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Paper Citation Record · LEDGER

Comfortability of quantum walks on embedded graphs on surfaces

As of 18 August 2026, this Paper Citation Record lists 24 of 24 outbound references and 1 inbound Pith citation observation for arXiv:2501.06765.

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

pith.paper-citation-record.v1
2501.06765 v2

Coverage vector

measured 24 of 24 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-10T21:03:50.173518Z

measured 25 of 25 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-18T06:34:40.430872+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-02T01:25:40.012201Z

measured 0 of 1 external citation measurements

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

Source: cited_works

Reference resolution

24 of 24 outbound references displayed

  • verified exact1
  • verified fuzzy14
  • unresolved9
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 58553248-9c9c-4baf-87ba-9c09d299a83d · outbound

This paper cites and Watrous, J., One-dimensional quantum walks, Proc.

Comfortability of quantum walks on embedded graphs on surfaces and Watrous, J., One-dimensional quantum walks, Proc

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.874270Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:49.562533Z digest=sha256:3a87a946b884ceeb762ba0981a23cd14b6785deeb88d1bfa30950cbfc4370172

Observation 30a1fe6f-09a9-4128-b308-106c46855330 · outbound

This paper cites and Sarlette, A., Quantum fast-forwarding; Markov chains and graph property testing, Quantum Information and Computation 19 (2019) 181–213.

Comfortability of quantum walks on embedded graphs on surfaces and Sarlette, A., Quantum fast-forwarding; Markov chains and graph property testing, Quantum Information and Computation 19 (2019) 181–213

Reference 2

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.847686Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:49.614752Z digest=sha256:d34e9cb21415ae6fa109b890c7a926ba82fad5c008c6d3481e9065ad0c24260f

Observation ea6fe20e-c0fe-4430-bc27-d4889be17c14 · outbound

This paper cites and Kokainis, M., Quadratic speedup for finding marked vertices by quantum walks, Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing 19 (2020) 412–424.

Comfortability of quantum walks on embedded graphs on surfaces and Kokainis, M., Quadratic speedup for finding marked vertices by quantum walks, Proceedings of the 52nd Annual ACM SIGACT Symposium on Theory of Computing 19 (2020) 412–424

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.824561Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:49.638763Z digest=sha256:404687bc49b50da2292a55cd64397ab8a3448aa5ca8eb99f3471c237b0b4c887

Observation cd850c2a-5498-4888-8e8f-22561536dd13 · outbound

This paper cites an unresolved cited work.

Comfortability of quantum walks on embedded graphs on surfaces Unresolved cited work

Reference 4

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:03:50.794726Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:49.671954Z digest=sha256:824cb37bcbc0ff89a227701ee2d7b9c413cd868b8fa8dce457c64ac7996f5862

Observation e3d75d1d-a2fb-4435-a1e7-f648bb46aace · outbound

This paper cites an unresolved cited work.

Comfortability of quantum walks on embedded graphs on surfaces Unresolved cited work

Reference 5

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:03:50.767788Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:49.714754Z digest=sha256:501bf98b20ea53d0b5887d884c333638cea020548912ebdea17b169b14b11b4f

Observation 4ae428d6-511f-4d18-846f-20f91665fdd8 · outbound

This paper cites an unresolved cited work.

Comfortability of quantum walks on embedded graphs on surfaces Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:03:50.750302Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:49.756130Z digest=sha256:0913d1167f672dcfdd6e72d5bd54e6ea83200b5eb201b548b62b40e5f72450d9

Observation 8873b3b4-1bf3-4c69-baea-ff02dfa1300f · outbound

This paper cites an unresolved cited work.

Comfortability of quantum walks on embedded graphs on surfaces Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:03:50.731037Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:49.804775Z digest=sha256:5888da5d2f34c852e590c7e0f47264410b6fdd8532ec06ccd49524b593872b24

Observation 71627f4d-415c-45cb-a05e-1e392235a3e1 · outbound

This paper cites an unresolved cited work.

Comfortability of quantum walks on embedded graphs on surfaces Unresolved cited work

Reference 8

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:03:50.711689Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:49.844764Z digest=sha256:968ad6764b0385577cc12538291a2ccf023125aac475a3cf091ab83b40072ccd

Observation f4f8f626-65aa-4f96-b927-f9bd9c1596ac · outbound

This paper cites Higuchi, N.

