Paper Citation Record · LEDGER

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation

As of 19 August 2026, this Paper Citation Record lists 22 of 22 outbound references and 0 inbound Pith citation observations for arXiv:2507.06237.

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

pith.paper-citation-record.v1
2507.06237 v2

Coverage vector

measured 22 of 22 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:51:49.700699Z

measured 22 of 22 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

22 of 22 outbound references displayed

verified exact11
verified fuzzy6
unresolved5
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5212909c-e684-47ca-a1be-c49f116cd989 · outbound

This paper cites and Patrizio, G., Finsler Metrics: A Global Approach with Applications to Geo- metric Function Theory, Springer, Berlin, 1994.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation and Patrizio, G., Finsler Metrics: A Global Approach with Applications to Geo- metric Function Theory, Springer, Berlin, 1994

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:51:49.891778Z

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 4cf2ca3d-2b01-4301-b22a-51cad9943e65 · outbound

This paper cites and Shen, Z., An Introduction to Riemann–Finsler Geometry , Springer, New York, 2012.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation and Shen, Z., An Introduction to Riemann–Finsler Geometry , Springer, New York, 2012

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:51:49.884769Z

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 52dd283e-6fd6-4da1-8451-3e10371d869a · outbound

This paper cites and Lieb, E.H., Sharp uniform convexity and smoothness inequalities for trace norms, Invent.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation and Lieb, E.H., Sharp uniform convexity and smoothness inequalities for trace norms, Invent

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:51:49.876191Z

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 6197c412-9508-4aa5-86dc-8c42867adb85 · outbound

This paper cites an unresolved cited work.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:51:49.867245Z

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 fcf22397-5a7c-497c-ae9e-13d792cb589b · outbound

This paper cites Hopf’s maximum principle with an application to Riemannian geometry, Duke Math.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation Hopf’s maximum principle with an application to Riemannian geometry, Duke Math

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:51:49.858915Z

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 4bcfc476-a9d1-43f8-b569-ca542cf35d7b · outbound

This paper cites and Zhang, Z., Differential Harnack estimates for parabolic equations, in: Complex and Differential Geometry, Springer, Berlin, 2011, pp.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation and Zhang, Z., Differential Harnack estimates for parabolic equations, in: Complex and Differential Geometry, Springer, Berlin, 2011, pp

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:51:49.850592Z

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 8f598e0f-f4a1-489f-9af6-5bd51088b6be · outbound

This paper cites and Yan, D., Ground states for logarithmic Schr¨ odinger equations on locally finite graphs, J.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation and Yan, D., Ground states for logarithmic Schr¨ odinger equations on locally finite graphs, J

Reference 7

Resolution: verified exact; doi, observed 2026-08-15T19:51:49.810185Z

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 94c41007-7b3d-471f-a761-4c435d2c3836 · outbound

This paper cites and Khanh, N.N., Gradient estimates of Hamilton–Souplet–Zhang type for a general heat equation on Riemannian manifolds, Arch.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation and Khanh, N.N., Gradient estimates of Hamilton–Souplet–Zhang type for a general heat equation on Riemannian manifolds, Arch

Reference 8

Resolution: verified exact; doi, observed 2026-08-15T19:51:49.802964Z

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 c27ee959-ebc4-414e-9ed8-c96d5135becc · outbound

This paper cites and Ma, B., Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds, Arch.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation and Ma, B., Gradient estimates for a nonlinear parabolic equation on Riemannian manifolds, Arch

Reference 9

Resolution: verified exact; doi, observed 2026-08-15T19:51:49.795808Z

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 3eca5d20-d875-4406-b374-13dcc3ef5d4b · outbound

This paper cites an unresolved cited work.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation Unresolved cited work

Reference 10

Resolution: verified exact; doi, observed 2026-08-15T19:51:49.788252Z

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 2a82b8d0-7327-4180-9895-eea2709c02d1 · outbound

This paper cites et al., Logarithmic Schr¨ odinger-like equation as a model for magma transport, Europhys.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation et al., Logarithmic Schr¨ odinger-like equation as a model for magma transport, Europhys

