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Paper Citation Record · LEDGER

Breaking Symmetry in Graphs by Resolving Sets

As of 23 August 2026, this Paper Citation Record lists 38 of 38 outbound references and 0 inbound Pith citation observations for arXiv:2412.15781.

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

pith.paper-citation-record.v1
2412.15781 v2

Coverage vector

measured 38 of 38 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T11:16:50.292696Z

measured 38 of 38 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+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

38 of 38 outbound references displayed

  • verified exact0
  • verified fuzzy24
  • unresolved14
  • parse uncertain0
  • malformed identifier0
  • metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation c1f0c2c5-47a7-4063-aef4-4a8ec1612085 · outbound

This paper cites Ahmadi, F.

Breaking Symmetry in Graphs by Resolving Sets Ahmadi, F

Reference 1

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.769240Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.134090Z digest=sha256:834ea0de8b7f0d3b2b227d5cd80b5db0edea340c922519bcce2c90507c6e8d97

Observation 543dd4d1-2c73-4a10-b1bd-1809dfdfdc81 · outbound

This paper cites an unresolved cited work.

Breaking Symmetry in Graphs by Resolving Sets Unresolved cited work

Reference 2

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:16:50.758035Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.139737Z digest=sha256:38a1cb16c4a8ed92e0e2edf8f11e39c1de9e0626bf731443e549df3a6a242498

Observation c01a9d15-1dc2-4097-88c3-c4dd6dff2516 · outbound

This paper cites Arumugam, V.

Breaking Symmetry in Graphs by Resolving Sets Arumugam, V

Reference 3

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.746130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.144805Z digest=sha256:408e15e5dd51bfefeaf47f08cc377cb81cd6a3715e9b08568d594bb6c5dccc46

Observation 576df2be-f2ac-489d-a30e-210d71db95fb · outbound

This paper cites Babai, Asymmetric coloring of locally finite graphs and profinite permutation groups: Tucker’s Conjecture confirmed, J.

Breaking Symmetry in Graphs by Resolving Sets Babai, Asymmetric coloring of locally finite graphs and profinite permutation groups: Tucker’s Conjecture confirmed, J

Reference 4

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.734855Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.149655Z digest=sha256:6157e3af8511b93c9cde1a5ff6a2264327a450ea02a39854ad4617b9b66b892d

Observation d0ad13b4-3102-4b5e-8776-76aa1f31f73c · outbound

This paper cites Babai, Asymmetric trees with two prescribed degrees, Acta Math.

Breaking Symmetry in Graphs by Resolving Sets Babai, Asymmetric trees with two prescribed degrees, Acta Math

Reference 5

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.723330Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.154421Z digest=sha256:afbfe7355066f1839bf78ce775e282f1fb5c10f03308e6f7ab2f0bad067ed5c8

Observation da377bec-f487-4130-8f30-c7d07ce80f9b · outbound

This paper cites an unresolved cited work.

Breaking Symmetry in Graphs by Resolving Sets Unresolved cited work

Reference 6

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:16:50.712149Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.158812Z digest=sha256:7e367201a0ce869697bd7cd4eed4a864fc1cd3783170f5e3d5bce8c5afd9c721

Observation f0a81567-a3f7-413b-bef7-5683930f9925 · outbound

This paper cites an unresolved cited work.

Breaking Symmetry in Graphs by Resolving Sets Unresolved cited work

Reference 7

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:16:50.700183Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.163566Z digest=sha256:c7f6368f67244d13e685f873a9d68c1f11ebe8fef88caf77aec616b5d9a6425c

Observation 1f155619-d7c4-4e8b-839b-28e9545bb973 · outbound

This paper cites Chan, The distinguishing number of the direct product and wreath product action, J.

Breaking Symmetry in Graphs by Resolving Sets Chan, The distinguishing number of the direct product and wreath product action, J

Reference 8

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.689148Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.167776Z digest=sha256:f65aaa2a56c305129ad569a1ff3fd96bf0fca19c3a60bc6a634230423eb70f8c

Observation eaa2e311-3b24-46bf-8685-964b5611784c · outbound

This paper cites Chartrand, L.

