Paper Citation Record · LEDGER

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete

As of 18 August 2026, this Paper Citation Record lists 31 of 31 outbound references and 0 inbound Pith citation observations for arXiv:2608.02726.

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

pith.paper-citation-record.v1
2608.02726 v1

Coverage vector

measured 31 of 31 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T15:13:01.362763Z

measured 31 of 31 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-17T06:30:58.91139+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

31 of 31 outbound references displayed

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verified fuzzy14
unresolved12
parse uncertain0
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metadata mismatch2

External citation measurements

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Outbound references

Observation 63075007-5a2c-488e-a114-127a6562d1b1 · outbound

This paper cites Clique Homology is QMA1-hard.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Clique Homology is QMA1-hard

Reference 1

Resolution: unresolved; no resolver link, observed 2026-08-15T15:13:01.224438Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation a904d74e-67e8-4d84-a7e4-29038b9fb604 · outbound

This paper cites Complexity of simplicial homology and independence complexes of chordal graphs , journal =.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Complexity of simplicial homology and independence complexes of chordal graphs , journal =

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.985192Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 789e4f94-5282-488c-8b07-2702a386eb33 · outbound

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

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Gapped Clique Homology on weighted graphs is $\text{QMA}_1$-hard and contained in $\text{QMA}$

Reference 3

Resolution: unresolved; no resolver link, observed 2026-08-15T15:13:01.235056Z

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Observation b447c897-d0ab-4f45-a879-f096fd88efd1 · outbound

This paper cites Nature Communications , volume =.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Nature Communications , volume =

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.970708Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d830f12e-973c-4c9e-a970-de1ee676843d · outbound

This paper cites Complexity-Theoretic Limitations on Quantum Algorithms for Topological Data Analysis.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Complexity-Theoretic Limitations on Quantum Algorithms for Topological Data Analysis

Reference 5

Resolution: unresolved; no resolver link, observed 2026-08-15T15:13:01.244655Z

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Observation 019dce4a-c969-410c-9113-21f1fd3633ff · outbound

This paper cites Quantum , year =.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Quantum , year =

Reference 6

Resolution: verified exact; doi, observed 2026-08-15T15:13:01.625052Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f47cc48c-632f-4b66-9dcf-39ce7d2a30c9 · outbound

This paper cites PRX Quantum 7, 020361 (2026) , year =.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete PRX Quantum 7, 020361 (2026) , year =

Reference 7

Resolution: unresolved; no resolver link, observed 2026-08-15T15:13:01.254326Z

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Observation 1f740f19-542a-42ec-bcd2-c0e11ddf653d · outbound

This paper cites arXiv preprint , year =.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete arXiv preprint , year =

Reference 8

Resolution: verified exact; doi, observed 2026-08-15T15:13:01.598919Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 12580fdb-1d37-401b-8151-e612b868cd32 · outbound

This paper cites Complexity of Normalized Persistence Problems for Topological Data Analysis and Local Hamiltonians.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Complexity of Normalized Persistence Problems for Topological Data Analysis and Local Hamiltonians

Reference 9

Resolution: verified exact; local_arxiv, observed 2026-08-15T15:13:01.526803Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f941be2c-1605-4e47-85c5-fc279c0dd00a · outbound

This paper cites Towards a universal gateset for $\mathsf{QMA}_1$.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Towards a universal gateset for $\mathsf{QMA}_1$

Reference 10

Resolution: unresolved; no resolver link, observed 2026-08-15T15:13:01.269192Z

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Observation 207be939-7ec1-4cc5-88fc-ed8ca0152113 · outbound

This paper cites Fermionic Independent Set and Laplacian of an independence complex are QMA-hard.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Fermionic Independent Set and Laplacian of an independence complex are QMA-hard

Reference 11

Resolution: unresolved; no resolver link, observed 2026-08-15T15:13:01.274213Z

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Observation 197b1555-9058-4cee-8c24-98681fd51088 · outbound

This paper cites The Bose-Hubbard model is QMA-complete.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete The Bose-Hubbard model is QMA-complete

Reference 12

Resolution: metadata mismatch; local_arxiv, observed 2026-08-15T15:13:01.738408Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4600c2ed-57a6-4892-8c19-1d96b40d19d0 · outbound

This paper cites The 7 faces of quantum NP.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete The 7 faces of quantum NP

Reference 13

Resolution: unresolved; no resolver link, observed 2026-08-15T15:13:01.283436Z

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Observation 3d7c22d0-7dbd-47ae-9823-518fcc277a2f · outbound

