Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-14T12:34:57.609288Z
Paper Citation Record · LEDGER
Solution of the 15 puzzle problem
As of 16 August 2026, this Paper Citation Record lists 21 of 21 outbound references and 0 inbound Pith citation observations for arXiv:1908.07106.
A citation records a reference. It does not transfer a finding from one paper to another.
Coverage vector
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-16T06:30:59.297886+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
Reference resolution
21 of 21 outbound references displayed
- verified exact0
- verified fuzzy20
- unresolved1
- parse uncertain0
- malformed identifier0
- metadata mismatch0
External citation measurements
No source-named external measurement is stored.
Outbound references
Observation 5134ffcb-61d2-4d8f-b836-55a5ad9536c6 · outbound
This paper cites Cut-off for conjugacy-invariant random walks on the permutation group.
Solution of the 15 puzzle problem Cut-off for conjugacy-invariant random walks on the permutation group
Reference 1
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.871108Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 6489f175-95cf-410f-870b-3db954f66537 · outbound
This paper cites Cut-off for random to random c ard shuffle.
Solution of the 15 puzzle problem Cut-off for random to random c ard shuffle
Reference 2
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.860251Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation f77c762e-1ece-44bc-af54-cfefb80f4f72 · outbound
This paper cites On the spectral gap for fin itely-generated subgroups of SU p2q.
Solution of the 15 puzzle problem On the spectral gap for fin itely-generated subgroups of SU p2q
Reference 3
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.848907Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 20c408fb-6fd8-4883-90ba-21bbf73728ec · outbound
This paper cites Uniform expansion bounds f or Cayley graphs of SL 2pFpq.
Solution of the 15 puzzle problem Uniform expansion bounds f or Cayley graphs of SL 2pFpq
Reference 4
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.837359Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2a040f71-4eea-4048-a85e-a6d537a637cc · outbound
This paper cites Group representations in probability and statistics.
Solution of the 15 puzzle problem Group representations in probability and statistics
Reference 5
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.825626Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e1ddd489-a2ea-442a-ab04-aaaf84f0cc0e · outbound
This paper cites Some things we’ve learned (about Markov chain M onte Carlo).
Solution of the 15 puzzle problem Some things we’ve learned (about Markov chain M onte Carlo)
Reference 6
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.814532Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 322afebb-46a9-4500-807a-90b2b2d95d38 · outbound
This paper cites Comparison techniq ues for random walk on finite groups.
Solution of the 15 puzzle problem Comparison techniq ues for random walk on finite groups
Reference 7
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.803098Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 3bd867ad-8ba1-4dfd-a456-5019d136711a · outbound
This paper cites Comparison theore ms for reversible Markov chains.
Solution of the 15 puzzle problem Comparison theore ms for reversible Markov chains
Reference 8
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.791829Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 2564f4ca-33cf-4dc6-8035-46d3d74ca7cb · outbound
This paper cites Generating a rando m permutation with random transpositions.
Solution of the 15 puzzle problem Generating a rando m permutation with random transpositions
Reference 9
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.780836Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 82094d89-17a5-44f1-ae9a-b64bc19c6b8a · outbound
This paper cites Probability: theory and examples.
Solution of the 15 puzzle problem Probability: theory and examples
Reference 10
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.769448Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d4c55f2e-5876-48c6-becd-86e49b2c2bfe · outbound
This paper cites Finding the shortest move-sequence in the g raph-generalized 15-puzzle is NP-hard.
Solution of the 15 puzzle problem Finding the shortest move-sequence in the g raph-generalized 15-puzzle is NP-hard
Reference 11
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.758270Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e4f5838c-e15e-4701-9b14-fd114b8846d7 · outbound
This paper cites Growth and generation in SL 2pZ{pZq.
Solution of the 15 puzzle problem Growth and generation in SL 2pZ{pZq
Reference 12
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.747115Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation ae7be6de-7fe9-47cb-89ff-93ebdad0f4c4 · outbound
This paper cites On the diameter of permutation groups.
Solution of the 15 puzzle problem On the diameter of permutation groups
Reference 13
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.736372Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 58bc0722-9df9-4d32-8179-3a4814606de8 · outbound
This paper cites Random generators of the symmetric group: diameter, mixing time and spectral gap.
Solution of the 15 puzzle problem Random generators of the symmetric group: diameter, mixing time and spectral gap
Reference 14
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.724721Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d8962b75-7731-491d-9f33-a05d66ab8225 · outbound
This paper cites The random k cycle walk on the symmetric group.
Solution of the 15 puzzle problem The random k cycle walk on the symmetric group
Reference 15
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.713555Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation e2c5a9a1-7114-4d00-bf4b-32935f94ecf5 · outbound
This paper cites Sandp iles on the square lattice.
Solution of the 15 puzzle problem Sandp iles on the square lattice
Reference 16
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.701510Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 7b92b560-8585-4d3a-918e-9edb0a58624e · outbound
This paper cites Notes on the ‘15 ’ puzzle.
Solution of the 15 puzzle problem Notes on the ‘15 ’ puzzle
Reference 17
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.689320Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation afb42cf0-00d1-43f1-a1aa-199aaddf9653 · outbound
This paper cites Peres, and E.L.
Solution of the 15 puzzle problem Peres, and E.L
Reference 18
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.677800Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 4f357277-5f8c-4057-a14d-1da7d441d804 · outbound
This paper cites A real-time algorithm for the pn2 ´ 1q-puzzle.
Solution of the 15 puzzle problem A real-time algorithm for the pn2 ´ 1q-puzzle
Reference 19
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.666030Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation 57cc80a0-e865-4a1d-9944-df3697e1b44c · outbound
This paper cites Finding a shortest s olution for the N ˆ N extension of the 15-puzzle is intractable.
Solution of the 15 puzzle problem Finding a shortest s olution for the N ˆ N extension of the 15-puzzle is intractable
Reference 20
- Resolution
- verified fuzzy
- raw_fallback, observed 2026-08-14T12:34:57.655491Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Observation d792bd49-f22f-498e-8305-8f1d7bc76460 · outbound
This paper cites an unresolved cited work.
Solution of the 15 puzzle problem Unresolved cited work
Reference 21
- Resolution
- unresolved
- raw_fallback, observed 2026-08-14T12:34:57.640302Z
Source-reported events for the cited work
No event found in the named queried sources as of 2026-08-16T06:30:59.297886+00:00.
Pith citing papers
No inbound Pith citation observations are available.