Breaking Symmetry in Graphs by Resolving Sets Chartrand, L

Reference 9

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.677077Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.171488Z digest=sha256:a3243eeb3868ac1607850a1c0e60270f6956a1ad6833e5b1695f30eab8908c69

Observation 0a7171d2-f5af-4753-8ba5-4504528cf8a8 · outbound

This paper cites an unresolved cited work.

Breaking Symmetry in Graphs by Resolving Sets Unresolved cited work

Reference 10

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:16:50.664254Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.175315Z digest=sha256:6efe0da85d257474e0170b850cc83c979d7a894129bfedcb40e5bf1df2829fb0

Observation 3f333e11-7516-4bca-a97b-882efd6ce84c · outbound

This paper cites an unresolved cited work.

Breaking Symmetry in Graphs by Resolving Sets Unresolved cited work

Reference 11

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:16:50.651992Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.180457Z digest=sha256:720c59d4a9df215c14f01314bd65deae45066cda0a5cf8e679941dfc647b3969

Observation f5dc4de5-c49b-4584-86b0-6c1f5ccbee88 · outbound

This paper cites Estrada-Moreno, I.

Breaking Symmetry in Graphs by Resolving Sets Estrada-Moreno, I

Reference 12

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.637837Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.184548Z digest=sha256:34f9853ca5bc1dbde144f4c91c36b29d90cbf563f9f399780e2e51bf52966d69

Observation 890c3c87-7266-45ac-b7f6-c5c41f899609 · outbound

This paper cites Garijo, A.

Breaking Symmetry in Graphs by Resolving Sets Garijo, A

Reference 13

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.626218Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.188491Z digest=sha256:83fdee3c947722943f7e8440b45cee4b0be9e35c05f4c5369d849ef32b36933a

Observation abe9571d-46c8-4bb6-9615-2f6c6c4ba41e · outbound

This paper cites Hakanen, V.

Breaking Symmetry in Graphs by Resolving Sets Hakanen, V

Reference 14

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.614084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.192705Z digest=sha256:4dd6acf65d05a37784ca07889ac8822125733b0b5884b6bb47dde5858bba77f7

Observation b3c8885e-e3fa-42bc-a56f-2277c1d9ba75 · outbound

This paper cites Harary, R.

Breaking Symmetry in Graphs by Resolving Sets Harary, R

Reference 15

Resolution
unresolved
no resolver link, observed 2026-08-11T11:16:50.196823Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T11:16:50.196823Z digest=sha256:997d3896bcaa22d1c7ecd9e0e10c6a58fa3220faefc7151057cd4ebaeb9d63a5

Observation 908a5e4b-3476-4b23-9321-42cbe9ed3128 · outbound

This paper cites Hernando, M.

Breaking Symmetry in Graphs by Resolving Sets Hernando, M

Reference 16

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.595230Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.200781Z digest=sha256:0e603d473c86de88953a7dd188904995f19d487950c2210e6ca97594367df6c0

Observation 01dbafbd-d40e-4885-adbf-c1194783e161 · outbound

This paper cites Imrich, S.

Breaking Symmetry in Graphs by Resolving Sets Imrich, S

Reference 17

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.583456Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.204808Z digest=sha256:33eb6550f48b074b201d7c17a5aafd01475f663907ff584ea20498c1f7629d42

Observation 6fca2794-9a78-4a02-8ca6-e4e1ce6ef578 · outbound

This paper cites Jannesari, B.

Breaking Symmetry in Graphs by Resolving Sets Jannesari, B

Reference 18

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.571462Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.209129Z digest=sha256:6e88052f37672222b34b421609787d89b815c14d3de2c0399934f207322daf59

Observation 3071f027-fa8f-4ffa-9897-922e4bb4dfad · outbound

This paper cites Jannesari, B.

