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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 2026-08-15T06:32:42.880941+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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.834247Z digest=sha256:21ec007593acaac208b0bbbe590b9f68fd3445642ca759d9721506e4d5debd47

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.838817Z digest=sha256:b09e14d1958b4d2a368e4794cfee58f4307ab0f28824c8ad37d5de98e5300c47

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.842783Z digest=sha256:13bf7d150a0d46bf1c673e01cce3c424ecbfa753bfdbf9199bb3b43b1f9b003a

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.846517Z digest=sha256:06e114c4209ce2b00887d750beda4f7a7869312923c6fa47f5a1c82d9af6139d

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.850691Z digest=sha256:70c68000208ae9791c0007c021918b98675ce552cb40130ce20d9f120aaba753

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.854525Z digest=sha256:4e23f3fd0e79b7b43a282c1d2fa8e022b14440cb28efa086ef4ce9adf6349268

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.858468Z digest=sha256:dce4bb449479d0efcd26a9df7707c6b6f4783a248c8800625b91321e20e1abfb

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.862189Z digest=sha256:f8eb4c3d2386bf0885ad6d04c00fa570d47a392c4951a97a617ee20cd68c0b95

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.865994Z digest=sha256:1c91279a5f66e2dec1e6016605bf24949c0c17d104482d4d6071496a01eec869

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.869831Z digest=sha256:f3eaf31badc483d3a1c84f41f360977d736a084a540443982beb931b1b84e04c

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.873517Z digest=sha256:3640d95bb4e1540a58662c909ae48a261a534e5b2b8e7ccf7a51fc9ade4161da

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.877193Z digest=sha256:872b9099e5dedadfa4ab14b7e8ec2faf85e3ae37a8dc74257db0b36165ecaea5

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.884738Z digest=sha256:2b1b721bc4886adb4ac32eb6cd4d9ef77c6f8b5b33d74edf315bc2b78e8161b5

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.888444Z digest=sha256:b227d7087ecb7c99edbeb2dcab46acd3d01e0e8f1baeb78daedcc491578a2d50

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.891931Z digest=sha256:7f3130536a151291a6272c4f35bffa0700b808d0567fd39f92b51512b614be36

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-08-10T21:23:43.895902Z digest=sha256:5b1de38b6041e57eb84532cbff6d27f0ae35c05800ee7a05a65c4f9596e71248

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-06-27T23:29:21.691157Z digest=sha256:32f3c146df6d1231e64bb042a6cc0e6bdb5c016d7f200213aba48c8200b8ef76

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 2026-08-15T06:32:42.880941+00:00.

source=pdf_text observed=2026-06-30T07:08:38.467638Z digest=sha256:ee973d5606a684ad464277519dacf1d2569e1b62209e0bf98fdadd4bc31124e0