Paper Citation Record · LEDGER

Compact Geometric Representations of Hierarchies

As of 9 August 2026, this Paper Citation Record lists 55 of 55 outbound references and 0 inbound Pith citation observations for arXiv:2606.18520.

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

pith.paper-citation-record.v1
2606.18520 v1

Coverage vector

measured 55 of 55 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-06-26T22:12:38.245812Z

measured 55 of 55 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-09T06:31:02.800959+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

55 of 55 outbound references displayed

verified exact1
verified fuzzy0
unresolved49
parse uncertain0
malformed identifier0
metadata mismatch5

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation b724a6c9-fdf4-4f81-953a-bc185a9eec83 · outbound

This paper cites IEEE transactions on pattern analysis and machine intelligence , volume=.

Compact Geometric Representations of Hierarchies IEEE transactions on pattern analysis and machine intelligence , volume=

Reference 1

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 30f2d7ef-26db-4c20-97dd-c553667b007c · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Compact Geometric Representations of Hierarchies Advances in Neural Information Processing Systems , volume=

Reference 2

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

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Observation 4b959616-9f2c-4e71-85f5-1eb9a1750067 · outbound

This paper cites Communications of the ACM , volume=.

Compact Geometric Representations of Hierarchies Communications of the ACM , volume=

Reference 3

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

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Observation 92d94faa-f579-4ff1-8a4e-4e0806f51178 · outbound

This paper cites BRIGHT: A Realistic and Challenging Benchmark for Reasoning-Intensive Retrieval.

Compact Geometric Representations of Hierarchies BRIGHT: A Realistic and Challenging Benchmark for Reasoning-Intensive Retrieval

Reference 4

Resolution: metadata mismatch; arxiv_id, observed 2026-07-03T23:29:02.753895Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation d7e07387-9d39-4a40-b17a-3cfba1a228ab · outbound

This paper cites 2015 , publisher=.

Compact Geometric Representations of Hierarchies 2015 , publisher=

Reference 5

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation eeab2a0e-038c-465c-ab6e-98ec7d10e6fa · outbound

This paper cites Advances in neural information processing systems , volume=.

Compact Geometric Representations of Hierarchies Advances in neural information processing systems , volume=

Reference 6

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 824f9656-e785-4e3e-9f2a-9dff231c4d55 · outbound

This paper cites Advances in neural information processing systems , volume=.

Compact Geometric Representations of Hierarchies Advances in neural information processing systems , volume=

Reference 7

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation d0bb42d6-6b42-406b-a44d-bbd37790d469 · outbound

This paper cites Advances in Neural Information Processing Systems , volume=.

Compact Geometric Representations of Hierarchies Advances in Neural Information Processing Systems , volume=

Reference 8

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 289e942d-d0d5-4f00-a693-31f059141750 · outbound

This paper cites On the theoretical limitations of embedding-based retrieval.

Compact Geometric Representations of Hierarchies On the theoretical limitations of embedding-based retrieval

Reference 9

Resolution: metadata mismatch; arxiv_id, observed 2026-07-03T23:29:02.759242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 81626c37-09d4-4e7d-834a-35482ea069bb · outbound

This paper cites Approximation, Randomization, and Combinatorial Optimization.

Compact Geometric Representations of Hierarchies Approximation, Randomization, and Combinatorial Optimization

Reference 10

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 242fa007-cf4a-422a-96c7-f0c39d598ad6 · outbound

This paper cites The Thirty-ninth Annual Conference on Neural Information Processing Systems , year=.

Compact Geometric Representations of Hierarchies The Thirty-ninth Annual Conference on Neural Information Processing Systems , year=

Reference 11

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 123f2da8-6459-4259-8052-f4995888be3f · outbound

This paper cites SIAM journal on discrete mathematics , volume=.

Compact Geometric Representations of Hierarchies SIAM journal on discrete mathematics , volume=

Reference 12

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

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Observation 991df9a8-d906-4d84-84cd-643d1a1625dd · outbound

This paper cites Sign rank versus.

