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Paper Citation Record · LEDGER

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity

As of 16 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:1908.02989.

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

pith.paper-citation-record.v1
1908.02989 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T14:37:10.145987Z

measured 21 of 21 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-15T06:32:42.880941+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

21 of 21 outbound references displayed

  • verified exact4
  • verified fuzzy8
  • unresolved9
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 5f22d62c-68b8-45d6-a71c-a3f140cb4717 · outbound

This paper cites an unresolved cited work.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:37:10.579249Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.058654Z digest=sha256:c99d7cb49f224bfd563d17864845e2c16206a0667a0ff96e22a5c4bd31ca5ebe

Observation 5cc6b78a-d40e-4d09-acb5-b00a79993ddf · outbound

This paper cites an unresolved cited work.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:37:10.566342Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.063777Z digest=sha256:d551df47fa3cff066dfb1533ad7b189524c6a799a375283b9311108c6e6238c4

Observation d90419d0-f9b4-4c24-98b0-a75778c13b5b · outbound

This paper cites an unresolved cited work.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:37:10.552969Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.068100Z digest=sha256:b2bbb4595080a3deecebd7e88c3d00683bbc3cf622ef86acd5cd1a45414dd98c

Observation 7bd01792-041a-428d-9db2-3ca27b7b04db · outbound

This paper cites an unresolved cited work.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:37:10.539701Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.072510Z digest=sha256:655c5ed3eac889e37e9d9c4080b9df0b39fa7fc369c26c286b286eb843b9e59c

Observation bcfae663-5dea-4654-a357-8b06d7726d3d · outbound

This paper cites Theory Adv.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Theory Adv

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:37:10.526975Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.077296Z digest=sha256:bba59bd4678fd2bcac8f091cf8c04e1b3233aa92189b7ab2372e82426ed113c1

Observation 3ffc9da7-77fd-455e-8b60-8ab53d49e5c4 · outbound

This paper cites an unresolved cited work.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Unresolved cited work

Reference 6

Resolution
verified exact
doi, observed 2026-08-14T14:37:10.180308Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.081777Z digest=sha256:1d34ac302ed4e9df660bf38bb11d1436c9b7066b7c95e6bedeed33abbc80a42a

Observation b4eadd6f-ada5-4867-a595-6acb99c31c40 · outbound

This paper cites an unresolved cited work.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:37:10.513697Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.086691Z digest=sha256:c5652089349b7128218217bafb64a6f66d708fc1407fa74824a380eafa00c79e

Observation 424e797d-7952-4f6b-858f-23ccea013e04 · outbound

This paper cites B, 34 (2013), 345-380.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity B, 34 (2013), 345-380

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:37:10.500512Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.090858Z digest=sha256:d60ec92c3989bf50ec0425831fba87a866732e920ac5367842e34e9e68d62182

Observation 59e7188c-3e03-4f4e-8324-a305715de1ce · outbound

This paper cites Qualitative pr operties of solutions, phase space analysis, semilinear models, Birkh¨ auser, Basel, 2018.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Qualitative pr operties of solutions, phase space analysis, semilinear models, Birkh¨ auser, Basel, 2018

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:37:10.486837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.094837Z digest=sha256:b6472062bcd75e4ed038be3e148bde92dabaf7aa47311973602a8c0f9ebcaeac

Observation 206a29b5-0ce5-47a7-aa36-8c2a26b86f8e · outbound

This paper cites Lifespan estimates for local in time solutions to the semilinear heat equation on the Heisenberg group.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Lifespan estimates for local in time solutions to the semilinear heat equation on the Heisenberg group

Reference 10

Resolution
verified exact
local_arxiv, observed 2026-08-14T14:37:10.347950Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.099236Z digest=sha256:9f9b973d02e23006d042f5628f2b8ca8ba4cf856257cfdfda01c88e5a917549f

