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Paper Citation Record · LEDGER

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two

As of 15 August 2026, this Paper Citation Record lists 32 of 32 outbound references and 0 inbound Pith citation observations for arXiv:2501.12555.

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

pith.paper-citation-record.v1
2501.12555 v1

Coverage vector

measured 32 of 32 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T17:19:10.216340Z

measured 32 of 32 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-14T06:32:32.682623+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

32 of 32 outbound references displayed

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  • unresolved8
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External citation measurements

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Outbound references

Observation f41d71aa-3ec8-4fd7-a408-d65869a2100d · outbound

This paper cites Singularities of linear systems and boundedness of Fano varieties.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Singularities of linear systems and boundedness of Fano varieties

Reference 1

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no resolver link, observed 2026-08-10T17:19:10.092493Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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Observation 82c6899b-dffb-41a6-a101-e6d31b5094c3 · outbound

This paper cites Anti-pluricanonical systems on Fano varieties.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Anti-pluricanonical systems on Fano varieties

Reference 2

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raw_fallback, observed 2026-08-10T17:19:10.625076Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation df3a7b87-9828-4790-8fd5-98c9abd13ebc · outbound

This paper cites Hacon, and James McKernan.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Hacon, and James McKernan

Reference 3

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raw_fallback, observed 2026-08-10T17:19:10.609517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation ea8fa6bb-fc71-4820-a089-599cc83bb9e2 · outbound

This paper cites Algebraic surfaces.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Algebraic surfaces

Reference 4

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.110346Z digest=sha256:70ee320135ad55a3a5b85a7d8b0676f1afb27e7b9f85f95eb883ec3c6e440966

Observation c53132e7-af1f-43a4-9674-5efafc1ebb05 · outbound

This paper cites Cone theorem via Deligne- Mumford stacks.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Cone theorem via Deligne- Mumford stacks

Reference 5

Resolution
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raw_fallback, observed 2026-08-10T17:19:10.575017Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 33364819-4f01-4733-bc3f-0b227bb9d537 · outbound

This paper cites Chen and Meng Chen.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Chen and Meng Chen

Reference 6

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.118476Z digest=sha256:87f4027129cf08e5bf0a305fb77123d32428cb0c299f50016fc2cebfc9fb25c2

Observation f4bbcab1-e428-4fb2-87ba-434e0d954507 · outbound

This paper cites On the anti-canonical geometry of Q-Fano threefolds.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two On the anti-canonical geometry of Q-Fano threefolds

Reference 7

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raw_fallback, observed 2026-08-10T17:19:10.553863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.123284Z digest=sha256:dacafecc78e06722122732f3a0f2ae3295423e9e4c46ba132745bc68b51958a9

Observation 91cccf51-97d1-46f9-b683-15348a1a2aa6 · outbound

This paper cites Hacon and James Mckernan.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Hacon and James Mckernan

Reference 8

Resolution
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raw_fallback, observed 2026-08-10T17:19:10.543127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.127771Z digest=sha256:a392a1219e9772d3251ec20394377eddb54d090047535839369e4f09e8c48129

Observation 481948f6-7b8a-402d-bcb6-70f6f632c223 · outbound

This paper cites Hacon and James McKernan.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Hacon and James McKernan

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:19:10.532698Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.131759Z digest=sha256:d8180748635ddcdb5d2c437ca1ac9b16f06028255912e2c545e043a479ca87f9

Observation b29d87de-06aa-4f59-97c4-1ba400a8b410 · outbound

This paper cites Algebraic geometry.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Algebraic geometry

Reference 10

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source=pdf_text observed=2026-08-10T17:19:10.135136Z digest=sha256:6a9f3b793f07ff6c3b0f47a1e59470d23d5f331078d8ec77c3dece09d84885e0

Observation b7ab5ffa-4a63-4290-b883-868250db8d14 · outbound

This paper cites Mori dream spaces and GIT.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Mori dream spaces and GIT

Reference 11

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation a1afcfed-c1ca-4b11-92e0-0b5f0806707d · outbound

This paper cites an unresolved cited work.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Unresolved cited work

Reference 12

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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.146398Z digest=sha256:aba25b0df99990b42515acf94cd5148a845fdbf47c207ccaeb984905a35d78f3

Observation 01a92746-f461-4fa0-bf87-14a804709019 · outbound

This paper cites an unresolved cited work.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Unresolved cited work

Reference 13

Resolution
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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.150174Z digest=sha256:90b1755afff7cbdc1a84730d05aa3d5d851deeadcf2e3da6e9aee5c5102657d4

Observation 3b41346f-d653-4e18-ac6b-12f4a2802eb0 · outbound

This paper cites The index of a threefold canonical singular ity.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two The index of a threefold canonical singular ity

Reference 14

Resolution
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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.153760Z digest=sha256:f48d355e64a16a75d42406f8274c435e4477300329052a0204a980db64a0f35c

Observation 87b5466e-5b0b-4e77-b2e0-412c22026300 · outbound

This paper cites Abundance theorem for minimal threefolds.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Abundance theorem for minimal threefolds

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:19:10.454688Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.157488Z digest=sha256:a117a15ab34c81bae142fd567d078e955000ee678844256da643f08d0312490f

