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Paper Citation Record · LEDGER

Number and location of pre-images under harmonic mappings in the plane

As of 24 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:1908.08759.

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

pith.paper-citation-record.v1
1908.08759 v2

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T11:43:02.951509Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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

38 of 38 outbound references displayed

  • verified exact0
  • verified fuzzy23
  • unresolved15
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 6496ce4a-db8d-4eba-b914-35124d5f3913 · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.372874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.821345Z digest=sha256:21e7b324fc447270cba8bee7a9da6cc8de43d8adef5bbe774971702bac6cd1df

Observation 5dfb6ae1-273e-41b0-9125-ca9c3b009923 · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.362895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.825846Z digest=sha256:b89dd4f340b0fde974c201f3efca6cabdfb373d36c30e6f969d04cfbcb08fda8

Observation e537cbc5-8468-4f99-94fd-83a6ea411863 · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.353659Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.829753Z digest=sha256:4d990ee48743cae18ccb68aa0b03000bbbc40ce59091f0e61c25a79fcca8f011

Observation 4dfc86bd-1111-46f5-9ef8-1875a03f2485 · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.344969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.833441Z digest=sha256:2a037b9afb9735c3584716dd7f2858f2e845204d08e24cffa23220dd67680613

Observation ec712c34-6f0a-459b-a513-1c0a22973be7 · outbound

This paper cites Bénéteau and N.

Number and location of pre-images under harmonic mappings in the plane Bénéteau and N

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.336000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.837221Z digest=sha256:96c92c5ec11e2f2e538a9f32eb8dd7f4dbe70239b2de0b73c37ad25afa7147cf

Observation 71b795b7-85ef-4bb5-ba7a-9b8abb9eb3a6 · outbound

This paper cites Bergweiler and A.

Number and location of pre-images under harmonic mappings in the plane Bergweiler and A

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.325722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.841113Z digest=sha256:267097fb1b0951f4a4098cc6393feeea48d2b453a570cffc6dce550713fc6564

Observation ff3ec7a2-b3e6-4650-9f7e-d9a264d784c4 · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.315408Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.844982Z digest=sha256:685412882c30238bdab2f93efcee219ec117eeb33ebd7a4443fc4662e4ccbbf6

Observation 86df6edb-7d2a-4004-a414-933c65f61c7d · outbound

This paper cites Bollobás, Modern graph theory, vol.

Number and location of pre-images under harmonic mappings in the plane Bollobás, Modern graph theory, vol

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.304774Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.848461Z digest=sha256:5bf42dfc828db1e942f19472d37ca8ddd47eff839bdb0bb1c360b8c755810d81

Observation 65db0059-cc3e-4020-8a3f-f74550ef7b7a · outbound

This paper cites Bshouty and A.

Number and location of pre-images under harmonic mappings in the plane Bshouty and A

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.292673Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.851964Z digest=sha256:020f722e34832c2031984ea26d8f81c3dc2041e9b2e249a7c3e825c963773672

Observation ffe78105-d04a-4bd4-8662-d9220afa4700 · outbound

This paper cites Clunie and T.

Number and location of pre-images under harmonic mappings in the plane Clunie and T

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.281670Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.855371Z digest=sha256:a1c95a8cf668c36ee7d930133a3b1fb90c1b0ff003b0ecb1beb63f27d7018b74

Observation f0f7cd50-9cc0-4072-b18c-ef50b56d6539 · outbound

This paper cites Duren, Harmonic mappings in the plane, vol.

Number and location of pre-images under harmonic mappings in the plane Duren, Harmonic mappings in the plane, vol

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.270647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.858592Z digest=sha256:97e49e2beeb4cb685d26c3b9e61c274d3b7e528e5c886676e6ca26d2a981615c

Observation 18bec793-6628-47fd-97a3-4818fc32d8fd · outbound

This paper cites Duren, W.

Number and location of pre-images under harmonic mappings in the plane Duren, W

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.260748Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.861979Z digest=sha256:188c20e34c3d64c4d81c3c94361b4034a124b668bf3c44b63c52f69b8951b2d0

Observation b24416b7-b017-4075-b93f-aa7a39a5ab0d · outbound

This paper cites Geyer, Sharp bounds for the valence of certain harmonic polynomials, Proc.