Observation c066e18d-7cb2-4029-ac4c-308e04de4f71 · outbound

This paper cites an unresolved cited work.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:37:10.473082Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.103862Z digest=sha256:3c4a058be2a7fdc11985674311865f5caa21433590837b956001d0dd7dc582e0

Observation 660e4edd-4629-418a-bb53-b0ac699fcaf1 · outbound

This paper cites 61(7) (2005), 1189-1208.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity 61(7) (2005), 1189-1208

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:37:10.459827Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.108128Z digest=sha256:7499fb7299fb4bbfef0a6125cf8f526eeaf72162ceba106a3c9b21532c93fb81

Observation c991c4cd-e824-4168-b177-8ef42041c8d9 · outbound

This paper cites an unresolved cited work.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:37:10.446237Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.112392Z digest=sha256:52708ece89994ebc23a7c35f9e4a9dbfd0f1eae4224eaddeef190bcf4722c377

Observation 68a86896-cd42-4fb8-9bdf-a25a68b487ce · outbound

This paper cites Steklov Inst.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Steklov Inst

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:37:10.433047Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.116492Z digest=sha256:48f31fe111f98b77857b24e1ba345f7c1bb49a88a4cf7653b12b350e2f3bc15a

Observation 832f26bc-389d-4ade-b0c0-8c49d32a23fe · outbound

This paper cites an unresolved cited work.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:37:10.419102Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.120603Z digest=sha256:f8b00eeb26b3e4896504c9972060a632c4db6edf5cc0833bcca48dfd51fec42d

Observation 4adbfb1f-c8e9-49ac-907a-794ba2978af7 · outbound

This paper cites an unresolved cited work.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-14T14:37:10.405384Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.124689Z digest=sha256:5ff66ebb279bb9dad4ee6e9f6988909909b81b36a174452be92e35b7381def69

Observation badfdb08-2ea0-4900-b228-282a5f20fa94 · outbound

This paper cites Decay estimates for the linear damped wave equation on the Heisenberg group.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Decay estimates for the linear damped wave equation on the Heisenberg group

Reference 17

Resolution
verified exact
local_arxiv, observed 2026-08-14T14:37:10.220942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.128752Z digest=sha256:a884b0f9751c0ca43df831cf873f29f0c8c2d4577d4e9e7c770a7625ab29d943

Observation 1e10e701-5639-45e1-80a3-4b73ee7b8cf9 · outbound

This paper cites Partial Differential Equations , 19(3/4) (1994), 655-676.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Partial Differential Equations , 19(3/4) (1994), 655-676

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:37:10.391855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.132979Z digest=sha256:b2629bf58b7e59e064dac259d76258dbff58d872b5b125fdd0e3134a0c5239db

Observation 9cc9f5cf-ca8c-49f0-afa7-8b6613cf0930 · outbound

This paper cites Differential Equations 265 (2018), 5212-5236.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Differential Equations 265 (2018), 5212-5236

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:37:10.377510Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.137129Z digest=sha256:752e33ee0c12f364b5bea08c589fa78979df4dbfad9945545d8fce797d68a47d

Observation 181a76a6-057a-41b7-b37a-9a36763b44af · outbound

This paper cites Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Existence and non-existence of global solutions for semilinear heat equations and inequalities on sub-Riemannian manifolds, and Fujita exponent on unimodular Lie groups

Reference 20

Resolution
verified exact
local_arxiv, observed 2026-08-14T14:37:10.201824Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.141193Z digest=sha256:d29abdb0df6d09edba813be186001b69eae11e49df6ff4cd4d7ab78aeb0b90a7

Observation 432f8c74-5a62-41d3-aa7e-2f606e1094f9 · outbound

This paper cites Differential Equations 174(2) (2001), 464-489.

Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity Differential Equations 174(2) (2001), 464-489

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T14:37:10.362838Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-14T14:37:10.145987Z digest=sha256:d044b18b2962512b5aa9d694b05d952ec959ab7a27b9e7ee6ad04fac1700291e

Pith citing papers

No inbound Pith citation observations are available.