Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-07T11:09:10.490738Z
Paper Citation Record · LEDGER
Constancy of the index for gradient mappings
As of 8 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2506.03906.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
35 of 35 outbound references displayed
- verified exact2
- verified fuzzy22
- unresolved11
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation c13ba6dc-c08b-4629-8ae9-8b25f84a2ab5 · outbound
This paper cites Astala, T.
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:18.238060Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation a6e930f2-8799-4660-8cb5-0fb3e8a2cd2d · outbound
This paper cites Baernstein and L.
Constancy of the index for gradient mappings Baernstein and L
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:18.125624Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ad993854-367c-4fed-b1de-43f7187c2c7c · outbound
This paper cites an unresolved cited work.
Constancy of the index for gradient mappings Unresolved cited work
Reference 3
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:09:17.959074Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation fd2d8773-295d-4f20-a5c0-fe8e53bdef67 · outbound
This paper cites an unresolved cited work.
Constancy of the index for gradient mappings Unresolved cited work
Reference 4
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:09:17.821036Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 77aaf604-2d00-4dbe-83af-2730f4b813a4 · outbound
This paper cites $C^{1,\frac{1}{3}-}$ very weak solutions to the two dimensional Monge-Amp\'ere equation.
Constancy of the index for gradient mappings $C^{1,\frac{1}{3}-}$ very weak solutions to the two dimensional Monge-Amp\'ere equation
Reference 5
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T11:09:11.015432Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b49b78fa-e4d4-40ad-8619-7d083c98ca8d · outbound
This paper cites Chang.Infinite Dimensional Morse Theory and Multiple Solution Problems.
Constancy of the index for gradient mappings Chang.Infinite Dimensional Morse Theory and Multiple Solution Problems
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:17.689231Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 19c2b6dc-c5a7-426b-b088-a0da07f85af9 · outbound
This paper cites Conti, C.
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:17.557791Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation fabf4a7e-f77f-4bca-9bbc-b24cd979da40 · outbound
This paper cites De Philippis, A.
Constancy of the index for gradient mappings De Philippis, A
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:17.419654Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 405d73cd-9502-404e-84a4-1555de2d1d99 · outbound
This paper cites an unresolved cited work.
Constancy of the index for gradient mappings Unresolved cited work
Reference 9
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:09:17.281182Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 04655312-278c-4867-9b10-f008fee0dd96 · outbound
This paper cites Faraco and J.
Constancy of the index for gradient mappings Faraco and J
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:17.169714Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation fee8a225-0d13-41a1-9405-27fe57670826 · outbound
This paper cites Faraco, C.
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:17.038665Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 2f92a40e-d652-4a3d-a33b-f18ff6b4aebe · outbound
This paper cites Faraco and L.
Constancy of the index for gradient mappings Faraco and L
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:16.113482Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7118331d-fbab-4c21-a3ef-e94563adcf4e · outbound
This paper cites Fonseca and W.
Constancy of the index for gradient mappings Fonseca and W
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:14.778327Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4492de51-a63a-4ec0-a29d-4513d98b0212 · outbound
This paper cites an unresolved cited work.
Constancy of the index for gradient mappings Unresolved cited work
Reference 14
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:09:14.668572Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 159fc67e-7b01-455a-a537-cf50206250c9 · outbound
This paper cites an unresolved cited work.
Constancy of the index for gradient mappings Unresolved cited work
Reference 15
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:09:14.534210Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation ce0f9cfb-4b35-4080-a497-d8966c635220 · outbound
This paper cites Hatcher.Algebraic Topology.
Constancy of the index for gradient mappings Hatcher.Algebraic Topology
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:14.334530Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 1823168c-200a-4d23-932a-c9b391c416ad · outbound
This paper cites Hencl and P.
Constancy of the index for gradient mappings Hencl and P
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:14.232054Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 8e21e81c-121e-403d-ac99-eb52710289a1 · outbound
This paper cites The Monge-Ampere system in dimension two and codimension three.
