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Paper Citation Record · LEDGER

Special Cycle on Shtukas and Categorical Trace

As of 12 August 2026, this Paper Citation Record lists 27 of 27 outbound references and 0 inbound Pith citation observations for arXiv:2509.05526.

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

pith.paper-citation-record.v1
2509.05526 v1

Coverage vector

measured 27 of 27 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-05T05:29:45.386729Z

measured 27 of 27 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-12T06:34:41.77262+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

27 of 27 outbound references displayed

  • verified exact0
  • verified fuzzy12
  • unresolved15
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 1c070a46-76e7-4021-b93e-b534b5c4d9f0 · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.623870Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.318937Z digest=sha256:4e7c2c77328c33f0936cb274e01a74ee860298e07cee3e525c615ca3b9978efa

Observation 93b1d627-ce4e-401f-b6fb-a2e1694c9087 · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.616337Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.322026Z digest=sha256:489613470c588831756a62cd66346cd385d777ea6b322af745c3c37f8e03f9a2

Observation efbc5a4d-a128-45c6-b897-6fe0a93385bc · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.609724Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.324828Z digest=sha256:5c62d39e067586f88d8d9247a0b303fa11e295dd63cab50913f5e948e11b9f49

Observation 502735a4-69f2-4c67-9084-4379d7fb3c2a · outbound

This paper cites 8, 1724--1765.

Special Cycle on Shtukas and Categorical Trace 8, 1724--1765

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:29:45.602506Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.327315Z digest=sha256:ae58620bddbcf9cb2b99c3a52e4f1c6e67eb3ddf5e878ba435b53c32e4b61022

Observation d937ec35-77ef-452a-8747-5e99fb33a89b · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.594681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.330432Z digest=sha256:f78561bb14227b7726e445a05dd6b5f6d7a38498b02a3977984f578e3b0a900d

Observation 42db3d07-4e64-4227-b0c4-641f382a7a7e · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.587216Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.333159Z digest=sha256:fedf9170fad83753296b41cd042769c29b8de555da873c22b354e0bfa3c825d1

Observation 3f71fa09-845c-456b-9c66-39bdb9ec3809 · outbound

This paper cites 2, 367--417.

Special Cycle on Shtukas and Categorical Trace 2, 367--417

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:29:45.579623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.335799Z digest=sha256:fba0c9955509ff1a988f648723a1e45f3648def6d4942a81628c6d863ca8d7bd

Observation f1e1510a-2e6a-4be2-bcf1-c69336a79a21 · outbound

This paper cites Khan, Modularity of higher theta series II : C how group of the generic fiber , 2024.

Special Cycle on Shtukas and Categorical Trace Khan, Modularity of higher theta series II : C how group of the generic fiber , 2024

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:29:45.571718Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.338320Z digest=sha256:b62449f2e6a62a4b6465d7f1dd4c86e526a02434dce09e2c01e7103efbac87ff

Observation f35e2bd8-a577-4916-b56d-cda01aed9694 · outbound

This paper cites 2, 683--729.

Special Cycle on Shtukas and Categorical Trace 2, 683--729

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:29:45.562457Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.340849Z digest=sha256:6602fc8805c8beb53b5c14446e6e5718ca9c70b8941afbe5519771af2b7c0f3f

Observation d540bfea-ec38-41d9-949f-b0ba7881426f · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.554743Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.343683Z digest=sha256:737afc945d3982c2ca3dcdc9225870529223844221d7f04204871c348242e89f

Observation 70f45cc4-c20b-42b4-bf4c-ea214ed9022a · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.547112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.346250Z digest=sha256:b440f19895f5b77d2bd1686d3e3d036b6b0ea037afcb45dc2a0fb568e6cf0ba9

Observation e970bb11-5df5-45ec-8606-c7436821bfad · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.539643Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.348513Z digest=sha256:4138bc6bbe8c9dae11f05f9cd2dabade27a7833cd38f4b9da4f252ec3e89eda0

Observation 6991034a-ba1b-4a59-bf0d-b37d60ed3115 · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.531864Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.351426Z digest=sha256:d21299eeb68f6396abc08cfd970f8958caf29525349a7daed33fa92d73c6f7e2

Observation b15e8cdf-a274-4039-97db-ccf2de087e8a · outbound

This paper cites Gross and Don B.

Special Cycle on Shtukas and Categorical Trace Gross and Don B

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:29:45.523172Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.354101Z digest=sha256:1d60debaf6bb19744ce625ad41fd28d560a954d5d6f89b63fb58a6fe69f3a56d

Observation 90e485cc-e318-4335-8c24-c5daebab6ab8 · outbound

This paper cites 107, American Mathematical Soc., 2003.

