{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:AEKPBB66CSUKAYB2PXFPPHCKOM","short_pith_number":"pith:AEKPBB66","schema_version":"1.0","canonical_sha256":"0114f087de14a8a0603a7dcaf79c4a73042245e998318afca75080ee78514df1","source":{"kind":"arxiv","id":"1310.6900","version":4},"attestation_state":"computed","paper":{"title":"Unsplittable coverings in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.MG","authors_text":"D\\\"om\\\"ot\\\"or P\\'alv\\\"olgyi, J\\'anos Pach","submitted_at":"2013-10-25T13:02:36Z","abstract_excerpt":"A system of sets forms an {\\em $m$-fold covering} of a set $X$ if every point of $X$ belongs to at least $m$ of its members. A $1$-fold covering is called a {\\em covering}. The problem of splitting multiple coverings into several coverings was motivated by classical density estimates for {\\em sphere packings} as well as by the {\\em planar sensor cover problem}. It has been the prevailing conjecture for 35 years (settled in many special cases) that for every plane convex body $C$, there exists a constant $m=m(C)$ such that every $m$-fold covering of the plane with translates of $C$ splits into "},"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":"1310.6900","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-10-25T13:02:36Z","cross_cats_sorted":["cs.DM","math.CO"],"title_canon_sha256":"ab74cad1d51f730618f8d6104d81f254e70d04955de2987010b9da562013d5ce","abstract_canon_sha256":"7216ed7d8c6b633fa5822eb86f971161fd53bfe86430a6b626c5216b5711febd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:38.020337Z","signature_b64":"8Httzl9ea/JH1f/68vSw7KuSE+MtwtzdYWXj2ftj4LOXP4DGHxfS1VQEYnIkAokcWBvljb7BC7hCMBa0ZOTqCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0114f087de14a8a0603a7dcaf79c4a73042245e998318afca75080ee78514df1","last_reissued_at":"2026-05-18T02:03:38.019626Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:38.019626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Unsplittable coverings in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"math.MG","authors_text":"D\\\"om\\\"ot\\\"or P\\'alv\\\"olgyi, J\\'anos Pach","submitted_at":"2013-10-25T13:02:36Z","abstract_excerpt":"A system of sets forms an {\\em $m$-fold covering} of a set $X$ if every point of $X$ belongs to at least $m$ of its members. A $1$-fold covering is called a {\\em covering}. The problem of splitting multiple coverings into several coverings was motivated by classical density estimates for {\\em sphere packings} as well as by the {\\em planar sensor cover problem}. It has been the prevailing conjecture for 35 years (settled in many special cases) that for every plane convex body $C$, there exists a constant $m=m(C)$ such that every $m$-fold covering of the plane with translates of $C$ splits into "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6900","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1310.6900","created_at":"2026-05-18T02:03:38.019729+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.6900v4","created_at":"2026-05-18T02:03:38.019729+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.6900","created_at":"2026-05-18T02:03:38.019729+00:00"},{"alias_kind":"pith_short_12","alias_value":"AEKPBB66CSUK","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"AEKPBB66CSUKAYB2","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"AEKPBB66","created_at":"2026-05-18T12:27:38.830355+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AEKPBB66CSUKAYB2PXFPPHCKOM","json":"https://pith.science/pith/AEKPBB66CSUKAYB2PXFPPHCKOM.json","graph_json":"https://pith.science/api/pith-number/AEKPBB66CSUKAYB2PXFPPHCKOM/graph.json","events_json":"https://pith.science/api/pith-number/AEKPBB66CSUKAYB2PXFPPHCKOM/events.json","paper":"https://pith.science/paper/AEKPBB66"},"agent_actions":{"view_html":"https://pith.science/pith/AEKPBB66CSUKAYB2PXFPPHCKOM","download_json":"https://pith.science/pith/AEKPBB66CSUKAYB2PXFPPHCKOM.json","view_paper":"https://pith.science/paper/AEKPBB66","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.6900&json=true","fetch_graph":"https://pith.science/api/pith-number/AEKPBB66CSUKAYB2PXFPPHCKOM/graph.json","fetch_events":"https://pith.science/api/pith-number/AEKPBB66CSUKAYB2PXFPPHCKOM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AEKPBB66CSUKAYB2PXFPPHCKOM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AEKPBB66CSUKAYB2PXFPPHCKOM/action/storage_attestation","attest_author":"https://pith.science/pith/AEKPBB66CSUKAYB2PXFPPHCKOM/action/author_attestation","sign_citation":"https://pith.science/pith/AEKPBB66CSUKAYB2PXFPPHCKOM/action/citation_signature","submit_replication":"https://pith.science/pith/AEKPBB66CSUKAYB2PXFPPHCKOM/action/replication_record"}},"created_at":"2026-05-18T02:03:38.019729+00:00","updated_at":"2026-05-18T02:03:38.019729+00:00"}