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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 2026-08-16T06:30:59.297886+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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.058654Z digest=sha256:21c32c9de32465c1ca107b6d4ac349e03ac07a98652c6f76880494fe8e573119

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.063777Z digest=sha256:9e76b22c72c8f15e23b014e3b56acfc434135edb33a201267f68340bbd102b75

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.068100Z digest=sha256:39d7a0659636e004b4a91aadf6217f6a78c262bf01449f362aedd5c648b9a3a0

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.072510Z digest=sha256:9c82cb5d944ca08e6ed35fc3f67fddda46818f6f6bcee52dc2a9ae1dab7e94d8

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.077296Z digest=sha256:5601440f6e6daef41e27c26a00ab20e48977793b027720481567e214440e41a0

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.081777Z digest=sha256:fb853bd57c41f94a8ee79bceae71c61001b05270fcc3747f6afa76939d0f5372

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.086691Z digest=sha256:b4fdbc06ef04f8fa09316dfed3ab87eede9eb38867c9ceb08bd6d069a0f0f51d

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.090858Z digest=sha256:ff0779f0695c2cd26c64d34aefd065dc068616460ecbd53133c31737d2a708a3

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.094837Z digest=sha256:0b4bc6fb69b734f01d1f7ecb3ba2f5752805152120705c6b277944ee8be3ebe4

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.099236Z digest=sha256:41e88476de1d451bf61f3353afeb17b4ae9696beef2b2f2cba8de75f030ed502

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.103862Z digest=sha256:fa8dbf27ecd57cf0e933e079ce0d7f084e6956adf608a9440dff6bcafad034cc

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.108128Z digest=sha256:554192b5b876639eca89bb7cc867263415e4017b95c124bbe19922983159fe44

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.112392Z digest=sha256:a41fd991ca5db4fb206a711dffa3ff42ab4827a19dc47ca4d5b1f0f59b31762f

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.116492Z digest=sha256:6fd25c73e8eb91d7a5ba3af62fd992da4a68402b45a32767a41bf51ccddfdb4b

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.120603Z digest=sha256:2efc85a51301357954dd8fad5ba6fa0a42c073d22c7f430537407e8ec4e77b55

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.124689Z digest=sha256:c509734ffc9f944801372da8920c5d9ef39537cc16f859b1f199e2c3fbb6f7f4

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.128752Z digest=sha256:ce45d1a4266a5f1c53f92588d5b4cbcce7cf0e9c44dc8c8e602c3d2b9916e787

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.132979Z digest=sha256:05153d6c4dd24d898acc05fd7d8c2623f89327d8d53f5c370b92caa81854d5ce

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.137129Z digest=sha256:4ce191ac4c12a3cb0da007592c08b6664b12f504df8442a076846ccfc38ab44a

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.141193Z digest=sha256:9e8f9692d3ffc60540cabcb8c5657e1f505cd3adfc65eb92c04e3a13ec788939

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 2026-08-16T06:30:59.297886+00:00.

source=pdf_text observed=2026-08-14T14:37:10.145987Z digest=sha256:6fb8af7aadf41751c10780d75b0571abc196df242df221ce88736b61fbebc44d

Pith citing papers

No inbound Pith citation observations are available.