{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:EYZMALAO7LIINBFYT5TEHVXHWK","short_pith_number":"pith:EYZMALAO","schema_version":"1.0","canonical_sha256":"2632c02c0efad08684b89f6643d6e7b2bf28b5f59a3ac33ac3d1ea910f4f6ac9","source":{"kind":"arxiv","id":"2410.07059","version":1},"attestation_state":"computed","paper":{"title":"Online Epsilon Net and Piercing Set for Geometric Concepts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.LG","authors_text":"Devdan Dey, Satyam Singh, Sujoy Bhore","submitted_at":"2024-10-09T16:58:36Z","abstract_excerpt":"VC-dimension and $\\varepsilon$-nets are key concepts in Statistical Learning Theory. Intuitively, VC-dimension is a measure of the size of a class of sets. The famous $\\varepsilon$-net theorem, a fundamental result in Discrete Geometry, asserts that if the VC-dimension of a set system is bounded, then a small sample exists that intersects all sufficiently large sets.\n  In online learning scenarios where data arrives sequentially, the VC-dimension helps to bound the complexity of the set system, and $\\varepsilon$-nets ensure the selection of a small representative set. This sampling framework i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2410.07059","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-10-09T16:58:36Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"ec1a1a23279a9b2430daf779637d55c2b2f6ab1dfcbf88094273e7d4d397fb51","abstract_canon_sha256":"2128ed1b9dfd24ca6837122bf4b6411db591781ce75653f4daf818287a1c5499"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:18:10.397890Z","signature_b64":"3LG6KdMYv7YQnKZiDoOJra6zJ0Yj6OHYFzQVx2OyeDOdr7SXQR5iCbWIZF89IIARqGPbT+aUssIiddg5KKAiBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2632c02c0efad08684b89f6643d6e7b2bf28b5f59a3ac33ac3d1ea910f4f6ac9","last_reissued_at":"2026-07-05T09:18:10.397385Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:18:10.397385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Online Epsilon Net and Piercing Set for Geometric Concepts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.LG","authors_text":"Devdan Dey, Satyam Singh, Sujoy Bhore","submitted_at":"2024-10-09T16:58:36Z","abstract_excerpt":"VC-dimension and $\\varepsilon$-nets are key concepts in Statistical Learning Theory. Intuitively, VC-dimension is a measure of the size of a class of sets. The famous $\\varepsilon$-net theorem, a fundamental result in Discrete Geometry, asserts that if the VC-dimension of a set system is bounded, then a small sample exists that intersects all sufficiently large sets.\n  In online learning scenarios where data arrives sequentially, the VC-dimension helps to bound the complexity of the set system, and $\\varepsilon$-nets ensure the selection of a small representative set. This sampling framework i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.07059","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.07059/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2410.07059","created_at":"2026-07-05T09:18:10.397443+00:00"},{"alias_kind":"arxiv_version","alias_value":"2410.07059v1","created_at":"2026-07-05T09:18:10.397443+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.07059","created_at":"2026-07-05T09:18:10.397443+00:00"},{"alias_kind":"pith_short_12","alias_value":"EYZMALAO7LII","created_at":"2026-07-05T09:18:10.397443+00:00"},{"alias_kind":"pith_short_16","alias_value":"EYZMALAO7LIINBFY","created_at":"2026-07-05T09:18:10.397443+00:00"},{"alias_kind":"pith_short_8","alias_value":"EYZMALAO","created_at":"2026-07-05T09:18:10.397443+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.08758","citing_title":"On Fair Epsilon Net and Geometric Hitting Set","ref_index":12,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/EYZMALAO7LIINBFYT5TEHVXHWK","json":"https://pith.science/pith/EYZMALAO7LIINBFYT5TEHVXHWK.json","graph_json":"https://pith.science/api/pith-number/EYZMALAO7LIINBFYT5TEHVXHWK/graph.json","events_json":"https://pith.science/api/pith-number/EYZMALAO7LIINBFYT5TEHVXHWK/events.json","paper":"https://pith.science/paper/EYZMALAO"},"agent_actions":{"view_html":"https://pith.science/pith/EYZMALAO7LIINBFYT5TEHVXHWK","download_json":"https://pith.science/pith/EYZMALAO7LIINBFYT5TEHVXHWK.json","view_paper":"https://pith.science/paper/EYZMALAO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2410.07059&json=true","fetch_graph":"https://pith.science/api/pith-number/EYZMALAO7LIINBFYT5TEHVXHWK/graph.json","fetch_events":"https://pith.science/api/pith-number/EYZMALAO7LIINBFYT5TEHVXHWK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EYZMALAO7LIINBFYT5TEHVXHWK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EYZMALAO7LIINBFYT5TEHVXHWK/action/storage_attestation","attest_author":"https://pith.science/pith/EYZMALAO7LIINBFYT5TEHVXHWK/action/author_attestation","sign_citation":"https://pith.science/pith/EYZMALAO7LIINBFYT5TEHVXHWK/action/citation_signature","submit_replication":"https://pith.science/pith/EYZMALAO7LIINBFYT5TEHVXHWK/action/replication_record"}},"created_at":"2026-07-05T09:18:10.397443+00:00","updated_at":"2026-07-05T09:18:10.397443+00:00"}