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Paper Citation Record · LEDGER

Quantum cohomology and birational geometry of Verra fourfolds

As of 10 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 2 inbound Pith citation observations for arXiv:2605.30450.

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

pith.paper-citation-record.v1
2605.30450 v1

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-29T00:17:17.542615Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-10T06:31:04.303077+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-07-30T23:05:18.395069Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-03T23:09:01.502009Z

Reference resolution

19 of 19 outbound references displayed

  • verified exact6
  • verified fuzzy0
  • unresolved13
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 9e2a3772-fa7e-4fb5-b9cc-683b6087918a · outbound

This paper cites Quantum cohomology and irrationality of Gushel-Mukai fourfolds.

Quantum cohomology and birational geometry of Verra fourfolds Quantum cohomology and irrationality of Gushel-Mukai fourfolds

Reference 1

Resolution
verified exact
local_arxiv, observed 2026-06-29T00:22:51.548395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:072233585720956473fe2cdc85f9a1c4b601d60a5cd5640dd0669b3c8a1aaa8b

Observation cfd353cb-bb43-4c3c-b0b8-b80ef5faa5b3 · outbound

This paper cites Fano fourfolds of K3 type.

Quantum cohomology and birational geometry of Verra fourfolds Fano fourfolds of K3 type

Reference 2

Resolution
verified exact
arxiv_id, observed 2026-06-29T00:22:51.551264Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:da4ee4153b721815bb34ccfb412b6b7cb3afe486beb69658766f5510375b09ab

Observation 813c9684-d6ed-4a47-b33b-38c4f1550a9c · outbound

This paper cites an unresolved cited work.

Quantum cohomology and birational geometry of Verra fourfolds Unresolved cited work

Reference 3

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:59eeda2d79d394a5f2870aeb34527b332075a89d1773acf89dac07c20ad35a30

Observation d5d03536-d708-4119-9ad4-0e14b0e10471 · outbound

This paper cites an unresolved cited work.

Quantum cohomology and birational geometry of Verra fourfolds Unresolved cited work

Reference 4

Resolution
verified exact
arxiv_id, observed 2026-06-29T00:22:51.545934Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:33574e8f49038316f508578b4fa332e5d0765ffb67f9595f2db57d17c488d117

Observation 1af4e332-e936-44b6-ae98-a6411f3ec8a0 · outbound

This paper cites an unresolved cited work.

Quantum cohomology and birational geometry of Verra fourfolds Unresolved cited work

Reference 5

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:02a2e07746da87437330d201a293548b900073c5819168a344e152dc59607014

Observation 33fc5947-267d-412b-8e6e-327b12a5facb · outbound

This paper cites China Math.

Quantum cohomology and birational geometry of Verra fourfolds China Math

Reference 6

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:f365c97ab006efc2ad94f305605b4ddf4a47c50da141a9fd1b7e66d0c79dd2da

Observation 4027abc7-ef09-47b0-b038-730e2ca2d7b9 · outbound

This paper cites an unresolved cited work.

Quantum cohomology and birational geometry of Verra fourfolds Unresolved cited work

Reference 7

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:bf67582c1464a8c95f68674d3d6b8631628339a23e91187fd2fa8259a919d6cd

Observation e64c23c6-d467-4e9b-bce7-504b32b842fc · outbound

This paper cites an unresolved cited work.

Quantum cohomology and birational geometry of Verra fourfolds Unresolved cited work

Reference 8

Resolution
verified exact
arxiv_id, observed 2026-06-29T00:22:51.543045Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:f134fe1b9b3d1102b7327e014acb52e2b55004402d7f1e4d5a17fd7704b2a95f

Observation a294a787-8357-462e-8717-eab2c204b0cb · outbound

This paper cites [BMP26] Vladimiro Benedetti, Laurent Manivel, and Nicolas Perrin.

Quantum cohomology and birational geometry of Verra fourfolds [BMP26] Vladimiro Benedetti, Laurent Manivel, and Nicolas Perrin

Reference 9

Resolution
verified exact
arxiv_id, observed 2026-06-29T00:22:51.540237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:2d75e8e0b234b4c6f9602ab6b2557c5a7a49c7405c6b416bf3ca6227901a0218

Observation 7f3bafc0-8958-41be-9220-779fa45508fa · outbound

This paper cites Algebraic Geom.,8(1):103–114, 1999.

