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Paper Citation Record · LEDGER

Symmetric shift-invariant subspaces and harmonic maps

As of 16 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:1908.01557.

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

pith.paper-citation-record.v1
1908.01557 v2

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-14T15:23:44.543849Z

measured 21 of 21 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 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

21 of 21 outbound references displayed

  • verified exact1
  • verified fuzzy12
  • unresolved8
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3481ad99-8fa3-4380-9a06-7120bb0dfce4 · outbound

This paper cites Harmonic maps and shift-invariant subspaces.

Symmetric shift-invariant subspaces and harmonic maps Harmonic maps and shift-invariant subspaces

Reference 1

Resolution
verified exact
local_arxiv, observed 2026-08-14T15:23:44.581153Z

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=2026-08-14T15:23:43.827113Z digest=sha256:2fce95eaeb29c12678a1045ee91070381969b8971308c5cee7bc6770d932cad7

Observation 0db57cc7-0f2f-4c35-8349-fa84f98925e4 · outbound

This paper cites Black, Harmonic maps into homogeneous spaces , Pitman Res.

Symmetric shift-invariant subspaces and harmonic maps Black, Harmonic maps into homogeneous spaces , Pitman Res

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:23:45.850379Z

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=2026-08-14T15:23:43.852822Z digest=sha256:77f0ccdde3b7a63d9f0f968f60aaf35932f9419bf98c6dc86525064bc307cc2b

Observation 231cf52e-bd6b-47c4-8fa8-fe6af6908bc5 · outbound

This paper cites an unresolved cited work.

Symmetric shift-invariant subspaces and harmonic maps Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:23:45.752118Z

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=2026-08-14T15:23:43.980437Z digest=sha256:7f968c835a039d23cab7d6d152227211137dbbf9edc853b054c774f560f927de

Observation dc2f9f6d-5c49-4ab5-986e-cfa5ee936654 · outbound

This paper cites an unresolved cited work.

Symmetric shift-invariant subspaces and harmonic maps Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:23:45.739733Z

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=2026-08-14T15:23:44.066653Z digest=sha256:ebd7fecb2b939d820f9391a7e2ffddb39e2c7ab4a7b75d05e0df2ee14eafc2fe

Observation bb4f5f7d-709c-4642-bb47-937b4cd25c02 · outbound

This paper cites an unresolved cited work.

Symmetric shift-invariant subspaces and harmonic maps Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:23:45.724053Z

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=2026-08-14T15:23:44.098570Z digest=sha256:3946f4ec0214e441e485d7acd61933338132616e5d6e26f99d6a5c0e34c54646

Observation 2ee3e800-e945-46ef-8eb9-605c53538dd3 · outbound

This paper cites an unresolved cited work.

Symmetric shift-invariant subspaces and harmonic maps Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:23:45.710660Z

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=2026-08-14T15:23:44.122667Z digest=sha256:79a20b1be9d5fb30975e1a4e8cb2fb934f34a69885629f1f54a6289edc746c4d

Observation 6139a57f-d5d2-4c7a-ac3c-9fcefe55cc18 · outbound

This paper cites Correia and R.

Symmetric shift-invariant subspaces and harmonic maps Correia and R

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:23:45.504742Z

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=2026-08-14T15:23:44.138724Z digest=sha256:5f4ebeb0894d50aa197f0e67de5cb9b477520cef899a11d58e62783c42a76801

Observation 1030463a-f0d1-4b9f-840c-80672d6e48d9 · outbound

This paper cites Dorfmeister, F.

Symmetric shift-invariant subspaces and harmonic maps Dorfmeister, F

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:23:45.411794Z

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=2026-08-14T15:23:44.144364Z digest=sha256:09aa64f714c4d52cbc4205d4d7e05638bb843f7766b8724c18aab862073f15ff

Observation 442afd7b-474f-4e94-a168-384ee722e698 · outbound

This paper cites Eells and L.

Symmetric shift-invariant subspaces and harmonic maps Eells and L

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:23:45.396322Z

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=2026-08-14T15:23:44.148234Z digest=sha256:04abd66b104692fe18cab7daef8ea340cf7a5cad94914fe99fab92114c6a85c8

Observation d43700be-c577-49af-916a-340fee99e81b · outbound

This paper cites an unresolved cited work.

Symmetric shift-invariant subspaces and harmonic maps Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:23:45.381834Z

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=2026-08-14T15:23:44.151895Z digest=sha256:4e8626e6c92d2f0c8f04a0f97e8c09f49498b06fd6b25102de0f37da0825b890

Observation 3dde951f-82d2-4c37-91ff-f7fa6ce36221 · outbound

This paper cites Helson, Lectures on invariant subspaces.

