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Paper Citation Record · LEDGER

Understanding the well-rounded deformation retraction of Teichm\"uller space

As of 16 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 1 inbound Pith citation observation for arXiv:2509.06339.

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

pith.paper-citation-record.v1
2509.06339 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T16:23:47.426378Z

measured 32 of 32 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-06-26T12:55:45.826061Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-07-04T07:39:39.683615Z

Reference resolution

31 of 31 outbound references displayed

  • verified exact1
  • verified fuzzy15
  • unresolved15
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 83a9ec83-5f0e-4b29-8fc9-e0f1d3d95273 · outbound

This paper cites an unresolved cited work.

Understanding the well-rounded deformation retraction of Teichm\"uller space Unresolved cited work

Reference 1

Resolution
unresolved
no resolver link, observed 2026-08-15T16:23:47.273553Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T16:23:47.273553Z digest=sha256:366a2b07aae7f4b3ada55a6de0ef3810a5c6d334d2288758c6f9acf4fbf4543a

Observation 81c278bc-7990-4098-8019-9497a57b2b76 · outbound

This paper cites Small genus, small index critical points of the systole function.

Understanding the well-rounded deformation retraction of Teichm\"uller space Small genus, small index critical points of the systole function

Reference 2

Resolution
unresolved
no resolver link, observed 2026-08-15T16:23:47.279779Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T16:23:47.279779Z digest=sha256:43e1478284b9d5b93dff21ad59ec80b33f27939dceb80f072e2209944e601e5e

Observation 01501bd3-d614-47ee-bf36-107c54a7bf30 · outbound

This paper cites an unresolved cited work.

Understanding the well-rounded deformation retraction of Teichm\"uller space Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-15T16:23:47.881808Z

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=2026-08-15T16:23:47.285327Z digest=sha256:0d83d8b7b9f3ab2658e6f57f10ec6b928bd7c0aa635a57866951c1fb32df6dae

Observation 4700eb55-2816-46bd-94bb-aece194b7be6 · outbound

This paper cites Bestvina.

Understanding the well-rounded deformation retraction of Teichm\"uller space Bestvina

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.867803Z

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=2026-08-15T16:23:47.290942Z digest=sha256:4062d2acf70097965892780f6bc9b24edbcbcb9526b3c6bc92e35b858c390ffd

Observation dd31b855-c5d3-46ed-83c1-f574d724f9aa · outbound

This paper cites Bestvina, K.

Understanding the well-rounded deformation retraction of Teichm\"uller space Bestvina, K

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.854460Z

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=2026-08-15T16:23:47.295961Z digest=sha256:31d95f21d35a58132fc57ff13209b03f68f61883aea570571d07e068f285c0e6

Observation 35976da2-eca3-4eb1-bb93-7e7d82c85a24 · outbound

This paper cites Fortier Bourque.

Understanding the well-rounded deformation retraction of Teichm\"uller space Fortier Bourque

Reference 6

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.841727Z

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=2026-08-15T16:23:47.301048Z digest=sha256:df6e85d4ae6f1eaa87bdc5fe177497898507fcb402c4fca699326163c8344702

Observation 0f9340cb-8a23-44e1-92e6-405abd9053f8 · outbound

This paper cites Bridson and K.

Understanding the well-rounded deformation retraction of Teichm\"uller space Bridson and K

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.828940Z

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=2026-08-15T16:23:47.306797Z digest=sha256:04967172105bb5508839400035e86e7314d536a38ea89768181e895122db3802

Observation af49af64-dc19-4222-aff5-5411958f7dee · outbound

This paper cites Buser and P.

Understanding the well-rounded deformation retraction of Teichm\"uller space Buser and P

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.815801Z

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=2026-08-15T16:23:47.311715Z digest=sha256:f86f9b54bb7669e2456a0d614955ac1e61e151dcb3a4da31a7ce77ce1ab7a440

Observation a2aed448-9b8b-4da8-99ba-52c541355fd8 · outbound

This paper cites Elbaz-Vincent, H.

Understanding the well-rounded deformation retraction of Teichm\"uller space Elbaz-Vincent, H

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.802277Z

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=2026-08-15T16:23:47.319970Z digest=sha256:8b61169e5f8d904bfae61284e072016ad79ff969ad3e446594a7045d98987b11

Observation a0109314-e2c6-4731-9cdf-04e3e6d2ff29 · outbound

This paper cites Relative free splitting and free factor complexes I: Hyperbolicity.

Understanding the well-rounded deformation retraction of Teichm\"uller space Relative free splitting and free factor complexes I: Hyperbolicity

Reference 10

Resolution
unresolved
no resolver link, observed 2026-08-15T16:23:47.324019Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T16:23:47.324019Z digest=sha256:addb18860faea36b9956247f2f90223c9b5dac6f810084ef6d2f95da3ca86e0b

Observation 96e6a41e-6540-4f8c-9f0c-d78243057c57 · outbound

This paper cites an unresolved cited work.

