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Paper Citation Record · LEDGER

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach

As of 21 August 2026, this Paper Citation Record lists 43 of 43 outbound references and 1 inbound Pith citation observation for arXiv:1908.05025.

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

pith.paper-citation-record.v1
1908.05025 v2

Coverage vector

measured 43 of 43 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T13:40:14.422909Z

measured 44 of 44 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-21T06:32:19.484+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-04T16:59:16.680698Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

43 of 43 outbound references displayed

  • verified exact0
  • verified fuzzy19
  • unresolved24
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation a86fbbf7-b896-4b47-8d9f-4bcda8c2594b · outbound

This paper cites Achdou, G.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Achdou, G

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:15.182585Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 7060ebc4-a579-438d-9730-712b0c03a593 · outbound

This paper cites Alhasanat and C.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Alhasanat and C

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:15.169317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.245978Z digest=sha256:5844d15ad98cfef918413d4c20d8c02e68ffb74b9a5402b1d283d3a605d34230

Observation 2d947856-7fde-4e6b-9d3c-40a1e5c2f8fd · outbound

This paper cites Alhasanat and C.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Alhasanat and C

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:15.154273Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 422f2a69-ead0-4821-ac03-d406f6fec29c · outbound

This paper cites Barles, L.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Barles, L

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:15.140389Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 4cb2d42e-b91a-40f8-a9f9-917a93e1ddf7 · outbound

This paper cites Barles and B.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Barles and B

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:15.122641Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.259592Z digest=sha256:00af68906aa935e11d9610d9696dfcb6715b60ba15c4df43f2d3ab4412b65bf2

Observation c401a1a1-fd54-4d02-bf63-586e4136c4e5 · outbound

This paper cites Barles, H.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Barles, H

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:15.108863Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.263644Z digest=sha256:6e1e69022d6aef8eaf71ad256655efd81dea9ab5a601c41ebc78c356caf8299d

Observation 265c09da-e6c5-402d-be43-a98d989ed491 · outbound

This paper cites Berestycki and J.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Berestycki and J

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:15.092652Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.268165Z digest=sha256:a7d00d26f0e395a866c59c8d2c363d9bba033964e25e8b26d644cd97604c8580

Observation 679bdae0-a79e-4f33-9dd7-699e0a098ac1 · outbound

This paper cites Berestycki and G.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Berestycki and G

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:15.078674Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.272133Z digest=sha256:b0547c8860975ca14498ee41a217df056700740233e61da9fe511a4662440d2b

Observation 4c87bd44-ddaa-4f31-8bbd-875dfce31f6a · outbound

This paper cites Carr` ere, Spreading speeds for a two-species competitio n-diffusion system, J.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Carr` ere, Spreading speeds for a two-species competitio n-diffusion system, J

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:15.066158Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 6d9d5fe3-c2d2-49e1-8ba5-120cb1063837 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:15.051523Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 764946eb-d7c5-4376-be01-6d504abc97f2 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:15.033564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 7de26719-3aca-43c0-8f54-ca6158262b6a · outbound

This paper cites Ducrot, T.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Ducrot, T

Reference 12

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation a557a188-02c0-48d5-91e8-3f4e130eb08e · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.998906Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.293523Z digest=sha256:5a79f485a64f7b20e38aaf42a3c024108b9ec7f95a44efed1775fc2fb3724fad

Observation 892dff9f-f2c3-493c-9e41-36fae07f2f0b · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.985279Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation b591b55b-8467-42af-9acd-63104f471c1c · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 15

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.971737Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation af227c45-d930-4e11-9f98-b25d5a39d206 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 16

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 57a58e44-af8a-4508-8010-431de4724f6b · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.943947Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 3a7b666a-081e-44cc-b58b-37bf8034d5e7 · outbound

This paper cites Girardin and K.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Girardin and K

Reference 18

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 44d3f952-4e7a-436e-9fb8-ce74c3aae006 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.912289Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation d25cf7d2-5fc3-4eb6-a02d-605085ddfb43 · outbound

This paper cites Hamel and G.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Hamel and G

Reference 20

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation f1146011-54eb-41d5-b096-4586fc69c45d · outbound

This paper cites Holzer and A.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Holzer and A

Reference 21

Resolution
verified fuzzy
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 4489a7e2-054e-4de6-bf15-188f1b55875c · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 22

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 7b623eca-0ccd-4a62-be4c-894b297e7a6b · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 23