Number and location of pre-images under harmonic mappings in the plane Geyer, Sharp bounds for the valence of certain harmonic polynomials, Proc

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.251675Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.865484Z digest=sha256:ebb900564a3c78288f80d4e139fac02b7daed85ee21ea5d9add66cf2d3bc005b

Observation 5405aeb8-1621-4910-8fc3-ca5996ce5897 · outbound

This paper cites Hengartner and G.

Number and location of pre-images under harmonic mappings in the plane Hengartner and G

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.241655Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.869264Z digest=sha256:8286eed5b404387cddd5769b6f254ae8bcd69f578a01cfd2cb8d6c002f2821e5

Observation 9385f91c-87dc-4948-ae11-08fa8403b480 · outbound

This paper cites Henrici, Applied and computational complex analysis.

Number and location of pre-images under harmonic mappings in the plane Henrici, Applied and computational complex analysis

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.231318Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.872786Z digest=sha256:cfcfa63900e3ab26c1f26d2c11c5c413f2d7c3d67e67ed8b8162352204b876da

Observation 485c15c8-c124-48c4-9770-4194e11a2507 · outbound

This paper cites Khavinson, S.-Y.

Number and location of pre-images under harmonic mappings in the plane Khavinson, S.-Y

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.220992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.875553Z digest=sha256:954766c492f2016be0019280f5b0d1a788ef22b56edd935b669c724e5cf506d6

Observation 0caf992a-5e2b-47bf-85a1-1030672f27e7 · outbound

This paper cites Khavinson and G.

Number and location of pre-images under harmonic mappings in the plane Khavinson and G

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.210704Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.878419Z digest=sha256:ba642a914648a9ee77c8edfe3271221bd68b17b6eb679cfcbe7d3172051c0747

Observation 6c083d68-62c9-4438-bedc-b9ee3b104428 · outbound

This paper cites harmonious.

Number and location of pre-images under harmonic mappings in the plane harmonious

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.200392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.881314Z digest=sha256:0bac2bcc00d70ea08746106c1f39673162b3ad7e16e87ba800370210c49fa33b

Observation b8771eba-e4f0-46c6-80e9-c88ebd116810 · outbound

This paper cites Khavinson and G.

Number and location of pre-images under harmonic mappings in the plane Khavinson and G

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.189239Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.884154Z digest=sha256:d0fb1f4d951eeccf70bddd758ecd6ce788865efd3b68880f6fdeebe1467d06e9

Observation 61ece056-383d-44a6-bd82-f4b8f9b38a29 · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.179188Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.887110Z digest=sha256:471ca474e648abea0e6a5e62e2af0b35b8957477601e0144dd4c6b5df908e35a

Observation 678baed5-7840-4fac-bd6a-035ecaf79ade · outbound

This paper cites Liesen and J.

Number and location of pre-images under harmonic mappings in the plane Liesen and J

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.169087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.890378Z digest=sha256:f70205c1b257757bbd22610e7e561e086a8ece17edd8ba4d15a0e8e5f30e28e4

Observation b066a52a-de9a-4e8e-9a7e-215862d45455 · outbound

This paper cites Liesen and J.

Number and location of pre-images under harmonic mappings in the plane Liesen and J

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.158298Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.894311Z digest=sha256:b12a0fca8d0e026db44d6cde68f5423d827657bc815a0df87c076eaf366a738e

Observation e4b5ae65-4058-4f3f-b98a-3ff3e59326ec · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.148790Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.898009Z digest=sha256:9aeb2d88f1f008ccf7270d940891c22ba15f78ce34566ff43526bcf80f773681

Observation d8e3dc19-2e80-462c-837d-7ce98aabe822 · outbound

This paper cites Luce and O.

Number and location of pre-images under harmonic mappings in the plane Luce and O

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.138529Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.901936Z digest=sha256:efd01661f76926c6ea169e76006d979fe43dcd48f2f0e22986846fb11e4215e7

Observation 0f879ffd-1d50-444f-ada1-e07fdafc08ed · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.128446Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.905861Z digest=sha256:1606209a217ab2677120f4531a5ab676f48a44eb75ef8e3a02c49020da6e41a7

Observation a5a2a0ef-14c5-410d-a74d-7d6d5a574f04 · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.118395Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.910315Z digest=sha256:e191e66d57230a4d86bbb727550921f71680cc340465f35c1cd0c5e2acb88519

Observation ce9ff0aa-d152-4033-8c6a-6a240a40687c · outbound

This paper cites Lyzzaik, Local properties of light harmonic mappings, Canad.

