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Paper Citation Record · LEDGER

Geometric Properties and Distance Inequalities on Grassmannians

As of 12 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 1 inbound Pith citation observation for arXiv:2412.15161.

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

pith.paper-citation-record.v1
2412.15161 v1

Coverage vector

measured 21 of 21 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T11:43:48.483561Z

measured 22 of 22 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 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T12:49:54.904298Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T12:49:56.088902Z

Reference resolution

21 of 21 outbound references displayed

  • verified exact0
  • verified fuzzy8
  • unresolved13
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation f37eb1ed-e2f0-4493-8531-65dba1fac6a5 · outbound

This paper cites Absil, R.

Geometric Properties and Distance Inequalities on Grassmannians Absil, R

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:43:48.816977Z

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=pdf_text observed=2026-08-11T11:43:48.389523Z digest=sha256:5932777df651e35adb82a053ae108fded63e3580fbee8937401c5980fa7a34b0

Observation b53e744c-de11-4667-b6a7-9c26a2622f69 · outbound

This paper cites Batzies, K.

Geometric Properties and Distance Inequalities on Grassmannians Batzies, K

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:43:48.805309Z

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=pdf_text observed=2026-08-11T11:43:48.395168Z digest=sha256:46ac44afd59beb551a141fce6665323c5ec84553519c9d76c9564bed0e6ce718

Observation ebeeedd3-2251-4e55-8c7b-1d155fc7e4bb · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 3

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.793169Z

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=pdf_text observed=2026-08-11T11:43:48.399673Z digest=sha256:7bdb52d8e6de5a453417f28e04ac373da05dc367ae70b19668e5f4c06f574429

Observation a5a5eb47-79c3-4f4a-9f47-a623409b7f5a · outbound

This paper cites Cheeger and D.

Geometric Properties and Distance Inequalities on Grassmannians Cheeger and D

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:43:48.780732Z

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=pdf_text observed=2026-08-11T11:43:48.404527Z digest=sha256:a604d9d8181d86c01cc92464d3cc5982591a4491eebf2369774bff2b72d63d9c

Observation 22894ec5-fedb-4347-b6ec-f584076b4148 · outbound

This paper cites Conde and G.

Geometric Properties and Distance Inequalities on Grassmannians Conde and G

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:43:48.767785Z

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=pdf_text observed=2026-08-11T11:43:48.408988Z digest=sha256:4197dfa46c6a90cf510011e592f8b7edbb113b8070b50d6514eae736651ba044

Observation bc345937-ae00-4d0d-97b7-865b96ef4b28 · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.754385Z

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=pdf_text observed=2026-08-11T11:43:48.413769Z digest=sha256:9dcc30827181f79c66aa067dc336d4eccc74bb9a469c2529689890b08d5872fb

Observation 6f89290c-31b8-42d3-81da-97df06ae7d98 · outbound

This paper cites Grove and H.

Geometric Properties and Distance Inequalities on Grassmannians Grove and H

Reference 7

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:43:48.741655Z

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=pdf_text observed=2026-08-11T11:43:48.418579Z digest=sha256:550c4c6b0b87cab7fdad34c40c66394d6eeb612e48753bfa6e20b7385d5bced8

Observation fa49b267-6ff9-4ef6-af4b-9f970e20b975 · outbound

This paper cites Helgason.

Geometric Properties and Distance Inequalities on Grassmannians Helgason

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:43:48.728048Z

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=pdf_text observed=2026-08-11T11:43:48.423028Z digest=sha256:d1b4ca25736d828c6da8de4d5599d8c6fe28566d6e676e5bb67cf9fd5a78ad58

Observation 00b64718-1b62-4abb-81f3-4dcfa4eee5fe · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 9

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.714626Z

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=pdf_text observed=2026-08-11T11:43:48.428236Z digest=sha256:39327e01e007bfba306008896432ca65c0bf23dd462afa7611915797c53106b4

Observation b62d450c-9a7b-4192-a238-d76fc63dc64b · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.702347Z

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=pdf_text observed=2026-08-11T11:43:48.432829Z digest=sha256:9fa54409136658362573d61711fc01dcc1d056053fee2bfa2990bee097ac1a03

Observation a0f58109-4f68-4676-a29f-84540cda0cdf · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.685785Z

