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Paper Citation Record · LEDGER

On the Geometry of Positional Encodings in Transformers

As of 10 August 2026, this Paper Citation Record lists 13 of 13 outbound references and 0 inbound Pith citation observations for arXiv:2604.05217.

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

pith.paper-citation-record.v1
2604.05217 v1

Coverage vector

measured 13 of 13 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-10T19:03:38.644144Z

measured 13 of 13 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

13 of 13 outbound references displayed

  • verified exact1
  • verified fuzzy1
  • unresolved10
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f173044b-06e9-4e49-ba43-c35674995400 · outbound

This paper cites an unresolved cited work.

On the Geometry of Positional Encodings in Transformers Unresolved cited work

Reference 1

Resolution
unresolved
raw_fallback, observed 2026-05-16T09:12:40.790278Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:271838f2523660b991a013d20ca412aa96a56c1078d0d7b2792209044ce125d8

Observation 7585c774-a75a-45d3-a53b-d4c24287646d · outbound

This paper cites an unresolved cited work.

On the Geometry of Positional Encodings in Transformers Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-05-16T09:12:40.781763Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:cf89bdef161b72e04bece40a818242f35f1079f5da1b208388696d73dc710d8e

Observation 8274ed31-fbb2-4b0b-b84c-3207e95ba3aa · outbound

This paper cites an unresolved cited work.

On the Geometry of Positional Encodings in Transformers Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-05-16T09:12:40.773766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:3c0812d242bc1f77b85ba032d19662bac6c565a101a904378ba31915d078f418

Observation 85523676-9786-4b2e-80a8-a9f81ddd6891 · outbound

This paper cites an unresolved cited work.

On the Geometry of Positional Encodings in Transformers Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-05-16T09:12:40.787474Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:714a373ad2e78994e6d4e201f0b2ae9c175e596fe45bcee41244e51f37c07fb5

Observation 6bb80831-fbb1-4690-af13-0a93a509d4d5 · outbound

This paper cites an unresolved cited work.

On the Geometry of Positional Encodings in Transformers Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-05-16T09:12:40.776420Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:3d01c0ac2c745a9166ce5ba21af9745c27732a1dfed1ed4d5a482892c952ba8b

Observation 4ce85deb-125a-4a62-b8ab-2ae2f6edf4d8 · outbound

This paper cites an unresolved cited work.

On the Geometry of Positional Encodings in Transformers Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-05-16T09:12:40.771073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:aca375fb5fd943ecb98e20db0365f8dcc3a28f86832ed2e6151e7e76bf9f8a35

Observation aaf58418-b376-432a-a957-89911c99c16d · outbound

This paper cites an unresolved cited work.

On the Geometry of Positional Encodings in Transformers Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-05-16T09:12:40.784640Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:7f16095b9eefd0e52205a04edf3142cb9d7392b1f99dd85c17c71ab443ba26ad

Observation b385e4f0-f8ad-4266-9705-12d133d7ad87 · outbound

This paper cites 2024 , issn =.

On the Geometry of Positional Encodings in Transformers 2024 , issn =

Reference 8

Resolution
metadata mismatch
arxiv_id, observed 2026-05-10T19:05:44.977487Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:d2babc9c716b3347f00904ab82de805cf34898ad62848e904976a502d6ddc944

Observation 044fa230-b971-47f8-87a7-ca421b8bd892 · outbound

This paper cites an unresolved cited work.

On the Geometry of Positional Encodings in Transformers Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-05-16T09:12:40.779089Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:b1c7be07fd4deb243f83a9fb5bde75d5fe697300e78930ea938ecf255323ff6c

Observation 49d6f12f-8a31-4262-8591-ae6ba8595cde · outbound

This paper cites an unresolved cited work.

On the Geometry of Positional Encodings in Transformers Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-05-16T09:12:40.765332Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:58af9857c54f308b13a294104ae8be9c2b0db5b92ddd639fa7c02c0fbf6883a1

Observation 7781906e-9c3e-4206-ac07-ad59b4ed94f9 · outbound

This paper cites an unresolved cited work.

On the Geometry of Positional Encodings in Transformers Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-05-16T09:12:40.768625Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:3ce5740c315a44cba3315e404b94bfaac66f5e33459907901f8c85fcb3aa629b

Observation 27ccfb26-f977-4484-962f-79e5c5fa61f0 · outbound

This paper cites (2022).The Principles of Deep Learning Theory: An Effective Theory Approach to Understanding Neural Networks.

On the Geometry of Positional Encodings in Transformers (2022).The Principles of Deep Learning Theory: An Effective Theory Approach to Understanding Neural Networks

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-05-16T09:12:40.762163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:ee20a2071bace37c7f7bbba4c969a3268089665e28f1cdce064e1517d68bbdad

Observation 181927dd-3e5a-4b82-947f-5b7398ce1a53 · outbound

This paper cites The geometry of BERT.

On the Geometry of Positional Encodings in Transformers The geometry of BERT

Reference 13

Resolution
verified exact
arxiv_id, observed 2026-05-10T23:30:52.527120Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

source=pdf_text observed=2026-05-10T19:03:38.644144Z digest=sha256:7094f2e509dbde94b7b882fcb042bd2072c294a701499a6b58c4b5d14e9ed8c5

Pith citing papers

No inbound Pith citation observations are available.