Comfortability of quantum walks on embedded graphs on surfaces Higuchi, N

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.691163Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:49.897078Z digest=sha256:abd6a0474ecc21e488bfe3b57436fcfe95eaa92347229f47f2d9489bf89c0d1d

Observation 4ddf30c1-5860-445e-b690-c3e668bfef8e · outbound

This paper cites and Segawa, E., Dynamical system induced by quantum walks, Journal of Physics A: Mathematical and Theoretical 52 (2019) 39520.

Comfortability of quantum walks on embedded graphs on surfaces and Segawa, E., Dynamical system induced by quantum walks, Journal of Physics A: Mathematical and Theoretical 52 (2019) 39520

Reference 10

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.675853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:49.924637Z digest=sha256:d6c35dfa5b9e0e62ffb520c2222be9f75009aced6925d5371f41fea6c98364cb

Observation 67699c04-66bd-4886-a0ff-477ab373a0f7 · outbound

This paper cites and Segawa, E., Circuit equation of Grover walk, Annales Henri Poincar´ e25 (2024) 3739–3777.

Comfortability of quantum walks on embedded graphs on surfaces and Segawa, E., Circuit equation of Grover walk, Annales Henri Poincar´ e25 (2024) 3739–3777

Reference 11

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.661004Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:49.964944Z digest=sha256:21390fab5ead0e3b38e58f265978d9e6e7416975ea8ed472d3b10af900d42ab8

Observation 7f7e5525-2dfe-4201-a389-a57415260b5a · outbound

This paper cites Quantum walks on graphs embedded in orientable surfaces.

Comfortability of quantum walks on embedded graphs on surfaces Quantum walks on graphs embedded in orientable surfaces

Reference 12

Resolution
verified exact
local_arxiv, observed 2026-08-10T21:03:50.241210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:49.987924Z digest=sha256:090efb74a5f69f23696ef0622f2ea122d9e008c6d2e311d21386deb011908775

Observation f9904cb4-bc7e-41d2-88c2-ece351724b12 · outbound

This paper cites and Shirai, T., Weak Bloch property for discrete magnetic Schr¨ odinger operators, Nagoya Mathematical Journal 161 (2001) 127–154.

Comfortability of quantum walks on embedded graphs on surfaces and Shirai, T., Weak Bloch property for discrete magnetic Schr¨ odinger operators, Nagoya Mathematical Journal 161 (2001) 127–154

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.643000Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:50.002304Z digest=sha256:8de083900ef12f20c02c246da8f0985d1cf5c98eee156bdcd55109a86c09db8e

Observation a5f01169-2710-4bd4-9256-839143b6753e · outbound

This paper cites an unresolved cited work.

Comfortability of quantum walks on embedded graphs on surfaces Unresolved cited work

Reference 14

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:03:50.620545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:50.020641Z digest=sha256:b78337eafff08ffd1fc475402f73950d5ed2cc7f09c1be91ab821325679c8d63

Observation f7c85ed2-25ba-4297-bc4b-8b2e6bf52504 · outbound

This paper cites and Segawa, E., Partition-based discrete-time quantum walks, Quantum Information Processing 17 (2018) 1–35.

Comfortability of quantum walks on embedded graphs on surfaces and Segawa, E., Partition-based discrete-time quantum walks, Quantum Information Processing 17 (2018) 1–35

Reference 15

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.599564Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:50.035735Z digest=sha256:0648fedea79c4011c3a8ca536fe2d1ae427b287237a59e3b1cb7a110776f8042

Observation f3c8c55f-a42d-4240-adc3-69c680c7ebc7 · outbound

This paper cites and Brun, T.

Comfortability of quantum walks on embedded graphs on surfaces and Brun, T

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.574811Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:50.052686Z digest=sha256:f355f532461271e68c3e123e49b4f491e0e29724d7b0cba6479d78ddf46233d2

Observation ae8923cd-47ae-4dfa-95c2-b263f1473b29 · outbound

This paper cites and Segawa E., Implementation of a discrete-time quantum walk with a circulant matrix on a graph by optical polarizing elements, Physical Review A 106 (2022) 022402.