This paper cites arXiv:2510.07995 [quant-ph] , year =.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete arXiv:2510.07995 [quant-ph] , year =

Reference 14

Resolution: unresolved; no resolver link, observed 2026-08-15T15:13:01.288654Z

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Observation 25f5889e-ab27-4d47-90a0-c1586a9d1ddd · outbound

This paper cites Senior Thesis, Bard College , volume =.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Senior Thesis, Bard College , volume =

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.956676Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 5b3ee16c-f254-4e08-9464-3145e20dc63b · outbound

This paper cites On Eigenvalues of Random Complexes.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete On Eigenvalues of Random Complexes

Reference 16

Resolution: metadata mismatch; local_arxiv, observed 2026-08-15T15:13:01.702914Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d54f046f-408f-4e70-a458-ed06de9e7ce8 · outbound

This paper cites Advances in Mathematics , volume=.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Advances in Mathematics , volume=

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.943333Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 531f886e-f73c-4a18-9593-f6ba53cb9de9 · outbound

This paper cites Complexity of simplicial homology and independence complexes of chordal graphs.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Complexity of simplicial homology and independence complexes of chordal graphs

Reference 18

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.929645Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 6240b456-11b9-47fe-ba05-9b5ca0abb57c · outbound

This paper cites Marcos Crichigno and Tamara Kohler.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Marcos Crichigno and Tamara Kohler

Reference 19

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.915174Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation e8a7dd9d-564b-426b-b946-00556a56bb12 · outbound

This paper cites Goldberg.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Goldberg

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.900598Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ca5d1569-84d6-4ad3-8bc5-4c62742d6e30 · outbound

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

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Provable quantum speedups for computing persistence in topological data analysis

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.886620Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 1e306c75-1325-43c1-810c-818b59c13a5f · outbound

This paper cites On eigenvalues of random complexes.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete On eigenvalues of random complexes

Reference 22

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.871858Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation f99d2d88-047f-4af3-a939-02579f87b4ca · outbound

This paper cites Quantum algorithm for persistent B etti numbers and topological data analysis.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Quantum algorithm for persistent B etti numbers and topological data analysis

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.856084Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation ffce5a79-06f3-4f2a-916b-09cbcd1b266b · outbound

This paper cites Computational complexity of the homology problem with orientable filtration: MA -completeness.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Computational complexity of the homology problem with orientable filtration: MA -completeness

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.839433Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation 4f87f8cb-3ad5-41e9-b17e-3ee942e06b6d · outbound

This paper cites Spectra of combinatorial laplace operators on simplicial complexes.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Spectra of combinatorial laplace operators on simplicial complexes

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.824767Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation c3169588-1e82-4ad1-b50e-0aef0fd346fd · outbound

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

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Gapped Clique Homology on weighted graphs is $\text{QMA}_1$-hard and contained in $\text{QMA}$

Reference 26

Resolution: unresolved; no resolver link, observed 2026-08-15T15:13:01.339795Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0c7801b7-8a37-4455-957d-d85a4b8f9ba4 · outbound

This paper cites Quantum algorithms for topological and geometric analysis of big data.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Quantum algorithms for topological and geometric analysis of big data

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.810131Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation d5a90508-2634-4712-8db1-504bf563d833 · outbound

This paper cites an unresolved cited work.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Unresolved cited work

Reference 28

Resolution: unresolved; raw_fallback, observed 2026-08-15T15:13:01.796018Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Observation da7a1722-ab78-4dd8-ab52-4e03ca020745 · outbound

This paper cites Fermionic Independent Set and Laplacian of an independence complex are QMA-hard.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Fermionic Independent Set and Laplacian of an independence complex are QMA-hard

Reference 29

Resolution: unresolved; no resolver link, observed 2026-08-15T15:13:01.353784Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 8b23b0f7-9dc8-48ce-9541-5a5ef37a47af · outbound

This paper cites Towards a universal gateset for $\mathsf{QMA}_1$.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Towards a universal gateset for $\mathsf{QMA}_1$

Reference 30

Resolution: unresolved; no resolver link, observed 2026-08-15T15:13:01.358342Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 35588f4e-ee26-438a-954a-a6b336df7cd0 · outbound

This paper cites Complexity-theoretic limitations on quantum algorithms for topological data analysis.

Unweighted Gapped Clique Homology is $\mathsf{QMA}_1$-complete Complexity-theoretic limitations on quantum algorithms for topological data analysis

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T15:13:01.782175Z

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No event found in the named queried sources as of 2026-08-17T06:30:58.91139+00:00.

Pith citing papers

No inbound Pith citation observations are available.