Paper Citation Record · LEDGER

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes

As of 19 August 2026, this Paper Citation Record lists 29 of 29 outbound references and 0 inbound Pith citation observations for arXiv:2607.06069.

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

pith.paper-citation-record.v1
2607.06069 v1

Coverage vector

measured 29 of 29 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-07-08T17:56:09.032589Z

measured 29 of 29 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-19T06:32:44.657259+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

29 of 29 outbound references displayed

verified exact15
verified fuzzy4
unresolved0
parse uncertain0
malformed identifier3
metadata mismatch7

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation ac5f9235-319b-4da6-86e5-78b03186a720 · outbound

This paper cites 1007/s00453-001-0110-y,doi:10.1007/S00453-001-0110-Y.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes 1007/s00453-001-0110-y,doi:10.1007/S00453-001-0110-Y

Reference 1

Resolution: metadata mismatch; doi, observed 2026-07-08T18:05:18.046689Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation f809d711-d896-427c-9cd8-c961a482a57d · outbound

This paper cites Polynomial Time Approximation Schemes for Euclidean TSP and Other Geometric Problems.Journal of the ACM, 45(5):753–782, 1998.doi:10.1145/290179.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Polynomial Time Approximation Schemes for Euclidean TSP and Other Geometric Problems.Journal of the ACM, 45(5):753–782, 1998.doi:10.1145/290179

Reference 2

Resolution: verified exact; doi, observed 2026-07-08T18:05:18.054942Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 4d30cdce-1bce-4eca-8c87-c8184f3f58f1 · outbound

This paper cites Baker , title =.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Baker , title =

Reference 3

Resolution: verified exact; arxiv_id, observed 2026-07-08T18:05:18.049618Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 65e31a32-adba-4beb-ba9b-e4c6ea5c16b3 · outbound

This paper cites S., and Pasin Manurangsi.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes S., and Pasin Manurangsi

Reference 4

Resolution: verified exact; doi, observed 2026-07-08T18:05:18.060169Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 0ec3b8c0-15cf-4b33-9bf6-2ae012a0d323 · outbound

This paper cites Proceedings of the 58th ACM Symposium on Theory of Computing , pages =.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Proceedings of the 58th ACM Symposium on Theory of Computing , pages =

Reference 5

Resolution: metadata mismatch; arxiv_id, observed 2026-07-08T18:05:18.029666Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 784e8b7b-65d6-4b0a-9753-d58d26b75b62 · outbound

This paper cites an unresolved cited work.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Unresolved cited work

Reference 6

Resolution: verified exact; doi, observed 2026-07-08T18:05:18.056364Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3bc58b9a-9a55-4324-adca-e7fccf0402d2 · outbound

This paper cites Chalermsook, M.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Chalermsook, M

Reference 7

Resolution: metadata mismatch; doi, observed 2026-07-08T18:05:18.059130Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2b32bd89-6b1a-407f-842f-568c0b7a00dd · outbound

This paper cites doi:10.1016/S0196-6774(02)00294-8.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes doi:10.1016/S0196-6774(02)00294-8

Reference 8

Resolution: verified exact; doi, observed 2026-07-08T18:05:18.047472Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 31c6f57d-0bb4-44e0-8ce2-0e36dd946202 · outbound

This paper cites S., David Saulpic, and Chris Schwiegelshohn.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes S., David Saulpic, and Chris Schwiegelshohn

Reference 9

Resolution: verified exact; arxiv_id, observed 2026-07-08T18:05:18.303208Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 3ae556c8-a4ec-45a0-b145-8fa83a5c416a · outbound

This paper cites 6 Josep Díaz, Olli Pottonen, Maria J.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes 6 Josep Díaz, Olli Pottonen, Maria J

Reference 10

Resolution: metadata mismatch; doi, observed 2026-07-08T18:05:18.062322Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation dd2b0839-e7da-42bb-b45c-0fc382a7c228 · outbound

This paper cites Das, Paz Carmi, and Subhas C.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Das, Paz Carmi, and Subhas C

Reference 11

Resolution: verified exact; doi, observed 2026-07-08T18:05:18.032056Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 800be51e-f083-4c5c-bc7b-df5a09f2a00d · outbound

This paper cites A framework for exponential-time-hypothesis-tight algorithms and lower bounds in geometric intersection graphs.SIAM Journal on Computing, 49(6):1291–1331, 2020.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes A framework for exponential-time-hypothesis-tight algorithms and lower bounds in geometric intersection graphs.SIAM Journal on Computing, 49(6):1291–1331, 2020

Reference 12

Resolution: verified exact; doi, observed 2026-07-08T18:05:18.064749Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1c74cbc8-43f8-4641-a9eb-8a5d0b7886f4 · outbound

This paper cites Demaine and MohammadTaghi Hajiaghayi.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Demaine and MohammadTaghi Hajiaghayi

Reference 13

Resolution: metadata mismatch; arxiv_id, observed 2026-07-08T18:05:18.298159Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 83c93187-1ca5-442e-8721-ae385ac4094b · outbound

This paper cites Mildly exponential reduction from gap-3SAT to polynomial-gap label-cover.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Mildly exponential reduction from gap-3SAT to polynomial-gap label-cover