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.738383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 45f2fa10-5cc6-43a4-acce-8db322b88ed4 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 24

Resolution
unresolved
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Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 5365dcf3-fa8c-46af-87cc-d5201e650841 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 25

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.712257Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 9a0250ed-d688-4e56-8f10-b66b7e7a9017 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.695815Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 4b3c49a4-3142-449c-b5eb-cc79eff59840 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.682448Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation ab367772-9ace-49eb-adb9-b2d79b58a746 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.667860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation d46c9ac7-04c9-41ac-81e9-bc226fbf7109 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 29

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.655541Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 77e2be4e-7628-446e-8f31-e281e8ece98d · outbound

This paper cites Liang and X.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Liang and X

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:14.643341Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 1b61dd78-04be-403b-8949-ac1f51943f90 · outbound

This paper cites Lin and W.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Lin and W

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:14.628722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 15e2dee1-7283-48ce-8fc7-11e6d50db193 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.615174Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation a42bfda0-e92e-4e8e-afeb-80c289b96429 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.600540Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation d6b3a921-1cf8-4127-9577-775e20096fb1 · outbound

This paper cites M´ endez, J.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach M´ endez, J

Reference 34

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:14.588057Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 05c995c8-88b0-44b7-ae12-56b60eceef5b · outbound

This paper cites Roques, Y.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Roques, Y

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:14.575966Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

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Observation 7ee2987a-955b-4338-9d2b-ebc047d98442 · outbound

This paper cites Shigesada and K.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Shigesada and K

Reference 36

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:14.562722Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.393288Z digest=sha256:7de45fe0a5994f0b6ab80cc2e4cd9f4b0c9839ce8a3e5d760083b3a0a3ef57b2

Observation b67aaa47-20ad-40f6-bd1d-42411ab236e5 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 37

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.550401Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.397180Z digest=sha256:d197ee1d340d4765a874725658cc7e36bde6522a08533697c9e72dd84561f49c

Observation 1770a644-a532-4ebd-b28f-9e9d54489647 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.536213Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.401377Z digest=sha256:1a310586c6bfe42f83edd7f2213891f3906b37bf111fe01a80dac5188123c990

Observation 3e29f00c-7da8-4305-a002-2c71f012fafe · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 39

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.522686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.405045Z digest=sha256:8265e43906746d618cf8a69b3eb0fbe36d628f7ca4010a64b3d9554a8b58f895

Observation 7dad42ca-810a-4e63-b413-77b8748e138f · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 40

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.510809Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.409520Z digest=sha256:c3561e4920bfe10c42d2e37cbe10b43aa527a112d87de714e28ff9894df4c13b

Observation 0535904f-708b-4120-8c67-becb89678294 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 41

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.499015Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.413719Z digest=sha256:b52d9385dad391e5ed156f5bfda3c77ec4b2fccd6912292f93446a020f2a9220

Observation 4431e53f-c3a0-4074-b318-b9914fd208a1 · outbound

This paper cites an unresolved cited work.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Unresolved cited work

Reference 42

Resolution
unresolved
raw_fallback, observed 2026-08-14T13:40:14.486536Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.418124Z digest=sha256:a74b8be67baa9d619ade135e92a1f9003bb9e47c758fc186afb5fe275eab2884

Observation b21d44b4-0680-4bd5-9254-28a581f321cc · outbound

This paper cites Xin, Front propagation in heterogeneous media, SIAM Rev.

Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach Xin, Front propagation in heterogeneous media, SIAM Rev

Reference 43

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T13:40:14.473596Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-21T06:32:19.484+00:00.

source=pdf_text observed=2026-08-14T13:40:14.422909Z digest=sha256:a3508a2fd8eff2c87b363642e0ff873aaec998b30bb2ed5ac004d74219084489

Pith citing papers

Observation 736d2a34-db76-44bf-b947-3bc99b341059 · inbound

On the logarithmic correction of transition fronts in shifting environments cites this paper.

On the logarithmic correction of transition fronts in shifting environments Asymptotic spreading of interacting species with multiple fronts I: A geometric optics approach

Reference 36

Resolution
unresolved
no resolver link, observed 2026-08-04T16:59:16.680698Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=arxiv_source observed=2026-08-04T16:59:16.680698Z digest=sha256:940c9d4ea171f97d106b9cc721cf10f9e274ca931636f69a3d1cf010b3964e14