Quantum cohomology and birational geometry of Verra fourfolds Algebraic Geom.,8(1):103–114, 1999

Reference 10

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:8ff8f03249554d3f4aa4803d520b515f8a3d902260670a321f6f3bc3c3544f97

Observation bcf22a3e-9911-414b-87e7-1cd1f63c43c5 · outbound

This paper cites an unresolved cited work.

Quantum cohomology and birational geometry of Verra fourfolds Unresolved cited work

Reference 11

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:0c4346456809a627be46965c2bcdd55911c03bcab6b2113be169a8bfc9e33d80

Observation 392bac18-4357-490e-9be3-f5bdc060f579 · outbound

This paper cites an unresolved cited work.

Quantum cohomology and birational geometry of Verra fourfolds Unresolved cited work

Reference 12

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:bde20db3c56f9ea3d9118258ca097b4235fcb00c856fa1f623a6b626f48190ad

Observation 5ceab8da-0e15-4765-b1f0-2f40021e9801 · outbound

This paper cites Birational Invariants from Hodge Structures and Quantum Multiplication.

Quantum cohomology and birational geometry of Verra fourfolds Birational Invariants from Hodge Structures and Quantum Multiplication

Reference 13

Resolution
verified exact
arxiv_id, observed 2026-06-29T00:22:51.537656Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:f585aa5246c17b17d78e2e0296a69442c26d7d8814105e9b1928a8ecb17a9ca1

Observation c8bf8517-d9bd-4d07-af64-f7ca4123c0ef · outbound

This paper cites Math.60(2020), no.

Quantum cohomology and birational geometry of Verra fourfolds Math.60(2020), no

Reference 14

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:a85cde50cbd573a1fc6a9a31a121b41094755aef4f71834eb0af032357d44e2d

Observation 58ee54a6-fb1a-4120-a361-50a92fcaa13e · outbound

This paper cites Math.98(1989), no.

Quantum cohomology and birational geometry of Verra fourfolds Math.98(1989), no

Reference 15

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:5f6592a5104a218a52156d0ea2f6fce157bdcd359ce12078837542e0c61c2d2c

Observation 3343de44-3657-4e96-8353-cc507ca8baa3 · outbound

This paper cites an unresolved cited work.

Quantum cohomology and birational geometry of Verra fourfolds Unresolved cited work

Reference 16

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:4f6c1c19cf5696ab8cbd0865b2e11683e3c950a04dff5d771f06d4748eef061c

Observation 525079b0-e6e8-416e-afa4-e7785e8f25e3 · outbound

This paper cites an unresolved cited work.

Quantum cohomology and birational geometry of Verra fourfolds Unresolved cited work

Reference 17

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:79366e071e09973575fd7db8c18210f604f2be1b1329ba849267b5afb2b477f7

Observation f43ff743-6e32-4c2e-9176-0a60887c49e5 · outbound

This paper cites 2, 479–490.

Quantum cohomology and birational geometry of Verra fourfolds 2, 479–490

Reference 18

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:6ca684fd1e23ec4fd5481dbfea508ad8324d86b934adc0a689ee92b141ecfb7f

Observation c7cbcaa3-2e72-4941-947f-ef5c98546a6c · outbound

This paper cites Torino, Turin, 735–759, 2004.

Quantum cohomology and birational geometry of Verra fourfolds Torino, Turin, 735–759, 2004

Reference 19

Resolution
unresolved
no resolver link, observed 2026-06-29T00:17:17.542615Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:e339f15ad412a138abeaae2cdd992add09e79db133cf4ca9f5882896bd9058c1

Pith citing papers

Observation 2040de10-41d7-4e15-84ad-fb0837457b72 · inbound

Naive atoms of blowups: examples cites this paper.

Naive atoms of blowups: examples Quantum cohomology and birational geometry of Verra fourfolds

Reference 4

Resolution
verified exact
local_arxiv, observed 2026-07-03T23:09:01.503654Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-10T06:31:04.303077+00:00.

source=arxiv_source observed=2026-06-26T22:50:29.790480Z digest=sha256:e3fb0c899600dc038cd5a53cbc577dd251deba6ab99b80539fbbfe91ebdcdadd

Observation 24df78fd-6f56-4510-8ada-9713dac9d56f · inbound

An atomic criterion for irrationality without quantum computations cites this paper.

An atomic criterion for irrationality without quantum computations Quantum cohomology and birational geometry of Verra fourfolds

Reference 2

Resolution
unresolved
no resolver link, observed 2026-07-30T23:05:18.395069Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-07-30T23:05:18.395069Z digest=sha256:8e38fb22609cb3ba1db59bd35abbfb60cc16594281b0c360a52a4ff5a33492b1