Symmetric shift-invariant subspaces and harmonic maps Helson, Lectures on invariant subspaces

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:23:45.291821Z

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=2026-08-14T15:23:44.156519Z digest=sha256:d97ad020a69b9a95cae1dbab2306453147725acdb95bb332b8eda32d071d4fe2

Observation 3896a947-2e9b-4531-8a2d-9cd210caffd0 · outbound

This paper cites an unresolved cited work.

Symmetric shift-invariant subspaces and harmonic maps Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:23:45.075928Z

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=2026-08-14T15:23:44.160683Z digest=sha256:21c901f815f24545cebdcc7b87ef504e8e63b11310a3c3663188f53c4903348c

Observation ca324098-20cc-49da-91ea-6f9aedfce647 · outbound

This paper cites an unresolved cited work.

Symmetric shift-invariant subspaces and harmonic maps Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:23:44.986028Z

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=2026-08-14T15:23:44.164802Z digest=sha256:39b3bbe3dafa5cace85c892f4588b243840efdf4514ab9d267bab846b2015b03

Observation f54c4bf4-903e-4f56-9a5e-9c73906bfbd2 · outbound

This paper cites Pacheco, Twistor fibrations giving primitive harmonic maps of finite t ype, Int.

Symmetric shift-invariant subspaces and harmonic maps Pacheco, Twistor fibrations giving primitive harmonic maps of finite t ype, Int

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:23:44.881342Z

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=2026-08-14T15:23:44.168839Z digest=sha256:cbf1ff46e6ebf644fdc6296fb5cd5aece146b2c05dd564b9dff0e0a876f92aa6

Observation 1de4ef9c-83bb-4566-a813-d4d148b018e6 · outbound

This paper cites Pacheco, On harmonic tori in compact rank one symmetric spaces , Diff.

Symmetric shift-invariant subspaces and harmonic maps Pacheco, On harmonic tori in compact rank one symmetric spaces , Diff

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:23:44.844535Z

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=2026-08-14T15:23:44.172573Z digest=sha256:cbe2449ed6eed33e919fc178638c8f87a17ab7313fd40be7360d5ca5126e1ebb

Observation e1cbc0a8-450d-4e32-8f6b-bead94542b8e · outbound

This paper cites Pressley and G.

Symmetric shift-invariant subspaces and harmonic maps Pressley and G

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:23:44.829744Z

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=2026-08-14T15:23:44.176675Z digest=sha256:79f5cb0075078d2a80735c958f8e12920373098e46df1d41a6966c1d88397b79

Observation 867b477b-fa00-4051-a209-795bfcbd7ec1 · outbound

This paper cites Segal, Loop groups and harmonic maps , Advances in homotopy theory (Cortona, 1988), 153–164, London Math.

Symmetric shift-invariant subspaces and harmonic maps Segal, Loop groups and harmonic maps , Advances in homotopy theory (Cortona, 1988), 153–164, London Math

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:23:44.813448Z

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=2026-08-14T15:23:44.234034Z digest=sha256:79030cc107232ba9d00514439c86af26dc58081135328bc0293d7e8b0572eff4

Observation a70058a9-61e0-4cae-ab30-2b6148d410e5 · outbound

This paper cites Svensson and J.

Symmetric shift-invariant subspaces and harmonic maps Svensson and J

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:23:44.797936Z

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=2026-08-14T15:23:44.330005Z digest=sha256:a2ba57e41380c5322326cc66d801eefe0eb67a574f822fa97c06e91d0edff403

Observation 554831a8-9ea5-4283-883b-7ffef303d6ce · outbound

This paper cites Uhlenbeck, Harmonic maps into Lie groups: classical solutions of the ch iral model, J.

Symmetric shift-invariant subspaces and harmonic maps Uhlenbeck, Harmonic maps into Lie groups: classical solutions of the ch iral model, J

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:23:44.754168Z

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=2026-08-14T15:23:44.411800Z digest=sha256:b28b8279cd9f2c256ef2b0e706e18d24d58825e43db1007d30e0f98506dd25ce

Observation c1970ce5-9beb-421c-ad1b-e4454ab51620 · outbound

This paper cites Urakawa, Calculus of Variations and Harmonic Maps , Translations of Math.

Symmetric shift-invariant subspaces and harmonic maps Urakawa, Calculus of Variations and Harmonic Maps , Translations of Math

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-14T15:23:44.611828Z

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=2026-08-14T15:23:44.500287Z digest=sha256:9a39c9649364ddf07d96fb73a92f24b55c4e47d0ef3057e91b2ab8199dbd95b6

Observation c054e286-a678-41d1-a56b-497cffd8dbb0 · outbound

This paper cites an unresolved cited work.

Symmetric shift-invariant subspaces and harmonic maps Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-14T15:23:44.597068Z

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=2026-08-14T15:23:44.543849Z digest=sha256:08c853cae0a7bc85b983e38adf74ad4fdce45bb04941edf21e083ac9651503a5

Pith citing papers

No inbound Pith citation observations are available.