Paper Citation Record · LEDGER

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures

As of 18 August 2026, this Paper Citation Record lists 19 of 19 outbound references and 1 inbound Pith citation observation for arXiv:1908.02535.

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

pith.paper-citation-record.v1
1908.02535 v1

Coverage vector

measured 19 of 19 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:51:12.281751Z

measured 20 of 20 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:14:34.389698Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-14T11:14:34.475230Z

Reference resolution

19 of 19 outbound references displayed

verified exact0
verified fuzzy16
unresolved3
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3dd7d194-de7f-4a31-a85e-b4d16c3947e7 · outbound

This paper cites Barrett and J.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Barrett and J

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.604196Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c87202f4-322e-4003-95c3-9bceff610789 · outbound

This paper cites Buser and P.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Buser and P

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.589117Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation e04442bc-d659-470d-973a-085cabb53068 · outbound

This paper cites Buser, Geometry and spectra of compact Riemann surfaces, Modern Birkh¨ auser Classics.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Buser, Geometry and spectra of compact Riemann surfaces, Modern Birkh¨ auser Classics

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.573628Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation d5127d9b-5e5b-45b9-b5a0-4c5f028d19a4 · outbound

This paper cites Huang, Asymptotic ﬂatness of the Weil-Petersson metric on Teichm¨ uller space, Geom.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Huang, Asymptotic ﬂatness of the Weil-Petersson metric on Teichm¨ uller space, Geom

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.557879Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fda11b44-20e0-4750-a2d0-8ad894dd997a · outbound

This paper cites Huang, The Weil-Petersson geometry on the thick part of the moduli space of Riemann surfaces, Proc.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Huang, The Weil-Petersson geometry on the thick part of the moduli space of Riemann surfaces, Proc

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.542865Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation c6c20b9a-a218-40ab-a43a-3f877842bc0d · outbound

This paper cites Imayoshi and M.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Imayoshi and M

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.527727Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 62a8b049-bab1-4f9b-87ed-bdba438a4a52 · outbound

This paper cites an unresolved cited work.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Unresolved cited work

Reference 7

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:51:12.513001Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 9d98567b-b9fc-4ec2-a5e1-3ff0019adc1f · outbound

This paper cites Mirzakhani, Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Mirzakhani, Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.497785Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 086c9964-6d80-4efa-8754-fd4b03cbaaa2 · outbound

This paper cites Schumacher, Harmonic maps of the moduli space of compact Riemann surfaces, Math.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Schumacher, Harmonic maps of the moduli space of compact Riemann surfaces, Math

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.481607Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 66b8563e-f77d-4108-9909-3db339c23f62 · outbound

This paper cites an unresolved cited work.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:51:12.466889Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 1580eb39-6efb-466e-b281-ddab0e9c2a4d · outbound

This paper cites an unresolved cited work.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Unresolved cited work

Reference 11

Resolution: unresolved; raw_fallback, observed 2026-08-14T14:51:12.451915Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 169424bf-8500-4ea6-88b2-f858fa89eca1 · outbound

This paper cites Wolf, The Weil-Petersson Hessian of length on Teichm¨ uller space,J.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Wolf, The Weil-Petersson Hessian of length on Teichm¨ uller space,J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.436662Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 603613f3-ea72-4d5f-95d6-76e122f8dc01 · outbound

This paper cites Wolf and Y.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Wolf and Y

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.421576Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 560c265c-d65d-4a44-860c-87ae803d81fd · outbound

This paper cites Wolpert, Chern forms and the Riemann tensor for the moduli space of curves, Invent.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Wolpert, Chern forms and the Riemann tensor for the moduli space of curves, Invent

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.405141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 20f07cec-2416-44d7-98d6-d8a349369108 · outbound

This paper cites Wolpert, Behavior of geodesic-length functions on Teichm¨ uller space,J.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Wolpert, Behavior of geodesic-length functions on Teichm¨ uller space,J

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.386354Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation bc5be397-4272-4327-8a45-749ce4cae1ba · outbound

This paper cites Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical So- ciety, Providence, RI, 2010.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical So- ciety, Providence, RI, 2010

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.370028Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 970e90e3-4812-4a92-a5f8-67004b227587 · outbound

This paper cites Wolpert, Geodesic-length functions and the Weil-Petersson curvature tensor, J.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Wolpert, Geodesic-length functions and the Weil-Petersson curvature tensor, J

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.353047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation 81f6742f-6da3-4937-8b0a-60d3905860da · outbound

This paper cites Wu, The Riemannian sectional curvature operator of the Weil-Petersson metric and its application, J.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Wu, The Riemannian sectional curvature operator of the Weil-Petersson metric and its application, J

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.336144Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Observation fc1d6cf4-d87a-4e66-9003-25da1b996173 · outbound

This paper cites Wu, On the Weil-Petersson curvature of the moduli space of Riemann surfaces of large genus, Int.

Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures Wu, On the Weil-Petersson curvature of the moduli space of Riemann surfaces of large genus, Int

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-14T14:51:12.319980Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

Pith citing papers

Observation 797f0885-6ab1-4d4b-a898-68e3f2ee2fd6 · inbound

The vanishing rate of Weil-Petersson sectional curvatures cites this paper.

The vanishing rate of Weil-Petersson sectional curvatures Uniform bounds on harmonic Beltrami differentials and Weil-Petersson curvatures

Reference 4

Resolution: verified exact; local_arxiv, observed 2026-08-14T11:14:34.481488Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.