Special Cycle on Shtukas and Categorical Trace 107, American Mathematical Soc., 2003

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:29:45.514645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.356676Z digest=sha256:94f105e4010e4c82f48118bd1c685333dbaf81142dafca28e61f6286d572a12d

Observation 88ef1c49-dd7c-4b7a-bb20-57ca3268f7be · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.507158Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.359321Z digest=sha256:c6d6d9c15969caac656ec0c654f59d36999b7f413e4a31d3f5eb3154f40c5650

Observation c0879a42-a312-41fb-9e1c-76e7e3624685 · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 17

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.498860Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.361701Z digest=sha256:5c1eb2e7ce217542a6dcfd3a485fc1ee5b8dcd7c939c95ff63f2d136494be879

Observation 7cc2a7d5-518a-4388-934c-a7ecb1bcc643 · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.491215Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.364113Z digest=sha256:8a479cafa945c0a19a54c62f3c4f27310b815929707b6e1b4c4562577420323a

Observation 54287ca0-4552-4e44-a245-93198813a55f · outbound

This paper cites 10, Cambridge University Press, 2022, p.

Special Cycle on Shtukas and Categorical Trace 10, Cambridge University Press, 2022, p

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:29:45.482572Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.367042Z digest=sha256:d218e58cc84140bea20abf5322bf7250f318b43c896ea4a0cc94cdff6c768730

Observation ef443707-71c9-482b-933d-707a02ed6de7 · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.474132Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.369543Z digest=sha256:82c5e7f05593927b3201da3fb552435f7e02f2c33b1887db5b7baa45d5befcca

Observation 32970171-dbe1-4ee6-bae9-d6417a6c59d9 · outbound

This paper cites 3, 799--910.

Special Cycle on Shtukas and Categorical Trace 3, 799--910

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:29:45.466422Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.371976Z digest=sha256:e8df7c220834ef3f05f939e98769836e0c81c6b3f8a413c53f2fee0612f82f59

Observation f155cc8d-be7a-4dcd-b76d-43c7879e2b86 · outbound

This paper cites 1, 271--319.

Special Cycle on Shtukas and Categorical Trace 1, 271--319

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:29:45.457365Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.374497Z digest=sha256:e4b2f9500f4b753710a73d0d8607da54a9755c5210d9ceb279babeeeae8e3e20

Observation aa58b31c-870c-4a2c-bd0d-3b71dbc4ea11 · outbound

This paper cites 5, 2203--2220.

Special Cycle on Shtukas and Categorical Trace 5, 2203--2220

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:29:45.448141Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.376938Z digest=sha256:ac3c01b451427b703bd14ad1667eb9ed9b4c4d6eb90e0e969d51c7058f85ca4b

Observation b86f7924-a30a-467e-9887-1d2f3a987848 · outbound

This paper cites 3, 767 -- 911.

Special Cycle on Shtukas and Categorical Trace 3, 767 -- 911

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:29:45.439792Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.379154Z digest=sha256:f24978768493e124835f7dc2f544c2ae3b14e9ec8b00356b7d08cdcf4052b2b9

Observation d9229fd9-54e0-456b-98fb-13ed9b87b5c9 · outbound

This paper cites 2, 393--526.

Special Cycle on Shtukas and Categorical Trace 2, 393--526

Reference 25

Resolution
verified fuzzy
raw_fallback, observed 2026-08-05T05:29:45.431751Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.381353Z digest=sha256:bc94325aa19a618c6b2435d0bbe6aadceab0537153f82d97a4507690cd0e956b

Observation 1fa91d19-fc6a-4716-a234-54bb5e5bb0fc · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 26

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.422175Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.383885Z digest=sha256:8cead6f751cf2bc095313c989f48e4f4977eadc159786039f41f0766d7756846

Observation 872aa1c7-afb1-47a6-8552-52322e3f6948 · outbound

This paper cites an unresolved cited work.

Special Cycle on Shtukas and Categorical Trace Unresolved cited work

Reference 27

Resolution
unresolved
raw_fallback, observed 2026-08-05T05:29:45.412735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-12T06:34:41.77262+00:00.

source=arxiv_source observed=2026-08-05T05:29:45.386729Z digest=sha256:7e0ef30784c3eb67d5aa7febcb5784095ea870c2360f21e12186771f11d0f4b1

Pith citing papers

No inbound Pith citation observations are available.