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Paper Citation Record · LEDGER

Monotonicity results for semilinear parabolic equations on metric graphs

As of 8 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 2 inbound Pith citation observations for arXiv:2502.08361.

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

pith.paper-citation-record.v1
2502.08361 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-08T05:34:26.380886Z

measured 15 of 15 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-08T06:32:00.761636+00:00

measured 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T05:18:38.148063Z

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: arxiv_reference, observed 2026-07-02T23:17:29.611761Z

Reference resolution

13 of 13 outbound references displayed

  • verified exact0
  • verified fuzzy11
  • unresolved2
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 8dff4d10-696e-430d-a5a7-566a39471ae4 · outbound

This paper cites an unresolved cited work.

Monotonicity results for semilinear parabolic equations on metric graphs Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-08T05:34:26.628531Z

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.

source=pdf_text observed=2026-08-08T05:34:26.342815Z digest=sha256:8acbac1ef52a49f71ca0780eb726ad6daf7ae7f6347160a8bfbd560600704218

Observation 60dde15e-e2fc-4bf4-b455-9d603f737ccd · outbound

This paper cites Berkolaiko & P.

Monotonicity results for semilinear parabolic equations on metric graphs Berkolaiko & P

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T05:34:26.619209Z

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.

source=pdf_text observed=2026-08-08T05:34:26.346640Z digest=sha256:c3382cd420b15cf74d3f8b98e430b57b9a7cea47c60523429c0957c1258fc814

Observation db335d70-61fd-4b97-be2d-1bc5126989ae · outbound

This paper cites Cardanobile, The L2-strong maximum principle on arbitrary countable networks , Linear Algebra Appl.435 (2011), 1315-1325.

Monotonicity results for semilinear parabolic equations on metric graphs Cardanobile, The L2-strong maximum principle on arbitrary countable networks , Linear Algebra Appl.435 (2011), 1315-1325

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T05:34:26.610172Z

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.

source=pdf_text observed=2026-08-08T05:34:26.350013Z digest=sha256:bcd3cac95ba1fd861cc685238f39505da2362d1097302c695f2a41d2d5e8fea4

Observation 23a9e637-fca8-43fa-bcce-2e61760551f2 · outbound

This paper cites an unresolved cited work.

Monotonicity results for semilinear parabolic equations on metric graphs Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-08T05:34:26.599708Z

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.

source=pdf_text observed=2026-08-08T05:34:26.353508Z digest=sha256:8f6df9ee11aa02a64e9709f351a50bbe5fb89c3610d6e0f59b84e627809bb077

Observation 645a1f73-520d-4d8b-a264-b25fba25a723 · outbound

This paper cites Grillo, M.

Monotonicity results for semilinear parabolic equations on metric graphs Grillo, M

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T05:34:26.589367Z

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.

source=pdf_text observed=2026-08-08T05:34:26.357009Z digest=sha256:801af17fea3324f8a83ce551c8ae986a9690cb8db382b08d818987b0d5fd769f

Observation 8c1c2934-8092-4fce-8028-feaa553abe49 · outbound

This paper cites de Mottoni, A.

Monotonicity results for semilinear parabolic equations on metric graphs de Mottoni, A

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T05:34:26.578700Z

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.

source=pdf_text observed=2026-08-08T05:34:26.360910Z digest=sha256:e39acddf452964fcfec7cc24d7e1650b7ac24eb79fb91dc14f43edfb823ccfea

Observation 595d1bea-ab50-4f2d-9824-adc2c8e6289a · outbound

This paper cites Lakshmikantham, D.

Monotonicity results for semilinear parabolic equations on metric graphs Lakshmikantham, D

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T05:34:26.568896Z

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.

source=pdf_text observed=2026-08-08T05:34:26.364512Z digest=sha256:20695aca450ed04758b5bf17b6247ad6ec6febdd28d3645ca8739bc5b627367b

Observation 4b31f6a4-3749-4cd4-b9e9-5c631960caab · outbound

This paper cites Mugnolo, Semigroup Methods for Evolution Equations on Networks (Springer, 2014).