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T18:05:18.565425Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 36cf1a56-dbe8-4f6a-a692-3288110e00ee · outbound

This paper cites S., Euiwoong Lee, and Pasin Manurangsi.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes S., Euiwoong Lee, and Pasin Manurangsi

Reference 15

Resolution: verified exact; doi, observed 2026-07-08T18:05:18.060913Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 48c85e09-d792-4fb8-8ed0-9c1ca599ef55 · outbound

This paper cites Quentin Gendre and Tomoyuki Kaneko.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Quentin Gendre and Tomoyuki Kaneko

Reference 16

Resolution: metadata mismatch; doi, observed 2026-07-08T18:05:18.062899Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation fb2b79f4-d7f7-48ba-b55f-cc99e2928a72 · outbound

This paper cites Hochbaum and Wolfgang Maass.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Hochbaum and Wolfgang Maass

Reference 17

Resolution: malformed identifier; arxiv_id, observed 2026-07-08T18:05:18.305867Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b72a85bd-bd8a-4b37-85fb-8029ea5eb015 · outbound

This paper cites Which problems have strongly exponential complexity? J.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Which problems have strongly exponential complexity? J

Reference 18

Resolution: verified exact; arxiv_id, observed 2026-07-08T18:05:18.039679Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7118b0ed-add5-49ed-a326-3427f4fddc0d · outbound

This paper cites Minimum Dominating Set for a Point Set in $\IR^2$.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Minimum Dominating Set for a Point Set in $\IR^2$

Reference 19

Resolution: verified exact; local_arxiv, observed 2026-07-08T18:05:18.303258Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 2ab2c16d-1015-47d9-9ba5-6714ec2f21ce · outbound

This paper cites Phd the- sis, Technische Universiteit Eindhoven, Department of Mathematics and Computer Sci- ence, Eindhoven, The Netherlands, 2019.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Phd the- sis, Technische Universiteit Eindhoven, Department of Mathematics and Computer Sci- ence, Eindhoven, The Netherlands, 2019

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T18:05:18.567361Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d7884183-e865-4e08-91da-f468db5d49ca · outbound

This paper cites van der Zanden.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes van der Zanden

Reference 21

Resolution: malformed identifier; raw_fallback, observed 2026-07-08T18:05:18.569221Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 88a13c4a-a624-40c9-9af3-9dfdb7f11874 · outbound

This paper cites A gap-ETH-tight ap- proximation scheme for Euclidean TSP.Journal of the ACM, 72(6):42:1–42:48, 2025.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes A gap-ETH-tight ap- proximation scheme for Euclidean TSP.Journal of the ACM, 72(6):42:1–42:48, 2025

Reference 22

Resolution: verified exact; doi, observed 2026-07-08T18:05:18.054392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 23482e58-4b25-4516-935b-665b486e644c · outbound

This paper cites There is no EPTAS for two-dimensional knapsack.Infor- mation Processing Letters, 110(16):707–710, 2010.doi:10.1016/j.ipl.2010.05.031.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes There is no EPTAS for two-dimensional knapsack.Infor- mation Processing Letters, 110(16):707–710, 2010.doi:10.1016/j.ipl.2010.05.031

Reference 23

Resolution: verified exact; doi, observed 2026-07-08T18:05:18.057111Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 214e77d1-1438-483b-a3bf-376e04eff1c1 · outbound

This paper cites A Birthday Repetition Theorem and Com- plexity of Approximating Dense CSPs.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes A Birthday Repetition Theorem and Com- plexity of Approximating Dense CSPs

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T18:05:18.563545Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 1e64ebf9-2a48-4043-86a4-47145f49d200 · outbound

This paper cites Random separation: A new method for solving fixed-cardinality optimization problems.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Random separation: A new method for solving fixed-cardinality optimization problems

Reference 25

Resolution: verified exact; doi, observed 2026-07-08T18:05:18.058432Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation d1e5d985-2a9d-4a26-b8f1-e1864b3a3b5e · outbound

This paper cites On the optimality of planar and geometric approximation schemes.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes On the optimality of planar and geometric approximation schemes

Reference 26

Resolution: verified exact; doi, observed 2026-07-08T18:05:18.049710Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation b7a30d84-542f-49f9-993b-bb12e568502a · outbound

This paper cites ISBN 9781450325943.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes ISBN 9781450325943

Reference 27

Resolution: metadata mismatch; arxiv_id, observed 2026-07-08T18:05:18.052955Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7fd354a0-f471-4a5b-8c78-97f632c55f7d · outbound

This paper cites Miller, Shang-Hua Teng, William P.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Miller, Shang-Hua Teng, William P

Reference 28

Resolution: malformed identifier; arxiv_id, observed 2026-07-08T18:05:18.300552Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Observation 7c8136f4-94ec-4d05-a54c-864a3ee6a0ef · outbound

This paper cites Papadimitriou.Computational Complexity.

Shifting is Optimal under Gap-ETH: A Lower Bound Framework for Geometric Approximation Schemes Papadimitriou.Computational Complexity

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-07-08T18:05:18.560974Z

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No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.

Pith citing papers

No inbound Pith citation observations are available.