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Paper Citation Record · LEDGER

Quantum cohomology and birational geometry of Verra fourfolds

As of 22 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 2026-08-22T06:32:14.747728+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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:dc6572eb8c1b8736d6b8631071315712dd0c44e961e57be5bfedec7da97835d2

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:6f8f6ec7c45cf541567d2fc25f1aaeb03a95ce0fbd3764ce310bfc0a0ad03a42

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=sha256:85086bd2e552625fb68fdd8ac78dcfc00ce98df97811b0c577b6de13ad9a6c4d

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:31f726fb7abb90317558e4d37a26439989fc21c56655d04658ceca57e059f0e2

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:c105dad2e5209453e86706ea67a0c52de84a652d22bec6f104d377c4365236f0

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=sha256:21691105288a26e32ac46926347cddeb942c4b2103a5518cfb6265ef3a362740

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=sha256:6ad5515821caa46e202b91df834b03a03e58b0d52ad1d6ba1237a3f853f26cd3

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:99d67a5270e22410249244fce6f66eb725fd3579701c1e092bb9f1c4d5e66188

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:41ad3af8dbfbf3839f872f06c7f89984253e7058b79dfbb9de55e5cbd179fd93

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=sha256:4e1f189794d6ee3f3b4f5b6f81d6160bfdc13233dbb8fd6935134a165024a6d4

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=sha256:096f4d1d85c986d21817b827fca34e731f2e9ac84ffb418337fc78da04a8ec8d

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:cf6fc69fbe58a7538dbdeaf2d217952ca62874078ebb4d90325f5dab6d5a9414

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 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-06-29T00:17:17.542615Z digest=sha256:536e264fbdcf7506ccfe40ea29a8bd096f37c71c91c03eab5a5898dcbc25a87f

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=sha256:4a71a56d859768b56fafcd0d77be6657f5ddee1ae5b880a854cf68edc8aabec0

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=sha256:9f78813763aa62f289eb5d144e9e9c97426eb3f5615c6ec7bf5c15ac7429dfb0

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:dc2bcb07440d351342af1231df279fdcfa93f7f92523406e968a578275b5f66e

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:cc5f0ccdf0db70f9c46e77101a575d1cde5b3ddd0a22c6793de5c0dfd95fdb34

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=sha256:4e4d737db5fed0570accf840fb273359c47ab3c7c4ec49d8fd71f2ec495c5603

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=sha256:04f7637120a7fb3cd6b021e42233fbd3563cf370b7ce3f881b13b849aad0d564

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 2026-08-22T06:32:14.747728+00:00.

source=arxiv_source observed=2026-06-26T22:50:29.790480Z digest=sha256:658bb05d083b501f8e3bf094e635db3c0f7f94d70206e081403960eebaee1e77

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=sha256:0df609da2ff8d76a2054ce3ca056aa109b25bc453ef0d92e50df661db8de885d