Monotonicity results for semilinear parabolic equations on metric graphs Mugnolo, Semigroup Methods for Evolution Equations on Networks (Springer, 2014)

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T05:34:26.557789Z

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.

source=pdf_text observed=2026-08-08T05:34:26.367128Z digest=sha256:d57108c99b5713d88c84cd4e266ca44c291ab3d8568c14beda46457936011a76

Observation b79147dd-2d2f-455c-b8a6-6c8d8cd71d44 · outbound

This paper cites Muratori, F.

Monotonicity results for semilinear parabolic equations on metric graphs Muratori, F

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T05:34:26.546905Z

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.

source=pdf_text observed=2026-08-08T05:34:26.369678Z digest=sha256:22a9c86ae8c31016d5fd30bd83adfa8b3730463be1c8ac79565577dccfc16fdb

Observation 8c5fed52-5195-48e4-8c5b-44f885415670 · outbound

This paper cites Naimark & M.

Monotonicity results for semilinear parabolic equations on metric graphs Naimark & M

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T05:34:26.537267Z

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.

source=pdf_text observed=2026-08-08T05:34:26.372218Z digest=sha256:503b72a8638725867ff8a529e2594562548c0804e868697033a5eb4a431d51f8

Observation 08203694-4682-460f-afc6-db0ff7eeef98 · outbound

This paper cites Rach˘ unkov´ a & J.

Monotonicity results for semilinear parabolic equations on metric graphs Rach˘ unkov´ a & J

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T05:34:26.527404Z

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.

source=pdf_text observed=2026-08-08T05:34:26.375132Z digest=sha256:f65c9458abdcb8706f5837431b15331133187c2bcde3cbf254db1bc91d4a7c86

Observation fdce3448-40d5-4f3a-9e02-3368e11265df · outbound

This paper cites von Below, A maximum principle for semilinear parabolic network equat ions.

Monotonicity results for semilinear parabolic equations on metric graphs von Below, A maximum principle for semilinear parabolic network equat ions

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T05:34:26.517478Z

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.

source=pdf_text observed=2026-08-08T05:34:26.378283Z digest=sha256:c5072c5d4b7eebe47768fe5fbe9d4e48a20b2998b6390aac243dd3785f849fb5

Observation 0f3a5b52-8fb4-4175-8bb6-04fe9230a076 · outbound

This paper cites G. Castelnuovo.

Monotonicity results for semilinear parabolic equations on metric graphs G. Castelnuovo

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-08T05:34:26.505745Z

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.

source=pdf_text observed=2026-08-08T05:34:26.380886Z digest=sha256:c70d5e04c8beb5a2ebe2afd857facb6f9b8df668b8db05b75938f10c17813244

Pith citing papers

Observation 8e64cf51-7c3c-49a5-8bad-14cdc9f7ac83 · inbound

Nonexistence results for the semilinear wave equation on graphs cites this paper.

Nonexistence results for the semilinear wave equation on graphs Monotonicity results for semilinear parabolic equations on metric graphs

Reference 37

Resolution
unresolved
no resolver link, observed 2026-08-07T05:18:38.148063Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-07T05:18:38.148063Z digest=sha256:e91952ed873dd8371d58636f232aa07afe6e21a3c8db049d65f623c95ceb57c2

Observation b8a83fd8-2398-4921-ba18-bcdd3c803410 · inbound

Nonexistence Results for Semilinear Parabolic and Hyperbolic Equations on Metric Graphs cites this paper.

Nonexistence Results for Semilinear Parabolic and Hyperbolic Equations on Metric Graphs Monotonicity results for semilinear parabolic equations on metric graphs

Reference 57

Resolution
verified exact
arxiv_id, observed 2026-07-02T23:17:29.613053Z

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.

source=pdf_text observed=2026-06-27T18:20:28.833245Z digest=sha256:a173be2149a84037174141f5ffc37322a40181f08dc7f0f6c69d7bffa7197046