Constancy of the index for gradient mappings The Monge-Ampere system in dimension two and codimension three
Reference 18
- Resolution
- unresolved
- no resolver link, observed 2026-08-07T11:09:08.503942Z
Source-reported events for the cited work
Unavailable: canonical work link unavailable.
Observation b53bfee0-829c-44a2-8f13-a471b2a2ab0b · outbound
This paper cites Iwaniec, L.
Constancy of the index for gradient mappings Iwaniec, L
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:14.053883Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 791abe69-1bde-4d76-823e-d6b5fed6066a · outbound
This paper cites Kirchheim and L.
Constancy of the index for gradient mappings Kirchheim and L
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:13.907974Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation f4afa483-b00c-474b-8b24-84f11afb0ff1 · outbound
This paper cites an unresolved cited work.
Constancy of the index for gradient mappings Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:09:13.786659Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 19485c9e-6098-471d-ad4b-8f904fbaa70e · outbound
This paper cites an unresolved cited work.
Constancy of the index for gradient mappings Unresolved cited work
Reference 22
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:09:13.601891Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 05882f19-aa4e-46a2-9998-e9e4c18ffcf2 · outbound
This paper cites an unresolved cited work.
Constancy of the index for gradient mappings Unresolved cited work
Reference 23
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:09:13.470586Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 54e256b4-a91d-405f-84e4-4775e21794dd · outbound
This paper cites an unresolved cited work.
Constancy of the index for gradient mappings Unresolved cited work
Reference 24
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:09:13.311240Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 7d116499-ea2b-482f-a7b0-7574ff67e5cb · outbound
This paper cites On regularity and rigidity of $2\times 2$ differential inclusions into non-elliptic curves.
Constancy of the index for gradient mappings On regularity and rigidity of $2\times 2$ differential inclusions into non-elliptic curves
Reference 25
- Resolution
- verified exact
- local_arxiv, observed 2026-08-07T11:09:10.767914Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation b6657b18-da89-487e-a69b-16274885dba3 · outbound
This paper cites Lewicka, L.
Constancy of the index for gradient mappings Lewicka, L
Reference 26
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:13.027831Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 222526d2-7533-4cfb-9710-100295158000 · outbound
This paper cites Mawhin and M.
Constancy of the index for gradient mappings Mawhin and M
Reference 27
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:12.908414Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation c3a1b9e0-056b-4813-88bb-d2bedd1af380 · outbound
This paper cites Milnor.Morse Theory.
Constancy of the index for gradient mappings Milnor.Morse Theory
Reference 28
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:12.735538Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 99e21092-4cd1-4e34-9ae7-c6662928bb56 · outbound
This paper cites M¨ uller and V.ˇSver´ ak.
Constancy of the index for gradient mappings M¨ uller and V.ˇSver´ ak
Reference 29
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:12.570083Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 4525d4f9-614c-4f4f-aab9-476384661262 · outbound
This paper cites Rickman.Quasiregular Mappings.
Constancy of the index for gradient mappings Rickman.Quasiregular Mappings
Reference 30
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:12.342828Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 98bfbc73-6084-4c93-8cf3-f318cf724f06 · outbound
This paper cites ˇSver´ ak.
Reference 31
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:12.158870Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 17560a8c-7986-46b4-84cb-c7eb8afc69db · outbound
This paper cites ˇSver´ ak.
Reference 32
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:12.026442Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation e905b7f0-f7f4-41d5-931f-14e4d925c339 · outbound
This paper cites ˇSver´ ak.
Reference 33
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:11.767278Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 1dc90f84-288a-45bb-a64c-899081e35184 · outbound
This paper cites Sz´ ekelyhidi.
Constancy of the index for gradient mappings Sz´ ekelyhidi
Reference 34
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-07T11:09:11.471286Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Observation 5ac4c2d6-76bf-4982-a529-f0c24f2383b0 · outbound
This paper cites an unresolved cited work.
Constancy of the index for gradient mappings Unresolved cited work
Reference 35
- Resolution
- unresolved
- raw_fallback, observed 2026-08-07T11:09:11.248910Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-08T06:32:00.761636+00:00.
Pith citing papers
No inbound Pith citation observations are available.