Paper Citation Record · LEDGER

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale

As of 11 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 2 inbound Pith citation observations for arXiv:2605.13684.

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

pith.paper-citation-record.v1
2605.13684 v1

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-14T20:33:27.226085Z

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 2 of 2 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links, observed 2026-08-07T15:05:21.675574Z

measured 0 of 1 external citation measurements

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

Source: pith, observed 2026-08-07T15:05:23.381557Z

Reference resolution

41 of 41 outbound references displayed

verified exact11
verified fuzzy25
unresolved4
parse uncertain0
malformed identifier0
metadata mismatch1

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 3be37867-1f1c-4e59-9031-a76b62d87292 · outbound

This paper cites Long , editor =.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Long , editor =

Reference 1

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Observation c3759116-f60a-475d-9f1c-a0c5767a3588 · outbound

This paper cites Inventiones Mathematicae , volume =.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Inventiones Mathematicae , volume =

Reference 2

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.488978Z

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Observation e030c66a-89ae-46df-beb2-280b8dbce5ae · outbound

This paper cites IEEE Transactions on Information Theory , volume =.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale IEEE Transactions on Information Theory , volume =

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.491920Z

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Observation 8682daf1-3dc2-450a-badd-c21ab030729a · outbound

This paper cites Bartlett and Sanjeev R.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Bartlett and Sanjeev R

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.494237Z

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Observation 42f13d9e-4284-4286-a24a-0e79295cd327 · outbound

This paper cites International Conference on Computational Learning Theory , pages=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale International Conference on Computational Learning Theory , pages=

Reference 5

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Observation 8c2d0ee7-b67b-4c61-adde-b9b79bb9b2ed · outbound

This paper cites A graph-theoretic generalization of the Sauer-Shelah lemma , journal =.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale A graph-theoretic generalization of the Sauer-Shelah lemma , journal =

Reference 6

Resolution: verified exact; doi, observed 2026-05-14T20:37:58.003156Z

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Observation db695366-54c9-4316-9504-6b228da84020 · outbound

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

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Journal of Combinatorial Theory, Series A , volume =

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.483657Z

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Observation 7c49c5f8-08e8-47ae-a7fe-0b9fc85fe168 · outbound

This paper cites 1994 , issn =.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale 1994 , issn =

Reference 8

Resolution: verified exact; doi, observed 2026-05-14T20:37:58.007939Z

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Observation af16b7c0-96e3-48e5-b920-798872034940 · outbound

This paper cites 1960 , month =.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale 1960 , month =

Reference 9

Resolution: verified exact; doi, observed 2026-05-14T20:37:57.998517Z

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Observation 24aa7db6-f142-431e-939a-6c0eb5b3bbd9 · outbound

This paper cites an unresolved cited work.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Unresolved cited work

Reference 10

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Observation 5a5536b6-ea16-4d4e-8dd9-f538bcf000d6 · outbound

This paper cites The Annals of Probability , pages=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale The Annals of Probability , pages=

Reference 11

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Observation 34210627-7a15-4215-9f1a-f048c9a39bae · outbound

This paper cites 1984 , url=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale 1984 , url=

Reference 12

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Observation 3cacd46a-92e6-4032-9eb7-0ecd3ad0bd43 · outbound

This paper cites Surveys in combinatorics , volume=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Surveys in combinatorics , volume=

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.472296Z

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Observation 95bc8c68-ab91-4697-86b9-ed34a0d00fa6 · outbound

This paper cites 1999 , publisher=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale 1999 , publisher=

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.477205Z

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Observation 4f370ced-04a6-41a5-a746-a48d8b13350f · outbound

This paper cites 1984 , url=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale 1984 , url=

Reference 15

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Observation e72584cf-8fc1-47bd-99c2-30661f9817fe · outbound

This paper cites Conference on Learning Theory , pages=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Conference on Learning Theory , pages=

Reference 16

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Source-reported events for the cited work

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Observation 32d9e6ec-4722-40fb-bddf-30df1fc6d9cc · outbound

This paper cites arXiv preprint arXiv:2510.15020 , year=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale arXiv preprint arXiv:2510.15020 , year=

Reference 17

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Source-reported events for the cited work

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Observation a0c2cadf-879c-4be3-b2da-91999dd3e23b · outbound

This paper cites arXiv preprint arXiv:2411.13029 , year=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale arXiv preprint arXiv:2411.13029 , year=

Reference 18

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Source-reported events for the cited work

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Observation ccd8e521-57f9-4829-8425-8eacf0f21551 · outbound

This paper cites Journal of Theoretical Probability , volume=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Journal of Theoretical Probability , volume=

Reference 19

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Observation 7ad7289d-7bdf-4ae3-ac49-94ceee0ee1cc · outbound

This paper cites Annals of Mathematics , pages=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Annals of Mathematics , pages=

Reference 20

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Observation ba9acf9c-8b70-423a-b8b4-ac5ad6b27b27 · outbound