Compact Geometric Representations of Hierarchies Sign rank versus

Reference 13

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation fdd1debc-3e31-4ec2-b701-7ba9413147f5 · outbound

This paper cites Asymptotic enumeration of partial orders on a finite set.

Compact Geometric Representations of Hierarchies Asymptotic enumeration of partial orders on a finite set

Reference 14

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

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Observation de4591f8-8cf7-40d0-ad58-8cad9a04ac90 · outbound

This paper cites Lower bound methods for sign-rank and their limitations.

Compact Geometric Representations of Hierarchies Lower bound methods for sign-rank and their limitations

Reference 15

Resolution: metadata mismatch; doi, observed 2026-06-26T22:20:10.257412Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 46b8f22a-e471-4ca1-85b1-271e89a121cc · outbound

This paper cites ACM SIGMOD Record , volume=.

Compact Geometric Representations of Hierarchies ACM SIGMOD Record , volume=

Reference 16

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 7370032a-cc90-4994-bfa6-b0da0450b862 · outbound

This paper cites Proceedings of the VLDB Endowment , volume=.

Compact Geometric Representations of Hierarchies Proceedings of the VLDB Endowment , volume=

Reference 17

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

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Observation 9f1d3f7b-f7fb-46c3-96f9-8b6e5816feb8 · outbound

This paper cites 22nd International Conference on Data Engineering (ICDE'06) , pages=.

Compact Geometric Representations of Hierarchies 22nd International Conference on Data Engineering (ICDE'06) , pages=

Reference 18

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation eda71de8-8512-42ce-95bd-72ccaded1c7e · outbound

This paper cites ACM Transactions on Database Systems (TODS) , volume=.

Compact Geometric Representations of Hierarchies ACM Transactions on Database Systems (TODS) , volume=

Reference 19

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 3200844d-4ece-4178-91a2-70ba1e9c80ec · outbound

This paper cites Proceedings of the 2008 ACM SIGMOD international conference on Management of data , pages=.

Compact Geometric Representations of Hierarchies Proceedings of the 2008 ACM SIGMOD international conference on Management of data , pages=

Reference 20

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation 0156c6e5-198d-47b4-97ae-15c31a7c9514 · outbound

This paper cites Proceedings of the 2007 ACM SIGMOD international conference on Management of data , pages=.

Compact Geometric Representations of Hierarchies Proceedings of the 2007 ACM SIGMOD international conference on Management of data , pages=

Reference 21

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

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Observation d66b9ba3-284b-49f9-97ce-921bb697fef9 · outbound

This paper cites 2022 , publisher=.

Compact Geometric Representations of Hierarchies 2022 , publisher=

Reference 22

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation e46b7eb7-c693-4ebd-8ef5-02be14779d4c · outbound

This paper cites an unresolved cited work.

Compact Geometric Representations of Hierarchies Unresolved cited work

Reference 23

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

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Observation 9702adad-3953-4544-88df-3fb8edf6d0d5 · outbound

This paper cites 2025 , publisher=.

Compact Geometric Representations of Hierarchies 2025 , publisher=

Reference 24

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

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Observation 1d7c9877-7d84-46dc-8213-e40e8aa742df · outbound

This paper cites SIAM Journal on Computing , volume=.

Compact Geometric Representations of Hierarchies SIAM Journal on Computing , volume=

Reference 25

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

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Observation 8a686073-1768-4faf-83b3-ad7e9c2ad20a · outbound

This paper cites Journal of Computer and System Sciences , volume=.

Compact Geometric Representations of Hierarchies Journal of Computer and System Sciences , volume=

Reference 26

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Unavailable: canonical work link unavailable.

Observation 257be791-8f25-4ae8-be8d-05df2d5fdf9c · outbound

This paper cites Proceedings of the American mathematical Society , volume=.

Compact Geometric Representations of Hierarchies Proceedings of the American mathematical Society , volume=

Reference 27

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 732ac477-14c9-4d14-816e-3f39b5ee2339 · outbound

This paper cites Proceedings of the 44th international ACM SIGIR conference on research and development in information retrieval , pages=.