Breaking Symmetry in Graphs by Resolving Sets Jannesari, B

Reference 19

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.558599Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.213087Z digest=sha256:d0f08f8027bfa23a5c40ea7bcdbbf7de1c9ab448f79c907bb79cf562c4d8730d

Observation 561488f4-50e7-4d3d-9f9b-62b62a0e4444 · outbound

This paper cites Kalinowski, M.

Breaking Symmetry in Graphs by Resolving Sets Kalinowski, M

Reference 20

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.545791Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.217066Z digest=sha256:83935079c15067d724e518d1268a00df2b17a1ef091e41c25f1f400c0646f1e4

Observation db34fea2-9246-4191-a5a9-dcdd22c9da36 · outbound

This paper cites Kalinowski, M.

Breaking Symmetry in Graphs by Resolving Sets Kalinowski, M

Reference 21

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.532681Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.221025Z digest=sha256:ac094b63fd24ce421dbbaf017eca4a5bd504d4e41c3e690e38be6bf98d7b9166

Observation 34df204e-f821-4714-a319-59a4977e32fa · outbound

This paper cites Kelenc, D.

Breaking Symmetry in Graphs by Resolving Sets Kelenc, D

Reference 22

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.519995Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.226711Z digest=sha256:773a407034f2715211e3f644658f6ff8e52fcd971772e4b3bee6ea0394e62dba

Observation 685aeda1-495e-4482-b999-9317a32a7c00 · outbound

This paper cites Kelenc, N.

Breaking Symmetry in Graphs by Resolving Sets Kelenc, N

Reference 23

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.507620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.231288Z digest=sha256:a3a3f0bd54e43670ad34b3ce7b651eceaa302abcdeeeb2a82e5cee10ee1391a2

Observation 8efdafb6-a875-4b5f-ac72-6fde8a1efac6 · outbound

This paper cites Khuller, B.

Breaking Symmetry in Graphs by Resolving Sets Khuller, B

Reference 24

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.494199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.235138Z digest=sha256:40ef878850c6979a4c2c79299239c04149a3e97db98a677442eef926af4b86c4

Observation 7e92096f-5b56-4ad7-b029-3f33ea7ba602 · outbound

This paper cites Klavˇ zar, D.

Breaking Symmetry in Graphs by Resolving Sets Klavˇ zar, D

Reference 25

Resolution
unresolved
no resolver link, observed 2026-08-11T11:16:50.238838Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T11:16:50.238838Z digest=sha256:f71a1225d034f4ebee78fb5a79dad22893f2a063c59cd963429fa5123575592e

Observation 51a5f156-785a-4019-8bfd-95f64a52fda5 · outbound

This paper cites Klavˇ zar, T.-L.

Breaking Symmetry in Graphs by Resolving Sets Klavˇ zar, T.-L

Reference 26

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.472684Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.242676Z digest=sha256:2db968c2b8f033cbb65108db8eb86d9c87bc11e3d2c63a0446abd4e95621b42e

Observation e40df4a4-6f87-4cb3-9a15-db5e9808398f · outbound

This paper cites Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results.

Breaking Symmetry in Graphs by Resolving Sets Metric dimension related parameters in graphs: A survey on combinatorial, computational and applied results

Reference 27

Resolution
unresolved
no resolver link, observed 2026-08-11T11:16:50.246463Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T11:16:50.246463Z digest=sha256:99b03d954b13737f2f5a1f51d3c8031b70f990264c1d7cf9d4357fd08e5d7a2a

Observation 8e0b5eb2-d523-4b00-9879-ab7039b29ebe · outbound

This paper cites Okamoto, B.

Breaking Symmetry in Graphs by Resolving Sets Okamoto, B

Reference 28

Resolution
unresolved
no resolver link, observed 2026-08-11T11:16:50.250832Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T11:16:50.250832Z digest=sha256:b250eac0c075e00c1f51986635e20fc1f479907c905ac60a1fa6dcb35ef7adb4

Observation fa08a4fa-ad9e-4463-95c2-c57d10e1d787 · outbound

This paper cites Russell, R.