Reference 11

Resolution: verified exact; doi, observed 2026-08-15T19:51:49.779358Z

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 a8899f7a-3cbf-4c10-a29f-9f05d7010540 · outbound

This paper cites an unresolved cited work.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation Unresolved cited work

Reference 12

Resolution: verified exact; doi, observed 2026-08-15T19:51:49.770982Z

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 98d5c0e6-9398-4b93-87a1-074d09d3f765 · outbound

This paper cites an unresolved cited work.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:51:49.840482Z

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 7daaa5ab-c7c5-4a1d-9985-a06e70006bd4 · outbound

This paper cites and Sturm, K.-T., Bochner–Weitzenb¨ ock formula and Li–Yau estimates on Finsler manifolds, Adv.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation and Sturm, K.-T., Bochner–Weitzenb¨ ock formula and Li–Yau estimates on Finsler manifolds, Adv

Reference 14

Resolution: verified exact; doi, observed 2026-08-15T19:51:49.761926Z

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 eb860578-4593-4a6f-8d5d-3f642531bca4 · outbound

This paper cites an unresolved cited work.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation Unresolved cited work

Reference 15

Resolution: unresolved; raw_fallback, observed 2026-08-15T19:51:49.833261Z

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 f44e52e7-7679-43a1-9292-3ec9eeef0ff1 · outbound

This paper cites Operators on nonlinear metric measure spaces I: A New Laplacian comparison theorem on Finsler manifolds and a generalized Li-Yau approach to gradient estimates of Finslerian Schr\"odinger equation.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation Operators on nonlinear metric measure spaces I: A New Laplacian comparison theorem on Finsler manifolds and a generalized Li-Yau approach to gradient estimates of Finslerian Schr\"odinger equation

Reference 16

Resolution: unresolved; no resolver link, observed 2026-08-15T19:51:49.680054Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3dc75cec-e391-4d2c-9de4-fac9447ff962 · outbound

This paper cites and Zhu, Y., Li–Yau estimates for a nonlinear parabolic equation on Finsler metric measure spaces, Manuscripta Math.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation and Zhu, Y., Li–Yau estimates for a nonlinear parabolic equation on Finsler metric measure spaces, Manuscripta Math

Reference 17

Resolution: verified exact; doi, observed 2026-08-15T19:51:49.754317Z

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 08c3fdd4-b4db-40e6-9354-c21d8ffe9a41 · outbound

This paper cites and Zhang, Q.S., Sharp gradient estimate and Yau’s Liouville theorem for the heat equation on noncompact manifolds, Bull.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation and Zhang, Q.S., Sharp gradient estimate and Yau’s Liouville theorem for the heat equation on noncompact manifolds, Bull

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T19:51:49.826006Z

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 4ff1c510-b602-4a2e-9b95-b2deecae14c7 · outbound

This paper cites an unresolved cited work.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation Unresolved cited work

Reference 19

Resolution: verified exact; doi, observed 2026-08-15T19:51:49.739176Z

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 d5144b56-7b51-4e62-946b-1a092593e49b · outbound

This paper cites an unresolved cited work.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation Unresolved cited work

Reference 20

Resolution: verified exact; doi, observed 2026-08-15T19:51:49.730264Z

Source-reported events for the cited work

correction dated 2023-05-08. Source: crossref record 10.1007/s12220-023-01292-z->10.1007/s12220-022-01103-x:correction, observed 2026-07-11T03:08:23.710027+00:00. This notice travels one citation hop only.

Observation 0481bd6e-4976-4bab-95a6-a168463f9314 · outbound

This paper cites an unresolved cited work.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation Unresolved cited work

Reference 21

Resolution: verified exact; doi, observed 2026-08-15T19:51:49.722609Z

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 f69fc993-032c-4229-bfb2-cb6fa3f01c39 · outbound

This paper cites an unresolved cited work.

A Li-Yau gradient estimate for the Finslerian logarithmic Schr\"{o}dinger equation Unresolved cited work

Reference 1053

Resolution: unresolved; no resolver link, observed 2026-08-15T19:51:49.691007Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.