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=pdf_text observed=2026-08-11T11:43:48.437099Z digest=sha256:7a0862cd3ae97059faf6323e9ef0e2e1f067bea29c64d3c7080bbb153633bc70

Observation fae9b621-4273-492c-aebc-f2fedb62926d · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 12

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.670134Z

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=pdf_text observed=2026-08-11T11:43:48.442620Z digest=sha256:13f76e64863f38a8d8a9af02b858cc225ed20d2b256f2670ea6bc61d06fa230d

Observation 27f741a5-fa56-40d1-af61-8eeb82634a72 · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 13

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.654086Z

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=pdf_text observed=2026-08-11T11:43:48.446818Z digest=sha256:ea05ccdf3d8a0c1d33f2986e5373319767530246b963f9eb32102d3e65072791

Observation be50b71a-e575-4974-ac61-b7a6f6c52c38 · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.635871Z

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=pdf_text observed=2026-08-11T11:43:48.451278Z digest=sha256:014ed82784ef9ed6cbd0b3a2c16ca0882fc0ec6dc338b3dc8e15e16efd69a4a0

Observation 64a2f46d-fad6-4174-a1f7-19be643e2114 · outbound

This paper cites Machado and F.

Geometric Properties and Distance Inequalities on Grassmannians Machado and F

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:43:48.623346Z

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=pdf_text observed=2026-08-11T11:43:48.455614Z digest=sha256:fd521a4b07a12d3a0aa560e3bb325e525d631ded28081d0dfcc9a702b3845f3d

Observation 7e3fdf04-8330-4be2-acfd-1bdd118ecf48 · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 16

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.610439Z

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=pdf_text observed=2026-08-11T11:43:48.461702Z digest=sha256:52a5427c8261845d702a4db49aa4afe35a5c34161f32ffe1d84926ba5c7370d8

Observation dd9ddc76-531d-4eaa-895a-d43963100f63 · outbound

This paper cites Pusz and S.

Geometric Properties and Distance Inequalities on Grassmannians Pusz and S

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:43:48.596210Z

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=pdf_text observed=2026-08-11T11:43:48.466294Z digest=sha256:28741a3a7a3ddea84363215fcdd1bf0ccec3b300899b12320dea9d49d734b2ab

Observation 38f247f0-7efc-44ba-85ba-faa6c51d3bf0 · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 18

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.577277Z

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=pdf_text observed=2026-08-11T11:43:48.470559Z digest=sha256:12fccb8409338559c1ab2cff0400ea6ae0f6aa0c39f4fbf83b54beb316e35d8f

Observation edab7bf8-8f9c-4b48-9782-0e9e8d9d250a · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 19

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.559219Z

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=pdf_text observed=2026-08-11T11:43:48.474918Z digest=sha256:f5c19e64430566ca4adec048b4cbd220f1f9257d3b60f6d1110bb8e52cd92b4d

Observation 06fb76c7-0780-4bfc-b9ae-ccc05b36733a · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.543670Z

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=pdf_text observed=2026-08-11T11:43:48.479178Z digest=sha256:98dd2e189f85b954fdc2988c4d700a948e61e33fed9e0078ced560e5a8a22459

Observation 02734692-1148-4ba8-a4b3-d20601aae152 · outbound

This paper cites an unresolved cited work.

Geometric Properties and Distance Inequalities on Grassmannians Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:43:48.527806Z

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=pdf_text observed=2026-08-11T11:43:48.483561Z digest=sha256:6626539d8d3e70aeebe8df1777aaf54e702c27d394a12e1335893517c3f75d55

Pith citing papers

Observation 59606cb7-ba2d-4614-8e48-2ddf0438319d · inbound

Color Image Set Recognition Based on Quaternionic Grassmannians cites this paper.

Color Image Set Recognition Based on Quaternionic Grassmannians Geometric Properties and Distance Inequalities on Grassmannians

Reference 30

Resolution
metadata mismatch
local_arxiv, observed 2026-08-07T12:49:56.163919Z

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=pdf_text observed=2026-08-07T12:49:54.904298Z digest=sha256:1f56740e58b6b383b7d5b4e1bfa27abb1a8425e90f0f9f8eb036c1b841563ef3