Understanding the well-rounded deformation retraction of Teichm\"uller space Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-15T16:23:47.788542Z

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=2026-08-15T16:23:47.328563Z digest=sha256:02140aa117cb7532709e1cadc0b4b8f80b9316061f86b09fd538dabd423d65d1

Observation ffb42a38-ca33-40de-81e5-bd3afb7d5f93 · outbound

This paper cites Hatcher and K.

Understanding the well-rounded deformation retraction of Teichm\"uller space Hatcher and K

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.774810Z

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=2026-08-15T16:23:47.333913Z digest=sha256:290655eac135d8708b954dc8ff27c2f8490fac015bbfbf559e41fabbfe4f32ff

Observation ac0cce00-d0e0-431d-a270-4edcd3e1686e · outbound

This paper cites An equivariant deformation retraction of the Thurston spine.

Understanding the well-rounded deformation retraction of Teichm\"uller space An equivariant deformation retraction of the Thurston spine

Reference 13

Resolution
unresolved
no resolver link, observed 2026-08-15T16:23:47.338818Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T16:23:47.338818Z digest=sha256:b0546d59c0949dd80986d73af2c1670119eadc2c1729615157d28333ecf1513e

Observation 98955f5d-1b2d-410c-938e-2f65dc233646 · outbound

This paper cites In the tradition of Thurston, IV.

Understanding the well-rounded deformation retraction of Teichm\"uller space In the tradition of Thurston, IV

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.760601Z

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=2026-08-15T16:23:47.343917Z digest=sha256:78d4fbb77d0ad4051798ef47da6180f6fb15fc070cca8b0ea4a60e8d47bedebe

Observation 4e7aa990-18a8-4fc3-9eac-7e40b0b9313a · outbound

This paper cites Bulletin of the Australian Mathe- matical Society.

Understanding the well-rounded deformation retraction of Teichm\"uller space Bulletin of the Australian Mathe- matical Society

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.746458Z

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=2026-08-15T16:23:47.349466Z digest=sha256:ab091425e867e404541b6cffbd3b23192876d18c433974ad1232fdd3d02fbed1

Observation 350dce4f-611d-496a-a91f-6b0fde73d403 · outbound

This paper cites an unresolved cited work.

Understanding the well-rounded deformation retraction of Teichm\"uller space Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-15T16:23:47.731523Z

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.

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Observation 49757d7e-1852-4c1b-9c2c-7f75dc94b5cd · outbound

This paper cites Schmutz-Thurston Duality.

Understanding the well-rounded deformation retraction of Teichm\"uller space Schmutz-Thurston Duality

Reference 17

Resolution
verified exact
local_arxiv, observed 2026-08-15T16:23:47.470810Z

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=2026-08-15T16:23:47.358640Z digest=sha256:27383873660770b76315cf5a91e2231db6a80c95fd735cbbb2d113460cd2a28f

Observation eab93847-70a7-49ab-8632-563bdcc212d7 · outbound

This paper cites an unresolved cited work.

Understanding the well-rounded deformation retraction of Teichm\"uller space Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-15T16:23:47.717324Z

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=2026-08-15T16:23:47.364395Z digest=sha256:fb42437bd99ef97e33a3593148f476d64fd471564e2d339f3657a1ade9f41975

Observation c36a7b3d-2b3d-433e-9daf-f6ff918fac70 · outbound

This paper cites Kerckhoff.

Understanding the well-rounded deformation retraction of Teichm\"uller space Kerckhoff

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.702983Z

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=2026-08-15T16:23:47.369481Z digest=sha256:8fbf008c6ca2fd4a7917cb29513f34bfc7ad6170f126b3a3e7c2a5262d43a4d6

Observation 6378d5bd-f5c1-4336-b6d0-4c5a90bdc164 · outbound

This paper cites Lojasiewicz.

Understanding the well-rounded deformation retraction of Teichm\"uller space Lojasiewicz

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.688556Z

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=2026-08-15T16:23:47.373661Z digest=sha256:3c2827570e2cad2207d7bfd1a91687f6855c79172187bc6baa6ad937e97f9638

Observation 52d7b310-28d8-41e8-a652-ab8980d18a73 · outbound

This paper cites an unresolved cited work.

Understanding the well-rounded deformation retraction of Teichm\"uller space Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-15T16:23:47.674287Z

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=2026-08-15T16:23:47.377780Z digest=sha256:42f09d49534ec6471dd62b9aace3f435de22f3bd06cd74ee71f1cb8f43181b9a

Observation 6a17c3da-1415-4b81-9296-5b0b969da13c · outbound

This paper cites an unresolved cited work.

