Paper Citation Record · LEDGER

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard

As of 11 August 2026, this Paper Citation Record lists 42 of 42 outbound references and 1 inbound Pith citation observation for arXiv:2412.14932.

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

pith.paper-citation-record.v1
2412.14932 v1

Coverage vector

measured 42 of 42 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-11T11:52:37.193625Z

measured 43 of 43 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-11T06:34:44.6726+00:00

measured 1 of 1 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-05-19T12:06:38.050214Z

measured 0 of 1 external citation measurements

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

Source: arxiv_reference, observed 2026-05-19T12:07:20.822570Z

Reference resolution

42 of 42 outbound references displayed

verified exact1
verified fuzzy27
unresolved14
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 63ad5cd3-456c-4f7e-b490-c99eac337fd5 · outbound

This paper cites S peciﬁcally, the Laplacian of a signed graph is symmetric and takes values in − 1,0,1, whereas the Laplacian of a directed graph is not symmetric a nd takes values in 0,1.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard S peciﬁcally, the Laplacian of a signed graph is symmetric and takes values in − 1,0,1, whereas the Laplacian of a directed graph is not symmetric a nd takes values in 0,1

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.904315Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 11ee5be7-cb87-4df4-a258-87621419bb47 · outbound

This paper cites an unresolved cited work.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-11T11:52:37.889295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 9485166c-f729-4717-87df-e560509434a9 · outbound

This paper cites Gharibian, Y.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Gharibian, Y

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.874835Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 937eaa50-3c37-487a-b815-0480359f7a56 · outbound

This paper cites Adamaszek and J.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Adamaszek and J

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.860073Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 0e6b3295-8a5c-4226-9756-6d27ac2ddf90 · outbound

This paper cites Clique Homology is QMA1-hard.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Clique Homology is QMA1-hard

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-11T11:52:37.022569Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation ec6435c9-2ce5-4fb6-8a07-401d77b84988 · outbound

This paper cites Gapped Clique Homology on weighted graphs is $\text{QMA}_1$-hard and contained in $\text{QMA}$.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Gapped Clique Homology on weighted graphs is $\text{QMA}_1$-hard and contained in $\text{QMA}$

Reference 6

Resolution: unresolved; no resolver link, observed 2026-08-11T11:52:37.027917Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cf6a3271-178b-49bc-a175-0fd8c7626fae · outbound

This paper cites Zaslavsky, Negative (and positive) circles in signed gra phs: A problem collection, AKCE International Journal of Gr aphs and Combinatorics 15, 31 (2018).

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Zaslavsky, Negative (and positive) circles in signed gra phs: A problem collection, AKCE International Journal of Gr aphs and Combinatorics 15, 31 (2018)

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.845874Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 68f1d899-95da-4025-95df-93ed08677118 · outbound

This paper cites Figueiredo and Y.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Figueiredo and Y

Reference 8

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.831295Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation a702d833-d5ae-43d6-bcaa-a1de708d91f9 · outbound

This paper cites an unresolved cited work.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-08-11T11:52:37.815861Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 62aa6c1b-395c-41aa-8961-deef0c3d55dd · outbound

This paper cites an unresolved cited work.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-11T11:52:37.801584Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6d1e26da-fc24-4910-996a-34a7632d85b1 · outbound

This paper cites Vicsek, A.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Vicsek, A

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.787209Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation df9fb79f-d0fc-44bf-99e6-7355549e6990 · outbound

This paper cites Ou-Yang, D.-Q.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Ou-Yang, D.-Q

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.772782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 8beebf47-907e-4316-8ad2-d57231db8bd0 · outbound

This paper cites an unresolved cited work.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Unresolved cited work

Reference 13

Resolution: unresolved; raw_fallback, observed 2026-08-11T11:52:37.758207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation fef9bf7d-ed7b-46ae-a536-eaa3c999b881 · outbound

This paper cites Camps, L.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Camps, L

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.743463Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation fbf4179e-18a0-4619-98fb-05f1dce4d0f7 · outbound

This paper cites Sünderhauf, E.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Sünderhauf, E

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.728766Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 5c8636e2-da5b-4381-866d-4f344d2bc7b6 · outbound

This paper cites Barabási and R.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Barabási and R

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.714227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 13415828-9fa7-4583-8865-5bd985005ba1 · outbound

This paper cites Spectral sparsification of matrix inputs as a preprocessing step for quantum algorithms.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Spectral sparsification of matrix inputs as a preprocessing step for quantum algorithms

Reference 17

Resolution: verified exact; local_arxiv, observed 2026-08-11T11:52:37.355207Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation be55d089-86a6-4acb-a5d1-69b1e7cdfe10 · outbound

This paper cites Apers and R.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Apers and R

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.699534Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 340f4dd9-2ed1-4eec-a160-60ebf195a3c6 · outbound

This paper cites an unresolved cited work.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-11T11:52:37.685383Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 6728f028-3445-470e-bfdb-8319a0a40260 · outbound

This paper cites Jost and D.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Jost and D

Reference 20

Resolution: unresolved; no resolver link, observed 2026-08-11T11:52:37.092842Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 2abe2a12-d11e-4005-bdc0-642e26c67969 · outbound