This paper cites An improved uniform convergence bound with fat-shattering dimension , journal =.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale An improved uniform convergence bound with fat-shattering dimension , journal =

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-05-14T20:37:58.021621Z

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Observation bb87a1f8-d55e-447d-8c11-d8e01e8f4a83 · outbound

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Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-05-15T14:51:09.446203Z

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 8670846a-0fcf-4620-90c4-574fc882b73a · outbound

This paper cites 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS) , pages=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale 2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS) , pages=

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.454494Z

Source-reported events for the cited work

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Observation 947450b1-da2b-4519-a4e3-c3f3e3417dc3 · outbound

This paper cites 1971 , url=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale 1971 , url=

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.440532Z

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Observation 31368b2c-c5e9-42bf-91d4-9aea462d04eb · outbound

This paper cites and Haussler, David and Warmuth, Manfred K.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale and Haussler, David and Warmuth, Manfred K

Reference 25

Resolution: verified exact; arxiv_id, observed 2026-05-14T20:37:58.014657Z

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 592e5ff1-ea4e-4430-bf5a-0f8d9e0b0a7e · outbound

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Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Unresolved cited work

Reference 26

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

Observation 57fcedc2-c310-41e3-a663-cc95f3235aec · outbound

This paper cites Scale-sensitive dimensions, uniform convergence, and learnability , year =.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Scale-sensitive dimensions, uniform convergence, and learnability , year =

Reference 27

Resolution: verified exact; arxiv_id, observed 2026-05-14T20:37:58.028341Z

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 af031b9e-2c43-40a8-84e8-794f3e08eff5 · outbound

This paper cites Primal and dual combinatorial dimensions , journal =.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Primal and dual combinatorial dimensions , journal =

Reference 28

Resolution: verified exact; doi, observed 2026-05-14T20:37:58.038484Z

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Observation fb0be55a-24cd-4262-a972-b90009aaaa8c · outbound

This paper cites Journal of Machine Learning Research , year =.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Journal of Machine Learning Research , year =

Reference 29

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Source-reported events for the cited work

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Observation 1ac4d7a8-45f1-4399-8220-b9b2f69f4360 · outbound

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Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Forty-first International Conference on Machine Learning , year=

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.469943Z

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Observation c68a227c-c3d7-4066-8b81-39828811723c · outbound

This paper cites Algorithmic Learning Theory , pages=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Algorithmic Learning Theory , pages=

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.465919Z

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Observation d56c9727-bfa3-4b5c-92fc-4a6a365d1dce · outbound

This paper cites Journal of the ACM (JACM) , volume=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Journal of the ACM (JACM) , volume=

Reference 32

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.448067Z

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Observation ff6422d6-974f-419d-918c-ad3d70637dd0 · outbound

This paper cites Bartlett and Philip M.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Bartlett and Philip M

Reference 33

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Source-reported events for the cited work

correction dated 2023-11-09. Source: crossref record 10.1016/j.jcss.2023.103465->10.1006/jcss.1997.1557:correction, observed 2026-07-11T03:14:16.87961+00:00. This notice travels one citation hop only.

Observation 17fcf15c-ff66-4c39-a77c-d6266560e004 · outbound

This paper cites A Theoretical Framework for Statistical Evaluability of Generative Models.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale A Theoretical Framework for Statistical Evaluability of Generative Models

Reference 34

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This paper cites Integral Probability Metrics and Their Generating Classes of Functions , urldate =.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Integral Probability Metrics and Their Generating Classes of Functions , urldate =

Reference 35

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Observation d3902b38-063c-408c-80c5-66bb76067758 · outbound

This paper cites Yatracos , journal =.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Yatracos , journal =

Reference 36

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.467827Z

Source-reported events for the cited work

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Observation 7bcb0c2b-970a-414e-9151-788a62c584cd · outbound

This paper cites 2025 , eprint=.

Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale 2025 , eprint=

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.452186Z

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

Observation 125853ee-59ca-4383-b06c-2a8920ef0587 · outbound

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Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale 2024 , eprint=

Reference 38

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Source-reported events for the cited work

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Observation 4aa1f21c-e530-47a3-b53e-00ae69c0dfa1 · outbound

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Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale 2021 , eprint=

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.464059Z

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 a16b82a7-7b4b-4259-85a0-ffbfcf611f1e · outbound

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Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale 2020 , eprint=

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-15T14:51:09.462187Z

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 7b311ec8-53ba-4521-ae40-d1d6bf738fdd · outbound

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Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale Unresolved cited work

Reference 41

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Pith citing papers

Observation 171582c1-5d1f-483e-afa8-18ea4fb7ee84 · inbound

Quantitative analytic stable regularity cites this paper.

Quantitative analytic stable regularity Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale

Reference 2

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Maximal pattern complexity and structure of null systems cites this paper.

Maximal pattern complexity and structure of null systems Scale-Sensitive Shattering: Learnability and Evaluability at Optimal Scale

Reference 3

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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.