8882bac84475e96c8929f43f8a28057d20c5bdb9ca42f44703

Observation 2113e541-119b-49a6-ac9b-3411d4d1b972 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.670440Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.377091Z digest=sha256:9840f1cb908ce72950ff17e6bfc3ffbb9125fcabce0cf3b83634654684d9836c

Observation 561cca5f-80d5-4c02-8cbb-aa424a450fbc · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.649276Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.384961Z digest=sha256:baace42d5e95d571dfb8714c1d10282e3f0d15d522af9f5e0412d9457c20f0d7

Observation de1f124a-1f87-4923-8fcf-2b30e34485ee · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.630119Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.391429Z digest=sha256:10279360810dc55ede92472c91200b78a1dbb5cf14c44c42e9e4cd2ee0ba6499

Observation 858ca5af-92de-4039-b8ce-1f98a64520f3 · outbound

This paper cites an unresolved cited work.

The two extremal rays of some Hyper-K\"ahler fourfolds Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-10T20:00:51.609703Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-20T06:33:59.587034+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.399985Z digest=sha256:2775370f4335609e611fd80a4b7a43f6389b27af44ab3c33449dd4e50e0b6ad8

Pith citing papers

No inbound Pith citation observations are available.