{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:GGKJC5VPHEGAHPE624ANWEZUFC","short_pith_number":"pith:GGKJC5VP","schema_version":"1.0","canonical_sha256":"31949176af390c03bc9ed700db1334288b36cc1ae7b95b04f620b99df3894f87","source":{"kind":"arxiv","id":"2502.10516","version":2},"attestation_state":"computed","paper":{"title":"A new lower bound for multi-color discrepancy with applications to fair division","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Ioannis Caragiannis, Kasper Green Larsen, Sudarshan Shyam","submitted_at":"2025-02-14T19:24:55Z","abstract_excerpt":"A classical problem in combinatorics seeks colorings of low discrepancy. More concretely, the goal is to color the elements of a set system so that the number of appearances of any color among the elements in each set is as balanced as possible. We present a new lower bound for multi-color discrepancy, showing that there is a set system with $n$ subsets over a set of elements in which any $k$-coloring of the elements has discrepancy at least $\\Omega\\left(\\sqrt{\\frac{n}{\\ln{k}}}\\right)$. This result improves the previously best-known lower bound of $\\Omega\\left(\\sqrt{\\frac{n}{k}}\\right)$ of Doe"},"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":"2502.10516","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.GT","submitted_at":"2025-02-14T19:24:55Z","cross_cats_sorted":[],"title_canon_sha256":"6daa520b09642e912d8cf0307f6bd6db1f1dc73a54da71caf781761df2ac4540","abstract_canon_sha256":"59ed27a760d9a8a6776f0bf22cd9f9b174027c278106005bd50c9c663345bc79"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:16:21.209181Z","signature_b64":"vBUzK5UnBFM4Kxk/bGWpfM78G8deOrTzXdy3abxaISyodgXF/rpAYAfcKiGrAUiwO3E/I1RCw12ueBxZwgu2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31949176af390c03bc9ed700db1334288b36cc1ae7b95b04f620b99df3894f87","last_reissued_at":"2026-07-05T10:16:21.208695Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:16:21.208695Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A new lower bound for multi-color discrepancy with applications to fair division","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.GT","authors_text":"Ioannis Caragiannis, Kasper Green Larsen, Sudarshan Shyam","submitted_at":"2025-02-14T19:24:55Z","abstract_excerpt":"A classical problem in combinatorics seeks colorings of low discrepancy. More concretely, the goal is to color the elements of a set system so that the number of appearances of any color among the elements in each set is as balanced as possible. We present a new lower bound for multi-color discrepancy, showing that there is a set system with $n$ subsets over a set of elements in which any $k$-coloring of the elements has discrepancy at least $\\Omega\\left(\\sqrt{\\frac{n}{\\ln{k}}}\\right)$. This result improves the previously best-known lower bound of $\\Omega\\left(\\sqrt{\\frac{n}{k}}\\right)$ of Doe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.10516","kind":"arxiv","version":2},"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/2502.10516/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":"2502.10516","created_at":"2026-07-05T10:16:21.208750+00:00"},{"alias_kind":"arxiv_version","alias_value":"2502.10516v2","created_at":"2026-07-05T10:16:21.208750+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.10516","created_at":"2026-07-05T10:16:21.208750+00:00"},{"alias_kind":"pith_short_12","alias_value":"GGKJC5VPHEGA","created_at":"2026-07-05T10:16:21.208750+00:00"},{"alias_kind":"pith_short_16","alias_value":"GGKJC5VPHEGAHPE6","created_at":"2026-07-05T10:16:21.208750+00:00"},{"alias_kind":"pith_short_8","alias_value":"GGKJC5VP","created_at":"2026-07-05T10:16:21.208750+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.21346","citing_title":"Simultaneously Efficient Allocation of Indivisible Items Across Multiple Dimensions","ref_index":8,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GGKJC5VPHEGAHPE624ANWEZUFC","json":"https://pith.science/pith/GGKJC5VPHEGAHPE624ANWEZUFC.json","graph_json":"https://pith.science/api/pith-number/GGKJC5VPHEGAHPE624ANWEZUFC/graph.json","events_json":"https://pith.science/api/pith-number/GGKJC5VPHEGAHPE624ANWEZUFC/events.json","paper":"https://pith.science/paper/GGKJC5VP"},"agent_actions":{"view_html":"https://pith.science/pith/GGKJC5VPHEGAHPE624ANWEZUFC","download_json":"https://pith.science/pith/GGKJC5VPHEGAHPE624ANWEZUFC.json","view_paper":"https://pith.science/paper/GGKJC5VP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2502.10516&json=true","fetch_graph":"https://pith.science/api/pith-number/GGKJC5VPHEGAHPE624ANWEZUFC/graph.json","fetch_events":"https://pith.science/api/pith-number/GGKJC5VPHEGAHPE624ANWEZUFC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GGKJC5VPHEGAHPE624ANWEZUFC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GGKJC5VPHEGAHPE624ANWEZUFC/action/storage_attestation","attest_author":"https://pith.science/pith/GGKJC5VPHEGAHPE624ANWEZUFC/action/author_attestation","sign_citation":"https://pith.science/pith/GGKJC5VPHEGAHPE624ANWEZUFC/action/citation_signature","submit_replication":"https://pith.science/pith/GGKJC5VPHEGAHPE624ANWEZUFC/action/replication_record"}},"created_at":"2026-07-05T10:16:21.208750+00:00","updated_at":"2026-07-05T10:16:21.208750+00:00"}