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Paper Citation Record · LEDGER

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation

As of 16 August 2026, this Paper Citation Record lists 28 of 28 outbound references and 1 inbound Pith citation observation for arXiv:2606.22967.

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

pith.paper-citation-record.v1
2606.22967 v1

Coverage vector

measured 28 of 28 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-26T07:55:56.635914Z

measured 29 of 29 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-06T05:24:51.170638Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-06T05:24:53.279446Z

Reference resolution

28 of 28 outbound references displayed

  • verified exact3
  • verified fuzzy0
  • unresolved25
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1ebed292-282d-4b0f-b638-9f0ef9f15df4 · outbound

This paper cites an unresolved cited work.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Unresolved cited work

Reference 1

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:b00b2c087cc878a03ccd4e7d4b723ae93833782831b87fae9f7830f3d0f7ebdb

Observation 6608506b-b052-4bb6-b7b5-8aa1bde5e337 · outbound

This paper cites Amorim, A.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Amorim, A

Reference 2

Resolution
verified exact
arxiv_id, observed 2026-07-04T11:29:51.338521Z

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=2026-06-26T07:55:56.635914Z digest=sha256:6a4ad456614d4768a5d42de6e79b149dcdf42a333c7ed625cd71452c88a1fce5

Observation 166debab-0972-465d-b724-dda9c7711b3d · outbound

This paper cites Andreis, T.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Andreis, T

Reference 3

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:dc908fd7e2fbf06de64a46155fb3ab694a199fd92ea6b8873239e31a08f59fc6

Observation 423f0f5c-22a0-4686-ad06-ff399f8e152b · outbound

This paper cites Andreis, T.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Andreis, T

Reference 4

Resolution
verified exact
doi, observed 2026-06-26T07:59:08.001735Z

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=2026-06-26T07:55:56.635914Z digest=sha256:d38ffdf20a29d0d6fa51bc689a9ceb711ee995e31e113ad30bf9da33a79c3be8

Observation 21d611be-de02-4831-a485-95b080775428 · outbound

This paper cites Andreis, W.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Andreis, W

Reference 5

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:ef5656a47ea4e6c53d8f5cda9ec0b2e3f5a881c8f81f4acd4d9fb6522185444d

Observation d7c4b54a-04fa-4b27-8a89-17aa8ebc8b1a · outbound

This paper cites Andreis, W.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Andreis, W

Reference 6

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:2498138b8b0cd4c7f70815e3ab51c8a23445754cb55815c02768f06f2a3b7b24

Observation 22d3d1bc-e8f0-46ac-8c37-ec6137df6292 · outbound

This paper cites Aronszajn.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Aronszajn

Reference 7

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:b4e22f6adedd7d3bc7c6b3e616a3dc96a285c5a7cc2c031a021bef23279720b1

Observation fd755198-418b-4d38-bcb6-e6791276797e · outbound

This paper cites Escobedo, P.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Escobedo, P

Reference 8

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:72545540083cf5a6a4e273957ac7b921d66b7f1a0ad5e9c76a77e20c60531875

Observation d25ed43b-24b0-4e4d-b219-7d2a8d94945f · outbound

This paper cites an unresolved cited work.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Unresolved cited work

Reference 9

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:b07e315bef3d7633146b19f53ea75729d4eac890463e08fa688a60b7efbf524b

Observation f521e674-2dea-498a-b2c3-d85b7113cf6f · outbound

This paper cites Global existence of measure-valued solutions to the multicomponent Smoluchowski coagulation equation.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Global existence of measure-valued solutions to the multicomponent Smoluchowski coagulation equation

Reference 10

Resolution
verified exact
arxiv_id, observed 2026-07-04T11:29:51.340939Z

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=2026-06-26T07:55:56.635914Z digest=sha256:2545aa74005cf65f33ea99345cc470a8e7b41ec4964b5af86ea30a22df1cca84

Observation d840c60b-20ac-46f6-a972-1a2960395f2f · outbound

This paper cites Fournier.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Fournier

Reference 11

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:ec293a70e657b9b52b86b02681731c2300d1dbd7cefea4b14d00739a736a032d

Observation 97bdcdfd-7416-4586-9e45-84b8dc5c1a83 · outbound

This paper cites Fournier and J.-S.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Fournier and J.-S

Reference 12

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:0064a0f336dd84acf242fd3b284c4ff2ecc75f74da31ffebf15b02ecc528c8cd

Observation ed570c24-dfec-4101-8952-9c2a8fb13a42 · outbound

This paper cites Fournier and P.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Fournier and P

Reference 13

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:b9a301b0f7a12aa8ce9b56d84e0f6b4bfecd5e601fb9d182ead81fb3253695b5

Observation c573f48e-8948-479c-b16b-267c04a9b433 · outbound

This paper cites Fournier and P.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Fournier and P