Compact Geometric Representations of Hierarchies Proceedings of the 44th international ACM SIGIR conference on research and development in information retrieval , pages=

Reference 28

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 0e6bac9d-4be8-43a8-a836-c180b62679ac · outbound

This paper cites ACM Transactions on Information Systems , volume=.

Compact Geometric Representations of Hierarchies ACM Transactions on Information Systems , volume=

Reference 29

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation 437b621c-7f6e-480b-9f7a-44cafc6fddd0 · outbound

This paper cites Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval , pages=.

Compact Geometric Representations of Hierarchies Proceedings of the 47th International ACM SIGIR Conference on Research and Development in Information Retrieval , pages=

Reference 30

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation 008a7a78-607d-4062-9311-64f5f3cb7d91 · outbound

This paper cites Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing , pages=.

Compact Geometric Representations of Hierarchies Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing , pages=

Reference 31

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation 70318728-cd75-4778-9971-82164e6c28aa · outbound

This paper cites Developments in Theoretical Computer Science , volume=.

Compact Geometric Representations of Hierarchies Developments in Theoretical Computer Science , volume=

Reference 32

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation 54228662-4942-4acd-b4b3-d949760aff28 · outbound

This paper cites Proceedings of the 55th Annual ACM Symposium on Theory of Computing , pages=.

Compact Geometric Representations of Hierarchies Proceedings of the 55th Annual ACM Symposium on Theory of Computing , pages=

Reference 33

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation 2bfbd855-28ea-4b23-bc51-5ed94182877f · outbound

This paper cites Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) , pages=.

Compact Geometric Representations of Hierarchies Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) , pages=

Reference 34

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation 57a52c78-594e-40ef-8543-f551d2f7624d · outbound

This paper cites Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) , pages=.

Compact Geometric Representations of Hierarchies Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) , pages=

Reference 35

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation eec3fe99-64bb-478e-bc77-64eeaf653005 · outbound

This paper cites Proceedings of the 57th Annual ACM Symposium on Theory of Computing , pages=.

Compact Geometric Representations of Hierarchies Proceedings of the 57th Annual ACM Symposium on Theory of Computing , pages=

Reference 36

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation cd2f8d21-da7b-49a2-a24b-8d4a2c1363ec · outbound

This paper cites Proceedings of the 55th Annual ACM Symposium on Theory of Computing , pages=.

Compact Geometric Representations of Hierarchies Proceedings of the 55th Annual ACM Symposium on Theory of Computing , pages=

Reference 37

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation 4d92da17-24fe-41aa-8804-9c295c504deb · outbound

This paper cites 2023 IEEE 64th annual symposium on foundations of computer science (FOCS) , pages=.

Compact Geometric Representations of Hierarchies 2023 IEEE 64th annual symposium on foundations of computer science (FOCS) , pages=

Reference 38

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation d82e2eca-06b4-451e-b079-ce81e55a8246 · outbound

This paper cites 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS) , pages=.

Compact Geometric Representations of Hierarchies 2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS) , pages=

Reference 39

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation e1638701-b945-4dbd-83a5-6ae60f99ce69 · outbound

This paper cites Proceedings of the 19th ACM international conference on Information and knowledge management , pages=.

Compact Geometric Representations of Hierarchies Proceedings of the 19th ACM international conference on Information and knowledge management , pages=

Reference 40

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation 9a349cc8-de80-4731-9526-5a248d355801 · outbound

This paper cites Artificial Intelligence and Statistics , pages=.

Compact Geometric Representations of Hierarchies Artificial Intelligence and Statistics , pages=

Reference 41

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation 04897490-8630-453b-b0b5-5b06b5ec15b0 · outbound

This paper cites Artificial Intelligence and Statistics , pages=.

Compact Geometric Representations of Hierarchies Artificial Intelligence and Statistics , pages=

Reference 42

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 793e700c-9346-47ee-9eb7-8758f61cd570 · outbound

This paper cites Journal of Combinatorial Theory, Series B , volume=.

