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Paper Citation Record · LEDGER

Sp(2)-invariant expanders and shrinkers in Laplacian flow

As of 16 August 2026, this Paper Citation Record lists 17 of 17 outbound references and 2 inbound Pith citation observations for arXiv:2501.05437.

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

pith.paper-citation-record.v1
2501.05437 v2

Coverage vector

measured 17 of 17 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T21:23:43.895902Z

measured 19 of 19 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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-30T07:08:38.467638Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-02T15:47:06.327407Z

Reference resolution

17 of 17 outbound references displayed

  • verified exact1
  • verified fuzzy10
  • unresolved6
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation d33e1fb3-9511-4113-aca8-cd74d27134fe · outbound

This paper cites an unresolved cited work.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:23:44.255741Z

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=2026-08-10T21:23:43.834247Z digest=sha256:fea1b48b21e946df88bdcad7d0bef03a2a5e8269c0b65e1c942606ce65a8a920

Observation 61f3b7ff-bdb5-4f72-9898-f4a116b8063b · outbound

This paper cites Atiyah and E.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Atiyah and E

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:23:44.244565Z

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=2026-08-10T21:23:43.838817Z digest=sha256:3f5b3bc8ab456655b0474407e08cc1ce6359bed9cccabdfbf24fae1d8de393c4

Observation 3cef6c49-2d50-40b7-b622-c26a356bfa33 · outbound

This paper cites Ball,Quadratic closedG2-structures, Journal of the London Mathematical Society107 (2023), no.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Ball,Quadratic closedG2-structures, Journal of the London Mathematical Society107 (2023), no

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:23:44.233194Z

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=2026-08-10T21:23:43.842783Z digest=sha256:40e3e615a1ab59f95c8d9669436afef59b1509620693bdc9b94b1aecc00f4e90

Observation 60dde2f3-5afb-4c93-97bb-ebaab3ac8c97 · outbound

This paper cites an unresolved cited work.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:23:44.221159Z

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=2026-08-10T21:23:43.846517Z digest=sha256:9b8f260e14d30de82ed006ff3ddb5e0d3f0e840f73a734e10a122fb89ffdb492

Observation 0fd35a1e-0353-4de0-99dd-bfb9534f3b9e · outbound

This paper cites an unresolved cited work.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:23:44.208721Z

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=2026-08-10T21:23:43.850691Z digest=sha256:ed481a032042ccec4dcdc7b68f99b16d829738bfb31e6a61f8ca97303fa30576

Observation 357552ea-25da-45fe-9f29-54040e058e33 · outbound

This paper cites an unresolved cited work.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:23:44.196874Z

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=2026-08-10T21:23:43.854525Z digest=sha256:bf74fb4cf75f2704c865f9bfd6f0e10d7c4f326d62ede1fb522fd5d25d3a8edc

Observation ae7ceb94-f967-4838-80a6-0b06214addd9 · outbound

This paper cites Chen,Rotational symmetry of solutions of mean curvature flow coming out of a double cone, J.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Chen,Rotational symmetry of solutions of mean curvature flow coming out of a double cone, J

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:23:44.185375Z

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=2026-08-10T21:23:43.858468Z digest=sha256:f4d3cc32a1977ae75bf85f5ac731c43c37804031aea3868293a8691f052eb55b

Observation 651009fb-6dfc-476b-bec4-45d4bacb6e44 · outbound

This paper cites Chodosh,Expanding Ricci solitons asymptotic to cones, Calc.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Chodosh,Expanding Ricci solitons asymptotic to cones, Calc

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:23:44.173884Z

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=2026-08-10T21:23:43.862189Z digest=sha256:6512ba66e5602ecec8b34f6e6f90d6f6baf1c11aeec6ab8a2de3e5eb94fc73e0

Observation 0a15b174-f1ee-4bbc-b87d-e1302bda8591 · outbound

This paper cites an unresolved cited work.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:23:44.162571Z

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=2026-08-10T21:23:43.865994Z digest=sha256:82d419828603adef1f69b4ad123c42690d1e74c49c0a90447bb9bb9fb50171b1

Observation a95aa920-ad48-4e15-bcd2-561f6e42455e · outbound

This paper cites Eschenburg and M.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Eschenburg and M

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:23:44.152040Z

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=2026-08-10T21:23:43.869831Z digest=sha256:cc10ee2c324d2e033df1bf2aba9923bd2b1102bac4aec29ed5f57ecea8f2820f