Understanding the well-rounded deformation retraction of Teichm\"uller space Unresolved cited work

Reference 22

Resolution
unresolved
raw_fallback, observed 2026-08-15T16:23:47.659642Z

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=2026-08-15T16:23:47.381697Z digest=sha256:63a8c2a1e95cdebc9710d6eaccc36047e3124cd07691281bc7e1632a6248275a

Observation a5a0537d-1490-4efa-a0c1-e58f310640b5 · outbound

This paper cites Penner and G.

Understanding the well-rounded deformation retraction of Teichm\"uller space Penner and G

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.643861Z

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=2026-08-15T16:23:47.385924Z digest=sha256:a91a168ece5ae46d97e7127c32111fdd3d0628b93eeae8aa2332aa18b5bfb48c

Observation 95c39bab-3c8b-469c-b30a-46cc17947256 · outbound

This paper cites Pettet and J.

Understanding the well-rounded deformation retraction of Teichm\"uller space Pettet and J

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.628078Z

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=2026-08-15T16:23:47.390147Z digest=sha256:a0d79c55fc5a9c77b14d2ef6920f3b93d501de8cfde978d31412e94015e172b1

Observation adbf6bf7-1122-4a47-8531-134374fdbaee · outbound

This paper cites Schmutz Schaller.

Understanding the well-rounded deformation retraction of Teichm\"uller space Schmutz Schaller

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.613537Z

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=2026-08-15T16:23:47.395895Z digest=sha256:a89c950afe41a4c32ecf2ffef530655377bc1f4f20d15680949b44e462fca55f

Observation b2814461-728a-4d45-92c3-d6c81cce364e · outbound

This paper cites Schmutz Schaller.

Understanding the well-rounded deformation retraction of Teichm\"uller space Schmutz Schaller

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-15T16:23:47.598546Z

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=2026-08-15T16:23:47.401581Z digest=sha256:7dba8cbdcb61e9928f6cf31321d39964d5da7cddb360d7f05ced1949f948f7b3

Observation a49ac3df-b2fb-4301-a05e-55b521704c81 · outbound

This paper cites an unresolved cited work.

Understanding the well-rounded deformation retraction of Teichm\"uller space Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-15T16:23:47.583660Z

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=2026-08-15T16:23:47.406540Z digest=sha256:e92ba35d38bd15593f55c04ffeb95226a842cc2e61c766e827835b992253b9ce

Observation 1ac16bae-3e85-4294-88cc-a897836ffa8e · outbound

This paper cites an unresolved cited work.

Understanding the well-rounded deformation retraction of Teichm\"uller space Unresolved cited work

Reference 28

Resolution
unresolved
raw_fallback, observed 2026-08-15T16:23:47.568731Z

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=2026-08-15T16:23:47.411929Z digest=sha256:2815d9af6979d3918e7163eed13a8cd0bed3d6d901d5baa15822ea68b7db00f2

Observation a7a539da-2d2b-4f48-b564-a9751bc9c756 · outbound

This paper cites Thurston.

Understanding the well-rounded deformation retraction of Teichm\"uller space Thurston

Reference 29

Resolution
unresolved
no resolver link, observed 2026-08-15T16:23:47.416894Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-15T16:23:47.416894Z digest=sha256:cea9db5e247507fd0ebbfc833672026803355d2affd59cea427d14c85dee1bb3

Observation bcdeb053-9751-43a6-ad24-738235a7e6f0 · outbound

This paper cites an unresolved cited work.

Understanding the well-rounded deformation retraction of Teichm\"uller space Unresolved cited work

Reference 30

Resolution
unresolved
raw_fallback, observed 2026-08-15T16:23:47.545852Z

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=2026-08-15T16:23:47.421539Z digest=sha256:ca7d97f5ba179d23f2fcc8d0e460abf1bdd6fc2bda17c31bb4451365715c2813

Observation 85404ae9-9c27-4fde-863e-023b3a471a9b · outbound

This paper cites an unresolved cited work.

Understanding the well-rounded deformation retraction of Teichm\"uller space Unresolved cited work

Reference 31

Resolution
unresolved
raw_fallback, observed 2026-08-15T16:23:47.531094Z

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=2026-08-15T16:23:47.426378Z digest=sha256:2179a698be67402ebac5271b1fc5fd3bf0f81478fb2d3a5b29a7a0ffa01cedd5

Pith citing papers

Observation 00c24a54-9757-4311-bc8a-f6cb3b66edfa · inbound

The diameter function is a topological Morse function cites this paper.

The diameter function is a topological Morse function Understanding the well-rounded deformation retraction of Teichm\"uller space

Reference 7

Resolution
verified exact
arxiv_id, observed 2026-07-04T07:39:39.687126Z

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=2026-06-26T12:55:45.826061Z digest=sha256:63cbc13c95172f7fe4a20afe5da4811abd7367108b8ef6a53c1b401b9868b964