Breaking Symmetry in Graphs by Resolving Sets Russell, R

Reference 29

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.451972Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.254662Z digest=sha256:6e233cfee3d646ca177ec2d235331050bec092c308d24c18c8a01cd47eada929

Observation e2dfc526-63c1-481b-a5a1-c021abd9cfe6 · outbound

This paper cites Seb¨ o, E.

Breaking Symmetry in Graphs by Resolving Sets Seb¨ o, E

Reference 30

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.437828Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.259009Z digest=sha256:50cb0d77effc24561b118378870aa49892f646b1358249752a6e0d14c074117d

Observation a2f524be-a13e-4641-bda0-3cd7090faf67 · outbound

This paper cites Shanmukha, B.

Breaking Symmetry in Graphs by Resolving Sets Shanmukha, B

Reference 31

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.424853Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.263712Z digest=sha256:14082ede0cbd012683ac9300dc3c7e29a5ab5721ff723c152845b26f0510b0a9

Observation ca88f374-36b5-47ff-966f-04fe7c013a61 · outbound

This paper cites an unresolved cited work.

Breaking Symmetry in Graphs by Resolving Sets Unresolved cited work

Reference 32

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:16:50.412414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.268250Z digest=sha256:2d65c0827aebfb231a703b17484a972026c0034c5b1f365c06574f0c00b41f14

Observation 806b6cc6-a688-4326-adfd-b8ae85a6a98a · outbound

This paper cites an unresolved cited work.

Breaking Symmetry in Graphs by Resolving Sets Unresolved cited work

Reference 33

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:16:50.398657Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.271835Z digest=sha256:9137f26ad66be6068c9a7643f766ee32ce765640395feaa8171ccb90962782fa

Observation f1da48e3-9d0e-44bc-9c48-e6e93ae9fbc8 · outbound

This paper cites an unresolved cited work.

Breaking Symmetry in Graphs by Resolving Sets Unresolved cited work

Reference 34

Resolution
unresolved
no resolver link, observed 2026-08-11T11:16:50.276311Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

source=pdf_text observed=2026-08-11T11:16:50.276311Z digest=sha256:dcc8f3d927807d9836a500b61ea163ec62d26cc1fc6603888c57f127a2710e01

Observation 757f7445-2a07-4f7e-b9dd-c5fca5234ad7 · outbound

This paper cites Trujillo-Ra´ sua, I.

Breaking Symmetry in Graphs by Resolving Sets Trujillo-Ra´ sua, I

Reference 35

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.379269Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.281158Z digest=sha256:dc0bf58d52ddb37bfa6d6ba26464010920ba57a2232cc2d12f0f29a423d74c99

Observation 3dea8758-8598-49f3-b39c-d225e615ff02 · outbound

This paper cites an unresolved cited work.

Breaking Symmetry in Graphs by Resolving Sets Unresolved cited work

Reference 36

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:16:50.365905Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.285255Z digest=sha256:12ddd4876ac9205a5e9f255654f20872fb7b415277b142c5cb55b31b843a5525

Observation 54a01ef2-baab-4291-8f97-81ff7f2ec27a · outbound

This paper cites Tymoczko, Distinguishing numbers for graphs and groups, Electron.

Breaking Symmetry in Graphs by Resolving Sets Tymoczko, Distinguishing numbers for graphs and groups, Electron

Reference 37

Resolution
verified fuzzy
raw_fallback, observed 2026-08-11T11:16:50.353554Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.289086Z digest=sha256:b2b1d1b898a6c0a7229f7eaca3f280fd55e8f13d3fc5e56def0d4cf9f525f78d

Observation a1cf3668-e59d-440e-9eef-c1cd6b2440a6 · outbound

This paper cites an unresolved cited work.

Breaking Symmetry in Graphs by Resolving Sets Unresolved cited work

Reference 38

Resolution
unresolved
raw_fallback, observed 2026-08-11T11:16:50.338611Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

source=pdf_text observed=2026-08-11T11:16:50.292696Z digest=sha256:1c9942b7309e457aa3a99258fa46a30bb776c367ea4578c1ba3ca5f910fcacb8

Pith citing papers

No inbound Pith citation observations are available.