Number and location of pre-images under harmonic mappings in the plane Lyzzaik, Local properties of light harmonic mappings, Canad

Reference 27

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.107874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.913837Z digest=sha256:67b2974657859f4d77dc032e36553e24c19c98a2639c2f89bba5a69022af133f

Observation 40c1cbbb-fbec-4c2b-841d-c7a951da06cb · outbound

This paper cites Neumann, Valence of complex-valued planar harmonic functions, Trans.

Number and location of pre-images under harmonic mappings in the plane Neumann, Valence of complex-valued planar harmonic functions, Trans

Reference 28

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.097471Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.917181Z digest=sha256:a6d0a573dcc1c6ce8b151d5e3a03d987809d4d2941c2e0932af5b3b9766770e6

Observation 7b9e36ca-bab0-4027-b6cb-84e8ed790b14 · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.086262Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.920499Z digest=sha256:4d9a63d3bdc6a370337d9017c255a6eab135ae398d8b066534b71e876152e9b8

Observation 42e58916-1336-41d0-b864-79c5b274fa98 · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.074383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.924183Z digest=sha256:29a297c64237dd992a7d0069eae3034c4a3f6918c8a65cfb51d20b7a5e711bf9

Observation f18dbc10-d6d7-4319-9f1a-576cb1ee80ae · outbound

This paper cites Roe, Winding around.

Number and location of pre-images under harmonic mappings in the plane Roe, Winding around

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.062810Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.927493Z digest=sha256:6bb9fed8256e704bf4478a4ff0d87293486e0c7c788ff15f763c617fc03b87e1

Observation 4a98b59d-f011-420a-aa43-cfb0a2867796 · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.050598Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.930597Z digest=sha256:1ae8beecda53a26f92f0baef22cdbfa02f6329c468c383cc464861634b22600d

Observation cbfea4c7-0b26-43dc-9e92-7a1ae0bb5b87 · outbound

This paper cites Sète and J.

Number and location of pre-images under harmonic mappings in the plane Sète and J

Reference 33

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.039142Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.934092Z digest=sha256:34bbc5c06b098e02d9ad76f77d154a90e31bff4a77927222911f4301018d5d40

Observation 73208049-a3af-43a4-8225-07b4538c2d6b · outbound

This paper cites Sheil-Small, Complex Polynomials, vol.

Number and location of pre-images under harmonic mappings in the plane Sheil-Small, Complex Polynomials, vol

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:03.027941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.937547Z digest=sha256:bcaaf262f8fb7107dcacf2a48b3b89e7188bab80bf9c09062fad8a645399d1b7

Observation bd85d9a6-9c52-4643-b742-40b3e2e3b256 · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 35

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.016550Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.940839Z digest=sha256:5bf029f8aadd7f5492e16c0d78caf3581bf844cabe901c75946b28b62c9ee72d

Observation ea3a2f5f-0c72-4bae-99db-7d691d042afd · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:03.006210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.944501Z digest=sha256:523d742f674e17c493d415895511b2a59b029be6eee98668dba24d1d54bfca2b

Observation 7cd159f9-2d18-43f8-b185-c4060d6e8b9d · outbound

This paper cites Wegert, Visual complex functions.

Number and location of pre-images under harmonic mappings in the plane Wegert, Visual complex functions

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T11:43:02.995208Z

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source=pdf_text observed=2026-08-14T11:43:02.947926Z digest=sha256:af5728d1f7207d51a63859a2c6789b120a034aa40387963f5955cab01511a4ac

Observation 9bd36903-6de1-4ab1-ba87-bc2ad0d233f9 · outbound

This paper cites an unresolved cited work.

Number and location of pre-images under harmonic mappings in the plane Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-14T11:43:02.982687Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-14T11:43:02.951509Z digest=sha256:5f66b7238917a805e8502692e7ce9b835de773cbe3d3a2768094a2da1904a40c

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