Paper Citation Record · LEDGER

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties

As of 23 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 0 inbound Pith citation observations for arXiv:2507.15406.

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

pith.paper-citation-record.v1
2507.15406 v2

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T15:48:25.244494Z

measured 28 of 28 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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

28 of 28 outbound references displayed

verified exact0
verified fuzzy23
unresolved4
parse uncertain0
malformed identifier1
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation cbc912bc-2a56-4a77-8b7b-fb68c9df41fc · outbound

This paper cites A proof of the lower bound conjecture for convex polytopes.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties A proof of the lower bound conjecture for convex polytopes

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:32.066407Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7dce1049-eac1-46af-8655-ea0fe4d98e0e · outbound

This paper cites an unresolved cited work.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:48:31.740379Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 1510711f-71b0-4695-b286-b6c90a73bb86 · outbound

This paper cites an unresolved cited work.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:48:31.492917Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 42909748-b0d9-4bd9-9f44-6fbcc2f5e81a · outbound

This paper cites Sur une conjecture de M ukai.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Sur une conjecture de M ukai

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:31.213722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 53aef192-c1f4-4a95-82d1-72e97f84078a · outbound

This paper cites Polyhedra: convex polyhedra.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Polyhedra: convex polyhedra

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:30.974924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 68737167-d25a-48d1-b898-e616cfc41702 · outbound

This paper cites Polyhedra: a package for computations with convex polyhedral objects.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Polyhedra: a package for computations with convex polyhedral objects

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:30.734822Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation e65b856a-0776-4382-9712-296b00f2398d · outbound

This paper cites Convex Polytopes.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Convex Polytopes

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:30.435924Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f087233a-6641-49d1-b446-09a6c6457433 · outbound

This paper cites The number of vertices of a F ano polytope.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties The number of vertices of a F ano polytope

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:30.161468Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation c3bd0b0e-7bed-46cc-aa87-04a284ef27af · outbound

This paper cites Cox, John B.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Cox, John B

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:29.898237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 633e89d4-b962-43ed-be1a-5caae91013b1 · outbound

This paper cites Toric F ano varieties , pages 93--132.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Toric F ano varieties , pages 93--132

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:29.625277Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6358dd70-6f4c-43f8-bcdd-5ae4b7566db6 · outbound

This paper cites The P icard group of a compact toric variety.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties The P icard group of a compact toric variety

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:29.359222Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation f96ee6a6-ae3f-4def-8e36-a68b79c394f9 · outbound

This paper cites P icard groups of compact toric varieties and combinatorial classes of fans.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties P icard groups of compact toric varieties and combinatorial classes of fans

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:29.083492Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 5206142e-4c66-4737-8f53-d7e5475c713a · outbound

This paper cites Combinatorial Convexity and Algebraic Geometry.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Combinatorial Convexity and Algebraic Geometry

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:28.797412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 9edbaa71-4798-4bc5-8184-bf54ad4c66da · outbound

This paper cites The generalized M ukai conjecture for toric log F ano pairs.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties The generalized M ukai conjecture for toric log F ano pairs

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:28.529271Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b130efcf-e223-4574-90db-da86c57e6508 · outbound

This paper cites Grayson and Michael E.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Grayson and Michael E

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-06T15:48:23.413825Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 78f8e82c-2ea9-4e6f-8d2a-e1724b0f4777 · outbound

This paper cites Graded ring database.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Graded ring database

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:28.264753Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 1a6a6168-d162-45cc-bb1a-4252e09fb93c · outbound

This paper cites Canonical toric F ano threefolds.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Canonical toric F ano threefolds

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:28.024606Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 714ecf4c-2f5a-43f2-be22-e83fa6a1b11c · outbound

This paper cites On the classification of reflexive polyhedra.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties On the classification of reflexive polyhedra

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:27.725349Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 80ac9622-743a-413a-a85d-7774d21d073a · outbound

This paper cites Classification of reflexive polyhedra in three-dimensions.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Classification of reflexive polyhedra in three-dimensions

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:27.453098Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 40925a36-74ac-4442-b8af-2db54728afa5 · outbound

This paper cites Complete classification of reflexive polyhedra in four dimensions.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Complete classification of reflexive polyhedra in four dimensions

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:27.187205Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4997fd45-7b27-4a6e-9241-42832aa66bb4 · outbound

This paper cites Reflexive polyhedra, weights and toric C alabi-yau fibrations.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Reflexive polyhedra, weights and toric C alabi-yau fibrations

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:26.965596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 2c3ac520-1b73-46e6-b87a-efdf17ddcb88 · outbound

This paper cites PALP : A package for analysing lattice polytopes with applications to toric geometry.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties PALP : A package for analysing lattice polytopes with applications to toric geometry

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:26.696692Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 46e11060-f3d2-42a5-85bd-11ce20b5575a · outbound

This paper cites Gorenstein toric F ano varieties.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Gorenstein toric F ano varieties

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:26.460148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 4624184a-35f6-46c2-b334-963b47da9bc0 · outbound

This paper cites Gorenstein toric F ano varieties.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Gorenstein toric F ano varieties

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:26.217152Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation b07585af-4200-40ff-9cde-c771bab79223 · outbound

This paper cites Toward the classification of higher-dimensional toric F ano varieties.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Toward the classification of higher-dimensional toric F ano varieties

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:25.979450Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 0139b683-3412-4f9d-a7e4-9f358b62d706 · outbound

This paper cites an unresolved cited work.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-06T15:48:25.725505Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 6aba2299-df11-49db-b975-3f347f41ae9d · outbound

This paper cites S ageMath, the S age M athematics S oftware S ystem ( V ersion 10.6) , 2025.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties S ageMath, the S age M athematics S oftware S ystem ( V ersion 10.6) , 2025

Reference 27

Resolution: malformed identifier; no resolver link, observed 2026-08-06T15:48:25.094548Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7dffc824-5a37-4e5d-bc90-ebb6d035393d · outbound

This paper cites Voskresenskiĭ and Alexander A.

Reflexive polytopes and the Picard ranks of Gorenstein toric Fano varieties Voskresenskiĭ and Alexander A

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T15:48:25.455668Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Pith citing papers

No inbound Pith citation observations are available.