Observation 8d8f9e60-406e-4e59-b216-ad9041a2c5e6 · outbound

This paper cites Fowdar,S1-Invariant Laplacian Flow, The Journal of Geometric Analysis32 (2021), no.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Fowdar,S1-Invariant Laplacian Flow, The Journal of Geometric Analysis32 (2021), no

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:23:44.140167Z

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=2026-08-10T21:23:43.873517Z digest=sha256:cde77ada8a5b25408b241e281f00c04389ab6d7a855d6d7427390671e404f76a

Observation a6704c2f-5cc1-4ad7-8b61-6ab098cce16a · outbound

This paper cites Haskins, I.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Haskins, I

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:23:44.128195Z

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=2026-08-10T21:23:43.877193Z digest=sha256:51c30dda19b39065f10f7e0ba08ed2818f5b291bcfab8cfc920a9ebc1f877a0b

Observation c1c579d6-de88-4774-a2c3-223b2fd863ba · outbound

This paper cites Haskins and J.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Haskins and J

Reference 13

Resolution
unresolved
no resolver link, observed 2026-08-10T21:23:43.880999Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-10T21:23:43.880999Z digest=sha256:68f565434dbab599c04c8a92054e1b8440553f88593af5963f74777aaee0c699

Observation 5f441763-6fd6-4ce0-9190-13cc86db352f · outbound

This paper cites Joyce,Compact manifolds with special holonomy, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2000.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Joyce,Compact manifolds with special holonomy, Oxford Mathematical Monographs, Oxford University Press, Oxford, 2000

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:23:44.115824Z

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=2026-08-10T21:23:43.884738Z digest=sha256:1ab6a4ec4ddb65588ec3263265089c9c9e800f4044499265f905aa9353be6282

Observation 692de9b9-6491-46ee-9e79-c583b85a301e · outbound

This paper cites Karigiannis and J.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Karigiannis and J

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:23:44.102336Z

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=2026-08-10T21:23:43.888444Z digest=sha256:017905457e44d6bc023ee9e3b05e34e07a03874817a43bbe3981c8edcb2df4ac

Observation 3e83f60f-4a8c-4157-9028-8429364865e2 · outbound

This paper cites Malgrange,Sur les points singuliers des équations différentielles linéaires, Enseign.

Sp(2)-invariant expanders and shrinkers in Laplacian flow Malgrange,Sur les points singuliers des équations différentielles linéaires, Enseign

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:23:44.090256Z

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=2026-08-10T21:23:43.891931Z digest=sha256:8966b896bf361ad07f7529b7c87ce677f7d8d36269854a41d7bcfe650557f694

Observation 17945a66-d40a-41cf-a153-8165cedad4be · outbound

This paper cites $G_2$-instantons on the ALC members of the $\mathbb{B}_7$ family.

Sp(2)-invariant expanders and shrinkers in Laplacian flow $G_2$-instantons on the ALC members of the $\mathbb{B}_7$ family

Reference 17

Resolution
verified exact
local_arxiv, observed 2026-08-10T21:23:43.932633Z

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=2026-08-10T21:23:43.895902Z digest=sha256:24ba285e99e089e32b7301b80058516e7a3f0158e027cc3b9eddbd7940efe8b3

Pith citing papers

Observation 0018971a-4861-407b-86ea-07dc331644ed · inbound

On the structure of complete $G_2$-solitons cites this paper.

On the structure of complete $G_2$-solitons Sp(2)-invariant expanders and shrinkers in Laplacian flow

Reference 33

Resolution
verified exact
arxiv_id, observed 2026-07-02T15:47:06.328822Z

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=2026-06-27T23:29:21.691157Z digest=sha256:d8b320c8a9aa6a6a2140b0dee5b6894c6964cbfe360bd7dab28371f3b1b2b007

Observation 00227098-7d37-4a26-b6c1-ee4964291791 · inbound

Integral Gauss formula and the Poisson equation for the $G_2$-Laplacian cites this paper.

Integral Gauss formula and the Poisson equation for the $G_2$-Laplacian Sp(2)-invariant expanders and shrinkers in Laplacian flow

Reference 28

Resolution
metadata mismatch
arxiv_id, observed 2026-06-30T07:14:21.456361Z

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=2026-06-30T07:08:38.467638Z digest=sha256:a782fe8ff72e02d45c1cdb4d8180a2fb6635bf322142833467f691869289370d