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Paper Citation Record · LEDGER

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions

As of 22 August 2026, this Paper Citation Record lists 11 of 11 outbound references and 0 inbound Pith citation observations for arXiv:2506.14966.

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

pith.paper-citation-record.v1
2506.14966 v1

Coverage vector

measured 11 of 11 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T19:55:48.358758Z

measured 11 of 11 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+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

11 of 11 outbound references displayed

  • verified exact0
  • verified fuzzy10
  • unresolved0
  • parse uncertain1
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 47a0efe3-2fae-4075-ade7-33b04b93bf8c · outbound

This paper cites Zeros of a one-parameter family of harmonic trinomials.

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions Zeros of a one-parameter family of harmonic trinomials

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:55:48.504973Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T19:55:48.320245Z digest=sha256:d6a09e2a3b9dd21c6163760bea6052b5ac67677422ec4cec7f1e314569738e76

Observation 83e5f414-e7cd-42c3-9c6f-d8e413a2cb7f · outbound

This paper cites Zeros of a family of complex-valued harmonic trinomials.

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions Zeros of a family of complex-valued harmonic trinomials

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:55:48.494632Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T19:55:48.325118Z digest=sha256:2ed65fd82186d41b0c90905ac739998b570e8a41645ea2d1fd2904d67a161928

Observation 9e15f451-dd69-4d6b-890c-f9ae9b9a9e6a · outbound

This paper cites Zeros of a family of complex-valued har- monic functions with poles.

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions Zeros of a family of complex-valued har- monic functions with poles

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:55:48.484541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T19:55:48.328956Z digest=sha256:85857e60c3ca675256a2dc1ca8388a1331cd732c5d7656543a5917f5675c0dea

Observation 5872bca6-2333-4d19-bba1-9c60433279b3 · outbound

This paper cites Location of the zeros of certain complex-valued harmonic polynomials.

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions Location of the zeros of certain complex-valued harmonic polynomials

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:55:48.472993Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T19:55:48.332492Z digest=sha256:6a7f98a8366dd823e1a5d2f2facd69da8dcd44326ee185d147f0b188301017fe

Observation 41c645c4-7056-43b0-bbca-b9ac13e0b4fd · outbound

This paper cites Geometry of trinomials.

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions Geometry of trinomials

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:55:48.462410Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T19:55:48.336344Z digest=sha256:0e976d071a755926893b6de341cde39552a5f57caec09dd57b61a3ee0044627c

Observation e0cb333d-98aa-4861-b830-c498c9a3dc5b · outbound

This paper cites Zero location for analytic and harmonic trinomials.

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions Zero location for analytic and harmonic trinomials

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:55:48.451585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T19:55:48.339875Z digest=sha256:ed496b69ae4f857860a73fd2a40781c193df450c796b3b4006ad47876e293292

Observation 8e183e60-4386-48e7-8fa9-05de06756348 · outbound

This paper cites Zeros of a family of complex harmonic polynomials.

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions Zeros of a family of complex harmonic polynomials

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:55:48.438941Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T19:55:48.344141Z digest=sha256:3635986c730a33ddba68c44686b2ceb2935c9360a80fc11718634e991825dc6a

Observation 674ae02f-3666-4cf3-92e2-11e79c725696 · outbound

This paper cites On the zeros of polyanalytic polynomials.

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions On the zeros of polyanalytic polynomials

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:55:48.426903Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T19:55:48.347720Z digest=sha256:2c6fd95f70981394b0cbda8b2d24787d00bcb57b3bab30ce2229bc94a329b7db

Observation 89775eea-a398-48c1-808f-71852b2176df · outbound

This paper cites Sheil-Small, 02 1992.

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions Sheil-Small, 02 1992

Reference 9

Resolution
parse uncertain
raw_fallback, observed 2026-08-15T19:55:48.415852Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T19:55:48.350987Z digest=sha256:d00ac195298df008045247f1f7d90a107d6493e610f73ed2d5674dce3007fcc2

Observation bbfc7b8b-2cf5-4250-b122-8e78eb6ddfcc · outbound

This paper cites The valence of harmonic polynomials.

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions The valence of harmonic polynomials

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:55:48.403684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T19:55:48.355207Z digest=sha256:b4cf20becc5c0811dc098b6b0960e71f4bd5b3eb7b6a6c99805efc4a2a5f3412

Observation cfed5a11-9873-4fa2-9b80-8a3f775b7778 · outbound

This paper cites Zeros of a two-parameter family of harmonic trinomials.

Using Real-Variable Techniques to Study Zeros of Complex-Valued Harmonic Functions Zeros of a two-parameter family of harmonic trinomials

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T19:55:48.391121Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

source=pdf_text observed=2026-08-15T19:55:48.358758Z digest=sha256:f4f89825fd0def1ec01cc0318a139b5bb581145355b825400e5d1715803d9c09

Pith citing papers

No inbound Pith citation observations are available.