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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 2026-08-19T06:32:44.657259+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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.201351Z digest=sha256:480203b5c81cf8204460dcc529b6910497f1cac85c53cfdae1e79cc9128b4603

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.209289Z digest=sha256:6304f78bec1cf5f7a6b06a5d428690b43d8a610c3a51675e71a5247a34cc1488

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.217429Z digest=sha256:2de0833744747f54036499ec60d34bad973e2b934f93405466cc40b02162ac1d

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.227120Z digest=sha256:c308c264f92e1d8157e4d9551a05273d62e2da03714e59c75e0a685088a78667

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=sha256:323595d3defcd016e5ca8df6eb822b004fd63feea2744e48dd4f2a050181d95f

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.243530Z digest=sha256:1bcd0122be0b8abb0f4e9fb40dd3fa1b54db63ace96e0f911943680ce35e8a27

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.249881Z digest=sha256:4a6e7e3547fc4a3a7d29b458d401923e00005217b2e6be491b3268c0e0d50a43

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.256552Z digest=sha256:33ffabfadce3e01b2a3dec87c1cc2b793324322ace7585e78d9d2830f29f1712

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.263499Z digest=sha256:22980775d92854c8235bcff23fcc99f82599a75a55eb6886e97e719c7e9e7aa9

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.270297Z digest=sha256:3b35b633757bacda812d7d6a258fbc658b118cc2ede47d79a275da0b54e4e8c8

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.275839Z digest=sha256:93304844ea587f0333d829b0e687a8ad9b55ded46dd37d0e7fa661ca5b0bd909

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.281323Z digest=sha256:20ab7f3ba942e881847aa729fd56325b13cec86286f9ec6f0d6ee30576a3179c

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.287532Z digest=sha256:d4f0fdff3828b414721c8a7c32e6f22dc2db4ecd0b63ca3b466500218d89c71b

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.293436Z digest=sha256:8577af7ecec7769c4f61e1da2de5b93dccd26050827e8a2265bf4d576da01106

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.298823Z digest=sha256:2799774900f1b194eaf60c63650c700fdcbad46c799c89eebe20f263b2a1f995

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.304360Z digest=sha256:4354dcaf6f37b0580e17697fa83a96be7f285fa75056712c69235dd99193d470

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.310504Z digest=sha256:f87cf6c286fc251785b641dadca1593a5dee5e13336892ad7225c9cffa25a9f0

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.316396Z digest=sha256:c7c400185c6edb90720b0bb44931f2fb86d070b6f0ff03986694062ff707686d

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.322286Z digest=sha256:3d7ddcbca74c310c98cc5efc56bef8be4d3caa10ec7d5bb5baf23ab5dfc26833

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.327829Z digest=sha256:0801cbd1d7138a04da6c81e84382e1fdc9630b80a70226394d99cfbdabbee2b3

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.334486Z digest=sha256:02a34756d904f0ed8250b983c17c86e3490c20c1c7cb18b403f6792fae6ccb9f

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.339997Z digest=sha256:9a77e5344ebd931a66d147dba4aa4352dc9a91417e0a27e1e394430d72939bf4

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.346128Z digest=sha256:7c934c722e9a0bf5e78a291847bf1aad214c8c2f44f70137b854e71d8b600685

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.355273Z digest=sha256:5b30f9edd278a9f02546aa7fdc1ede6599027e42de355072c87678a0bd3fe86f

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.366084Z digest=sha256:cb19b0514ef3857b00a5006e311ea10538fda0efa1eeec22f591037affb88b05

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.377091Z digest=sha256:94d7c008aae1dd79db0440306e604ceeccdeaa2d2c25832fdc7d0d3daa4aeb2a

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.384961Z digest=sha256:8cb485fed9a2f398e34bbf8fe635e48b46654514b902ee8b1c420b099a2c72c3

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.391429Z digest=sha256:42b9fbf7969be73185970fbefcdfba613c2ad08c4966670c77d5682a17fb2900

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 2026-08-19T06:32:44.657259+00:00.

source=arxiv_source observed=2026-08-10T20:00:51.399985Z digest=sha256:e7df58d139ce027b2a4ce01ef23b858061aa8996ebe2112d551cf4e19b7a1734

Pith citing papers

No inbound Pith citation observations are available.