Paper Citation Record · LEDGER

A Hilbert Series for Generalized Toric Polygons

As of 15 August 2026, this Paper Citation Record lists 20 of 20 outbound references and 3 inbound Pith citation observations for arXiv:2509.08876.

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

pith.paper-citation-record.v1
2509.08876 v1

Coverage vector

measured 20 of 20 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:09:54.137295Z

measured 23 of 23 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+00:00

measured 3 of 3 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-03T06:54:26.546344Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-07-11T05:27:49.648405Z

Reference resolution

20 of 20 outbound references displayed

verified exact2
verified fuzzy3
unresolved15
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d72322c9-b726-488b-8827-db0e43844c8a · outbound

This paper cites Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces.

A Hilbert Series for Generalized Toric Polygons Five-Dimensional Supersymmetric Gauge Theories and Degenerations of Calabi-Yau Spaces

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.036659Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dd5f0fb2-234b-4976-a1f6-40f04106e4bd · outbound

This paper cites Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams.

A Hilbert Series for Generalized Toric Polygons Webs of (p,q) 5-branes, Five Dimensional Field Theories and Grid Diagrams

Reference 2

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.043490Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f0799f78-5369-4af3-a3f8-59d0323324ea · outbound

This paper cites Branes and Toric Geometry.

A Hilbert Series for Generalized Toric Polygons Branes and Toric Geometry

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.050316Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 67823ab5-8324-47ba-b452-4d6671e19864 · outbound

This paper cites Webs of five-branes and N=2 superconformal field theories.

A Hilbert Series for Generalized Toric Polygons Webs of five-branes and N=2 superconformal field theories

Reference 4

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.056779Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2b804096-2d48-4515-933b-9795f4fccfaa · outbound

This paper cites Generalized Toric Polygons, T-branes, and 5d SCFTs.

A Hilbert Series for Generalized Toric Polygons Generalized Toric Polygons, T-branes, and 5d SCFTs

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.063558Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec903787-3663-40ce-ab2f-dac87db475a3 · outbound

This paper cites The Geometry of GTPs and 5d SCFTs.

A Hilbert Series for Generalized Toric Polygons The Geometry of GTPs and 5d SCFTs

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.068628Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ace2f60e-3a68-40d9-831f-dc8a2f07fbb4 · outbound

This paper cites The 5d Tangram: Brane Webs, 7-Branes and Primitive T-cones.

A Hilbert Series for Generalized Toric Polygons The 5d Tangram: Brane Webs, 7-Branes and Primitive T-cones

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.074670Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 425424a7-085b-46c3-a61d-4893dc33d828 · outbound

This paper cites Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics.

A Hilbert Series for Generalized Toric Polygons Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.078645Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dce3b513-ead1-4d6a-ba28-e837526d4f1e · outbound

This paper cites The Cat's Cradle: Deforming the higher rank $E_1$ and $\tilde{E}_1$ theories.

A Hilbert Series for Generalized Toric Polygons The Cat's Cradle: Deforming the higher rank $E_1$ and $\tilde{E}_1$ theories

Reference 9

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.082590Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 6a57f510-99a3-431c-8f59-32ba9586500d · outbound

This paper cites Shepherd-Barron, N.I.,Threefolds and deformations of surface singularities., Inventiones mathematicae91(1988) 299.

A Hilbert Series for Generalized Toric Polygons Shepherd-Barron, N.I.,Threefolds and deformations of surface singularities., Inventiones mathematicae91(1988) 299

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:09:54.513200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation be15b56e-ac25-491f-a70c-1e1873b9dc7e · outbound

This paper cites Galkin and A.

A Hilbert Series for Generalized Toric Polygons Galkin and A

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:09:54.497287Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 0845decf-eaf0-43e2-8f98-e06c92af75ed · outbound

This paper cites Sasaki-Einstein Manifolds and Volume Minimisation.

A Hilbert Series for Generalized Toric Polygons Sasaki-Einstein Manifolds and Volume Minimisation

Reference 12

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.098162Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation dbf7aeff-e929-4a0f-a4ea-da4eb7eaf453 · outbound

This paper cites an unresolved cited work.

A Hilbert Series for Generalized Toric Polygons Unresolved cited work

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.103870Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5b256c0e-7355-4e73-bfb6-b67c67b7ba77 · outbound

This paper cites The Exact Superconformal R-Symmetry Maximizes a.

A Hilbert Series for Generalized Toric Polygons The Exact Superconformal R-Symmetry Maximizes a

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.107909Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 1b0a6df5-54da-46da-9379-3f1838089313 · outbound

This paper cites The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds.

A Hilbert Series for Generalized Toric Polygons The Geometric Dual of a-maximisation for Toric Sasaki-Einstein Manifolds

Reference 15

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.112492Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation caafed34-56b3-4470-b652-e60950ff83a5 · outbound

This paper cites Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics.

A Hilbert Series for Generalized Toric Polygons Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.118393Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8f99bdd9-12d3-42a3-aee8-deeac7784272 · outbound

This paper cites Can you hear the shape of dual geometries?.

A Hilbert Series for Generalized Toric Polygons Can you hear the shape of dual geometries?

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:09:54.214456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 62e668fc-221d-41f4-b7e7-28eba5e74886 · outbound

This paper cites Akhtar, T.

A Hilbert Series for Generalized Toric Polygons Akhtar, T

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T16:09:54.484563Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 067ade1d-ac91-41f7-a6e0-7c4969a87469 · outbound

This paper cites Deformations of Dimer Models.

A Hilbert Series for Generalized Toric Polygons Deformations of Dimer Models

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-08-15T16:09:54.196214Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation b4ccf6ce-cb99-4679-8c72-521eb87d986d · outbound

This paper cites Twin Theories, Polytope Mutations and Quivers for GTPs.

A Hilbert Series for Generalized Toric Polygons Twin Theories, Polytope Mutations and Quivers for GTPs

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-15T16:09:54.137295Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

Observation 72a5b854-5521-4505-8b73-009e9f6a32d1 · inbound

M-theory geometries from five-brane webs, seven-branes, and T-branes cites this paper.

M-theory geometries from five-brane webs, seven-branes, and T-branes A Hilbert Series for Generalized Toric Polygons

Reference 2

Resolution: verified exact; local_arxiv, observed 2026-07-11T05:27:49.650039Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

Observation 9066078d-999d-4515-aa31-5bd6c4014ca7 · inbound

Towards Generalized Dimers for GTPs: $\mathcal{N}=2$ Fractional Branes at Infinite Coupling cites this paper.

Towards Generalized Dimers for GTPs: $\mathcal{N}=2$ Fractional Branes at Infinite Coupling A Hilbert Series for Generalized Toric Polygons

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-01T09:54:03.839206Z

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Unavailable: canonical work link unavailable.

Observation 2059651d-8139-493d-ad84-03deda42ddc6 · inbound

BPS Invariants for Generalized Toric Calabi-Yau Threefolds cites this paper.

BPS Invariants for Generalized Toric Calabi-Yau Threefolds A Hilbert Series for Generalized Toric Polygons

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-03T06:54:26.546344Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.