Observation 69c13d8f-3d1a-449a-bf0d-44c4bb483edf · outbound

This paper cites Boundedness of Q-Fano threefolds.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Boundedness of Q-Fano threefolds

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:19:10.442771Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.161388Z digest=sha256:378f9a4a36e7953c302ee0d1856e8fa11a23c83a3cbe3e764012a54783086489

Observation afdab9d2-acac-48d0-907e-290f3bd32eec · outbound

This paper cites Cambridge University Press, Cambridge, 2013.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Cambridge University Press, Cambridge, 2013

Reference 17

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.165203Z digest=sha256:372d3edc567e7bff57dcd92f1fe0f0d5d306c5cea240a625241ee4c07cab4e25

Observation 78ca2dd6-6485-4df4-a048-e35ea94c22c3 · outbound

This paper cites Boundedness of canonical Q-Fano 3-folds.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Boundedness of canonical Q-Fano 3-folds

Reference 18

Resolution
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.168834Z digest=sha256:c2b15a6ccdc3fa6d3d17a65bdc7e984a60135c66820a5752ad652c54916e3195

Observation 41bd1494-4626-49b3-8c59-2703a6745eaf · outbound

This paper cites Birational geometry of algebraic varieties , volume 134 of Cambridge Tracts in Mathematics.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Birational geometry of algebraic varieties , volume 134 of Cambridge Tracts in Mathematics

Reference 19

Resolution
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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 3809ed51-565a-4c81-9276-fde8994a52c3 · outbound

This paper cites Abundance conjecture for 3-folds: case ν = 1.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Abundance conjecture for 3-folds: case ν = 1

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:19:10.375851Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation aef46272-8f5e-4314-b4a3-f8e0861367e6 · outbound

This paper cites On the Kodaira dimension of minimal threefolds.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two On the Kodaira dimension of minimal threefolds

Reference 21

Resolution
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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation ebc095fe-ca3e-41b0-955b-94f0c756c21a · outbound

This paper cites Classification of Fano 3-folds with B2 ≥ 2.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Classification of Fano 3-folds with B2 ≥ 2

Reference 22

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 374fef5a-bb3f-4877-beeb-9cbc8edfd04a · outbound

This paper cites On Q-conic bundles.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two On Q-conic bundles

Reference 23

Resolution
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raw_fallback, observed 2026-08-10T17:19:10.328521Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation a2075051-426a-4d2c-b053-5d7fcf5e9c22 · outbound

This paper cites Smoothing Fano 3-folds.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Smoothing Fano 3-folds

Reference 24

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation fcdcff2d-32ef-4b6a-9aa8-3f9c4d07cf5a · outbound

This paper cites an unresolved cited work.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Unresolved cited work

Reference 25

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.204385Z digest=sha256:6ef82dd59e4a5be7398a27f8eb2f49d34f682d9843df39df11cd06c98ae5a3ae

Observation 81b81a8b-c108-4393-8b6e-cd92c3da2f0b · outbound

This paper cites an unresolved cited work.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Unresolved cited work

Reference 26

Resolution
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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.208533Z digest=sha256:1b626cf87243756a40549d4bdb0c95f0597c8560265a2a6dbf2bf31c2298e182

Observation b9fd1fb2-2478-4b36-9856-22c4a2c103b0 · outbound

This paper cites On Fano indices of Q-Fano 3-folds.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two On Fano indices of Q-Fano 3-folds

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T17:19:10.276175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 56882ea1-21c5-485e-9265-d1b49133b18c · outbound

This paper cites Rational connectedness of log Q-Fano varieties.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Rational connectedness of log Q-Fano varieties

Reference 28

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raw_fallback, observed 2026-08-10T17:19:10.262497Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Observation 6853ee4d-2772-45e5-9e3f-53074e21285d · outbound

This paper cites an unresolved cited work.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Unresolved cited work

Reference 1986

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.191448Z digest=sha256:aff89329ca61e0c752cf2acb313f8b12e39c784a67863601f5ef086a69554024

Observation e5d162fe-b442-48fd-9efb-a4f6fbaeec68 · outbound

This paper cites an unresolved cited work.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Unresolved cited work

Reference 1998

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.176361Z digest=sha256:9297228f801054a92c1158c001d0c6fb294132b180eba7e7df8f2e4cd8b7b899

Observation 8467c176-4d6b-4ca6-93d5-f0bdbfa307cc · outbound

This paper cites (Cited on page 9.).

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two (Cited on page 9.)

Reference 2000

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raw_fallback, observed 2026-08-10T17:19:10.499606Z

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

source=pdf_text observed=2026-08-10T17:19:10.142835Z digest=sha256:6a6d63acfb508b75afaf5436e8afbbae7a8d032921e6344239b1b993ab4a140d

Observation a3a4f6b6-bc59-4216-8852-6ab4caaeed4c · outbound

This paper cites an unresolved cited work.

On anticanonical volumes of weak $\mathbb{Q}$-Fano terminal threefolds of Picard rank two Unresolved cited work

Reference 2010

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No event found in the named queried sources as of 2026-08-14T06:32:32.682623+00:00.

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Pith citing papers

No inbound Pith citation observations are available.