This paper cites Goldreich and D.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Goldreich and D

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.671210Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation b602cfff-7ceb-42bd-b60d-ce8b893b3b75 · outbound

This paper cites Trevisan, Lecture notes on graph partitioning, expander s and spectral methods, Lecture notes (2016), available at https://lucatrevisan.github.io/books/expanders-2016.pdf.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Trevisan, Lecture notes on graph partitioning, expander s and spectral methods, Lecture notes (2016), available at https://lucatrevisan.github.io/books/expanders-2016.pdf

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.656694Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 60722214-98e0-4c33-89ff-25ed4aaeaca2 · outbound

This paper cites Cvetković, P.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Cvetković, P

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.641198Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 57fed74f-dbcb-4dae-b86a-be808238d2d2 · outbound

This paper cites Lloyd, S.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Lloyd, S

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.626112Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation e6193bb4-cf82-44a9-8a58-20d1b3f3ebd1 · outbound

This paper cites A streamlined quantum algorithm for topological data analysis with exponentially fewer qubits.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard A streamlined quantum algorithm for topological data analysis with exponentially fewer qubits

Reference 25

Resolution: unresolved; no resolver link, observed 2026-08-11T11:52:37.115029Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e7628f14-bf2e-4d21-ac10-c4c56b91282c · outbound

This paper cites an unresolved cited work.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Unresolved cited work

Reference 26

Resolution: unresolved; raw_fallback, observed 2026-08-11T11:52:37.612139Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 96423283-ec06-4919-94d2-168fedc45b02 · outbound

This paper cites Gyurik, C.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Gyurik, C

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.598200Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 0b9c914a-013e-47cc-a8b3-2f19c29cb0c8 · outbound

This paper cites Schmidhuber and S.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Schmidhuber and S

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.583807Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation c50a3e01-9fd4-4ed9-a41e-b636f11c713e · outbound

This paper cites Cade and P.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Cade and P

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.569281Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 925ce362-8e73-4767-85f5-72bb9b0e4454 · outbound

This paper cites Provable quantum speedups for computing persistence in topological data analysis.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Provable quantum speedups for computing persistence in topological data analysis

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-11T11:52:37.138169Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 26f1045b-0476-4a3e-a8b9-20d24be2350d · outbound

This paper cites The Complexity of Stoquastic Local Hamiltonian Problems.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard The Complexity of Stoquastic Local Hamiltonian Problems

Reference 31

Resolution: unresolved; no resolver link, observed 2026-08-11T11:52:37.143099Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation f9262e31-5098-475f-9000-3ed96dec8fce · outbound

This paper cites Bravyi, A.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Bravyi, A

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.555093Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 19e8009b-ca06-40fc-adf3-5679628947ea · outbound

This paper cites Aharonov and A.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Aharonov and A

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.540789Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 203d9e7f-8c88-425e-a6f3-f2a999db8759 · outbound

This paper cites an unresolved cited work.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-08-11T11:52:37.526438Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 28a5392f-b125-4529-a04d-74329ce033a6 · outbound

This paper cites an unresolved cited work.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Unresolved cited work

Reference 35

Resolution: unresolved; raw_fallback, observed 2026-08-11T11:52:37.510959Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 78f651aa-8558-456d-91e3-561007e4dcca · outbound

This paper cites Dittrich and G.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Dittrich and G

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.496696Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f798b90c-df7d-4ef3-980a-b02e09b65083 · outbound

This paper cites Kunegis, S.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Kunegis, S

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.481317Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 1afcb8d7-3ff8-4ebb-8014-bf2d1ef49312 · outbound

This paper cites Lim, Hodge laplacians on graphs, Siam Review 62, 685 (2020).

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Lim, Hodge laplacians on graphs, Siam Review 62, 685 (2020)

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.463570Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation bdda34b0-79f3-49b8-8c56-22dec36112ec · outbound

This paper cites Friedman, Computing betti numbers via combinatorial lap lacians, in Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing (1996) pp.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Friedman, Computing betti numbers via combinatorial lap lacians, in Proceedings of the twenty-eighth annual ACM symposium on Theory of Computing (1996) pp

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.448021Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation ff7015b4-6fd8-406a-b076-e87bf676ca27 · outbound

This paper cites She and Z.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard She and Z

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.432784Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation f5c60c44-2ee7-4d45-9e8b-7c351cf28483 · outbound

This paper cites Adriaens and S.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Adriaens and S

Reference 41

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.416817Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Observation 50327a29-b4ac-4cbb-a6f5-6cc76f1483f1 · outbound

This paper cites Desai and V.

Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard Desai and V

Reference 42

Resolution: verified fuzzy; raw_fallback, observed 2026-08-11T11:52:37.401532Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.

Pith citing papers

Observation 9e75a443-2302-433f-b463-bc14636cff64 · inbound

New aspects of quantum topological data analysis: Betti number estimation, and testing and tracking of homology and cohomology classes cites this paper.

New aspects of quantum topological data analysis: Betti number estimation, and testing and tracking of homology and cohomology classes Testing the presence of balanced and bipartite components in a sparse graph is QMA1-hard

Reference 5

Resolution: verified exact; arxiv_id, observed 2026-05-19T12:07:20.824728Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-11T06:34:44.6726+00:00.