Reference 14

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:d5db1915d2b2becdf3221cc2f3eda94b256e4f8ab0ef1d7ab7e197edd02ac05b

Observation 73ffdd1b-1442-476b-9b53-72a69a9223d0 · outbound

This paper cites an unresolved cited work.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Unresolved cited work

Reference 15

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:5bd1428bd9193f0a589b9e58dd28f7ab284a4c5202f22b73716a9736127c905e

Observation e2693d45-bee6-4f26-ae0a-1775e1ae31e1 · outbound

This paper cites Heydecker and R.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Heydecker and R

Reference 16

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:2a8885a054adc28736edddf3e569a962fa2493911ee40034ca0935acd127ee77

Observation 79b7d3ad-6858-4c30-8e19-ce0d49d446b2 · outbound

This paper cites Hofbauer and K.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Hofbauer and K

Reference 17

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:d51f9ee52eddf74336aff49f3ec2ecd6b155aa42dd9d0639623292248d9f623f

Observation e7d8a22c-13da-41e1-9f6f-302e28575c37 · outbound

This paper cites Hoogendijk, I.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Hoogendijk, I

Reference 18

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:d75c4bc8236d9a03582e31ae9f6818e1a3b266011bfb850241911c2973921aeb

Observation a7b23e36-5e73-4c1b-9e9d-6d2bf15a5b5f · outbound

This paper cites an unresolved cited work.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Unresolved cited work

Reference 19

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:4924cffdb1ae99040e9c725c2cdd3c332aac1b5b7db7f1566ec0bd46a8202d6f

Observation 6a334b37-a754-4319-9298-cf21482e804c · outbound

This paper cites an unresolved cited work.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Unresolved cited work

Reference 20

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:f92aaa3bacfe7295635bbc9f7d11361c49a64b544560a882f82e948346ef012a

Observation f4eec60b-ddf2-4ca3-ba9b-6a0f6d6cbe4b · outbound

This paper cites Lushnikov.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Lushnikov

Reference 21

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:0759c590f5f5350cd567e4b5b3dc7f965851aeec68daa97dfbe951c135613124

Observation bc78fbd8-27b0-4716-8869-ae3854c78c03 · outbound

This paper cites an unresolved cited work.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Unresolved cited work

Reference 22

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:7e77d27bcd7a37aec6517d405f99af45034c0059a44054563ee27772bae67c09

Observation 546b8c0b-a8b7-4cfd-ba1b-77ef2c558b03 · outbound

This paper cites an unresolved cited work.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Unresolved cited work

Reference 23

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:4ec09a5b6a8e9a01b534fed35b6b6701191e06a0790fdba4d23223cf93149d2d

Observation 96d8e04a-ed3c-4ec5-a02a-9df649de49c0 · outbound

This paper cites an unresolved cited work.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Unresolved cited work

Reference 24

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:61e24a2d105677b39b50f3758812ef8246de14b570fb5f0f8143e74a6436387c

Observation 955778c4-e87b-4395-87a8-bc706ade89bd · outbound

This paper cites an unresolved cited work.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Unresolved cited work

Reference 25

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:2ecae3ebba76ec02e32630a677fde47577b9a9dcf256f877e3566c9aa679c27e

Observation 6aa15b7d-12d9-4ca0-a01f-0af0b34989f6 · outbound

This paper cites Rezakhanlou.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Rezakhanlou

Reference 26

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:ffb6141da091f56fba7b43a1857d3a9b04696033fa9ab89d61a29a61ebdcc1f6

Observation b32cb55b-e7f1-47ff-9e5b-d93fd640ddce · outbound

This paper cites an unresolved cited work.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Unresolved cited work

Reference 27

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:3c4f44581113fc014b7ca7cd3688119114f524ea91f02b82739c63be58a891f1

Observation 896c74ad-d94f-439a-89a3-ddf0db861c76 · outbound

This paper cites an unresolved cited work.

Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation Unresolved cited work

Reference 28

Resolution
unresolved
no resolver link, observed 2026-06-26T07:55:56.635914Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-06-26T07:55:56.635914Z digest=sha256:f2ca77ee904aad3bb4f4d1dd17516f1d7b15d882cbfda5efbe1ebad8aa8cc48f

Pith citing papers

Observation 8f307007-7922-4d77-8a73-16611788a9f0 · inbound

Cluster-Cluster model in $\mathbb{Z}^d$ cites this paper.

Cluster-Cluster model in $\mathbb{Z}^d$ Spatial Coagulation Systems with Mercer Kernels: Replicator Dynamics and Gelation

Reference 17

Resolution
verified exact
local_arxiv, observed 2026-08-06T05:24:53.384472Z

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=2026-08-06T05:24:51.170638Z digest=sha256:967061d96f3f85e23f1a06838d7f2ad92cd2968747058ad4374c8d8669cd3e79