Paper Citation Record · LEDGER

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns

As of 19 August 2026, this Paper Citation Record lists 33 of 33 outbound references and 0 inbound Pith citation observations for arXiv:2507.03901.

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

pith.paper-citation-record.v1
2507.03901 v1

Coverage vector

measured 33 of 33 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-06T20:10:19.772356Z

measured 33 of 33 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

33 of 33 outbound references displayed

verified exact0
verified fuzzy18
unresolved15
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malformed identifier0
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External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 99132192-bf3d-44b3-a8ac-3a9ada32ecfd · outbound

This paper cites Angle, T.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Angle, T

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:20.073819Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2bab2c21-b5d9-4d12-ab4d-63d4f803f25d · outbound

This paper cites Beardon, K.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Beardon, K

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:20.064857Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d96e1f97-0260-4aeb-aaa3-5d2912c599ec · outbound

This paper cites Calabi, Extremal K¨ ahler metrics, Ann.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Calabi, Extremal K¨ ahler metrics, Ann

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:20.056097Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 6be5cb45-4bf3-413f-bdcc-718d7190b6c2 · outbound

This paper cites Calabi, Extremal K¨ ahler metrics II, Differential geometry and complex analysis, Springer, Berlin, (1985) 95-114.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Calabi, Extremal K¨ ahler metrics II, Differential geometry and complex analysis, Springer, Berlin, (1985) 95-114

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:20.047540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2ca93cf6-83d7-45f6-9427-147da7af2d48 · outbound

This paper cites Chang, Global existence and convergence of solutions of Calabi flow on surfaces of genus h ≥ 2 , Kyoto J.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Chang, Global existence and convergence of solutions of Calabi flow on surfaces of genus h ≥ 2 , Kyoto J

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:20.038453Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7b272534-7422-4bdc-9fda-aed8424d945d · outbound

This paper cites Chang, The 2-dimensional Calabi flow , Nagoya Math.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Chang, The 2-dimensional Calabi flow , Nagoya Math

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:20.029165Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f65066e2-fd03-4e43-b0a6-e449858113f3 · outbound

This paper cites Chen, Calabi flow in Riemann surfaces revisited: a new point of view , Int.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Chen, Calabi flow in Riemann surfaces revisited: a new point of view , Int

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:20.020804Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 860d672f-f4d1-4bbb-9dac-da08d0718ddb · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 8

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:20.011392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 386ee168-b21f-429d-9618-d846c5fae02e · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:20.003438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 43c072ac-ecf9-4513-b383-2c9f0dd8bcc8 · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:19.995114Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d30ace1b-88bd-4a06-91ed-20ba60ea725b · outbound

This paper cites Ge, Combinatorial methods and geometric equations, Thesis (Ph.D.)-Peking University, Beijing.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Ge, Combinatorial methods and geometric equations, Thesis (Ph.D.)-Peking University, Beijing

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:19.986323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation dce1410a-32c6-43e6-918a-a2d8e7799eb4 · outbound

This paper cites Ge, Combinatorial Calabi flows on surfaces , Trans.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Ge, Combinatorial Calabi flows on surfaces , Trans

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:19.976942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 80a31b37-193f-4837-ba4f-0439a0993c45 · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:19.968282Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0455f8ef-2060-44fe-82f8-7b3f5b869a50 · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:19.960061Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fbd80b17-54eb-40da-bb66-a7642eb5279e · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:19.951190Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation db2f076a-134d-42dc-aec8-bfb09240b521 · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 16

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:19.942884Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 023b5944-b5f0-4af7-8adf-14f289ba1ca2 · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:19.934562Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 17dcbdc9-897c-410c-94dd-9b322cd805b7 · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:19.926780Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 02d01c14-2a5f-4649-8607-b905bfc7a836 · outbound

This paper cites Glickenstein, J.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Glickenstein, J

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:19.918808Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 9401f067-4e19-4902-834e-ae58d3918456 · outbound

This paper cites Guo, Combinatorial Yamabe flow on hyperbolic surfaces with boundary , Comm.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Guo, Combinatorial Yamabe flow on hyperbolic surfaces with boundary , Comm

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:19.910266Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 8c6f4521-6100-4db8-957f-399886b94a2d · outbound

This paper cites Hamilton, Three-manifolds with positive Ricci curvature , J.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Hamilton, Three-manifolds with positive Ricci curvature , J

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:19.901679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c1b9e4a7-c953-4c30-b472-2220fd3e5e0e · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:19.892865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation a2f86c68-d54c-4687-bbf7-9f2d328db434 · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:19.884328Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 438e88fa-98a1-4dd0-bff7-276936f5beb9 · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 24

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:19.875449Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 47ba9178-2efc-4c2f-96b1-d8970425ed67 · outbound

This paper cites an unresolved cited work.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-08-06T20:10:19.867019Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b09c140f-694c-4117-902c-3b42eceeeb45 · outbound

This paper cites Luo, Combinatorial Yamabe flow on surfaces , Commun.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Luo, Combinatorial Yamabe flow on surfaces , Commun

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:19.858107Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d4115d21-f31c-49f1-9595-70aa4ceca1d7 · outbound

This paper cites Luo, A combinatorial curvature flow for compact 3-manifolds with boundary , Electron.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Luo, A combinatorial curvature flow for compact 3-manifolds with boundary , Electron

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:19.849240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1608875d-9b91-4806-bf86-8d3b3a34b99d · outbound

This paper cites Thurston, Geometry and Topology of 3-Manifolds , Princeton Lecture Notes, 1976.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Thurston, Geometry and Topology of 3-Manifolds , Princeton Lecture Notes, 1976

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:19.840125Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1bba8833-898c-4957-aa7a-408971cc757c · outbound

This paper cites Colin de Verdi` ere, Un principe variationnel pour les empilements de cercles , Invent.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Colin de Verdi` ere, Un principe variationnel pour les empilements de cercles , Invent

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:19.831359Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 16ca4c10-51a8-455d-a604-8cb4963ace21 · outbound

This paper cites Xu, Rigidity of inversive distance circle packings revisited , Adv.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Xu, Rigidity of inversive distance circle packings revisited , Adv

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:19.822010Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation c1879007-8e3d-46b5-ab47-200b26bdf62f · outbound

This paper cites Fractional combinatorial Calabi flow on surfaces.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Fractional combinatorial Calabi flow on surfaces

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-06T20:10:19.765744Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 39c9a241-92ca-4708-b26d-26a25c72aa23 · outbound

This paper cites Zhang, X.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Zhang, X

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-06T20:10:19.812659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation ae6e6320-6b6b-4a2e-822c-1ac9a6cba6a2 · outbound

This paper cites Circle patterns with obtuse exterior intersection angles.

Improved explicit estimates for the discrete Laplace operator with hyperbolic circle patterns Circle patterns with obtuse exterior intersection angles

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-06T20:10:19.772356Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

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