Comfortability of quantum walks on embedded graphs on surfaces and Segawa E., Implementation of a discrete-time quantum walk with a circulant matrix on a graph by optical polarizing elements, Physical Review A 106 (2022) 022402

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.543228Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:50.080068Z digest=sha256:d675365725675d4705ff73ca7dcc469fb19d82523692c042c682c4058ddca1d6

Observation 9fe0ca77-0958-4a8c-89f2-0633ce026b4b · outbound

This paper cites and Thomassen, C., Graphs on Surfaces, Johns Hopkins University Press (2001).

Comfortability of quantum walks on embedded graphs on surfaces and Thomassen, C., Graphs on Surfaces, Johns Hopkins University Press (2001)

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.512414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:50.086627Z digest=sha256:56807eb22f9834e052965bce6b7e09db5e1aabb4b41572ec9081e3b4dc28469f

Observation 4b7522a1-8e5b-42ca-a871-a032d400568d · outbound

This paper cites Kyokumenjou no Gurahu Riron.

Comfortability of quantum walks on embedded graphs on surfaces Kyokumenjou no Gurahu Riron

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.478623Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:50.097672Z digest=sha256:fcb46f17bb88b01767fb81963fec732f4595ce1fdcd6836bfc3994dcb0600f76

Observation 463de00b-1906-40b4-b174-eccece2c7445 · outbound

This paper cites an unresolved cited work.

Comfortability of quantum walks on embedded graphs on surfaces Unresolved cited work

Reference 20

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:03:50.455549Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:50.107453Z digest=sha256:672403e26e939284b4b67341d2e2f854cbf7fdeb44001578e792bc5246ddf6ad

Observation c546120b-c961-41fb-a378-904188b7a898 · outbound

This paper cites an unresolved cited work.

Comfortability of quantum walks on embedded graphs on surfaces Unresolved cited work

Reference 21

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:03:50.404162Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:50.117746Z digest=sha256:8e25486d7f8354d72575a3054fc928f5b1f6895b2a4145ffe0fcf2e9566297f6

Observation 90ac1679-df46-4f29-ac7c-a1a61487daaa · outbound

This paper cites and Youngs, J.

Comfortability of quantum walks on embedded graphs on surfaces and Youngs, J

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.337691Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:50.145901Z digest=sha256:beaa617b549e288b085d91d8194f9cd34692edb966e48173f006439710b0ca89

Observation 46e56186-dea0-4305-94f3-04cbfd7afe95 · outbound

This paper cites Tanner, From quantum graphs to quantum random walks, Non-Linear Dynamics and Fundamental Interactions NATO Science Series II: Mathematics, Physics and Chemistry, 213 (2006) 69-87.

Comfortability of quantum walks on embedded graphs on surfaces Tanner, From quantum graphs to quantum random walks, Non-Linear Dynamics and Fundamental Interactions NATO Science Series II: Mathematics, Physics and Chemistry, 213 (2006) 69-87

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-10T21:03:50.298575Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:50.168323Z digest=sha256:d731780c6dbca2d97710bb0434deff0a3f625ab5f97483fbeb78fc5e518b8194

Observation df16ab28-805d-4adc-abec-a91917145af6 · outbound

This paper cites an unresolved cited work.

Comfortability of quantum walks on embedded graphs on surfaces Unresolved cited work

Reference 24

Resolution
unresolved
raw_fallback, observed 2026-08-10T21:03:50.263467Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-18T06:34:40.430872+00:00.

source=pdf_text observed=2026-08-10T21:03:50.173518Z digest=sha256:79836ecc2375c5ef9b1fb1051c5d61c9412722992c4ec55c9a085eaa56f6269a

Pith citing papers

Observation b9c4aae5-6c3e-45c6-a48b-41ed36381391 · inbound

Robustness of periodicity in Grover walks under a magnetic vector potential cites this paper.

Robustness of periodicity in Grover walks under a magnetic vector potential Comfortability of quantum walks on embedded graphs on surfaces

Reference 15

Resolution
unresolved
no resolver link, observed 2026-08-02T01:25:40.012201Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-02T01:25:40.012201Z digest=sha256:52f0838cb76c8f42dd2be61ba092f6f273cb13a7a378986bf7fbd91a4aa4919b