Compact Geometric Representations of Hierarchies Journal of Combinatorial Theory, Series B , volume=

Reference 43

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Unavailable: canonical work link unavailable.

Observation 5c907c2e-8421-4e96-94be-d963a6402017 · outbound

This paper cites Journal of Combinatorial Theory, Series B , volume=.

Compact Geometric Representations of Hierarchies Journal of Combinatorial Theory, Series B , volume=

Reference 44

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 699fd949-69e5-47df-9561-41051d0a3213 · outbound

This paper cites ACM Computing Surveys , volume=.

Compact Geometric Representations of Hierarchies ACM Computing Surveys , volume=

Reference 45

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

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Observation 758eeabc-5b0b-48ea-97e2-2bd9559bb2ad · outbound

This paper cites Proceedings of the 31st international conference on Very large data bases , pages=.

Compact Geometric Representations of Hierarchies Proceedings of the 31st international conference on Very large data bases , pages=

Reference 46

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 4d611b75-550d-4c15-81e9-e174fa765590 · outbound

This paper cites 2012 , publisher=.

Compact Geometric Representations of Hierarchies 2012 , publisher=

Reference 47

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Unavailable: canonical work link unavailable.

Observation d0d6bfc6-31b9-4cfb-b152-bfc23dd8fc48 · outbound

This paper cites Think Locally, Act Globally: Highly Balanced Graph Partitioning.

Compact Geometric Representations of Hierarchies Think Locally, Act Globally: Highly Balanced Graph Partitioning

Reference 48

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation cb232100-cec9-4b63-aec4-e3ec9d87907e · outbound

This paper cites W ord N et: A Lexical Database for E nglish.

Compact Geometric Representations of Hierarchies W ord N et: A Lexical Database for E nglish

Reference 49

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation b0034135-d681-4aca-b9b5-cf66e7976a4b · outbound

This paper cites 10 Gene Ontology Consortium.

Compact Geometric Representations of Hierarchies 10 Gene Ontology Consortium

Reference 50

Resolution: metadata mismatch; doi, observed 2026-06-26T22:20:10.259242Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation 292585f0-d7c6-4b82-bd7a-e6edea6dfb95 · outbound

This paper cites Gene ontology: tool for the unification of biology.

Compact Geometric Representations of Hierarchies Gene ontology: tool for the unification of biology

Reference 51

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation dfbe4843-2e11-496c-9c4b-bc114b42c4e1 · outbound

This paper cites Cora Dataset.

Compact Geometric Representations of Hierarchies Cora Dataset

Reference 52

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Observation 57621589-748a-48fc-beba-93507cfef584 · outbound

This paper cites $\mathbb{R}^{2k}$ is Theoretically Large Enough for Embedding-based Top-$k$ Retrieval.

Compact Geometric Representations of Hierarchies $\mathbb{R}^{2k}$ is Theoretically Large Enough for Embedding-based Top-$k$ Retrieval

Reference 53

Resolution: verified exact; local_arxiv, observed 2026-07-03T23:29:02.756484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation bcb0e67b-fb10-487f-a91a-a3b6cf853ad7 · outbound

This paper cites Drex: Accurate and scalable dense retrieval acceleration via algorithmic-hardware codesign.

Compact Geometric Representations of Hierarchies Drex: Accurate and scalable dense retrieval acceleration via algorithmic-hardware codesign

Reference 54

Resolution: metadata mismatch; arxiv_id, observed 2026-06-26T22:20:09.843011Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-09T06:31:02.800959+00:00.

Observation a7145239-0552-4f9f-b356-a5058036fcaa · outbound

This paper cites 2026 , eprint=.

Compact Geometric Representations of Hierarchies 2026 , eprint=

Reference 55

Resolution: unresolved; no resolver link, observed 2026-06-26T22:12:38.245812Z

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Pith citing papers

No inbound Pith citation observations are available.