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We provide constructions of omnimosaics and show that for fixed $a$ the smallest possible size $\\omega(k,a)$ of an $O(n,k,a)$ omnimosaic satisfies \\[\\frac{ka^{k/2}}{e}\\le \\omega(k,a)\\le \\frac{ka^{k/2}}{e}(1+o(1))\\] for a well-specified function $o(1)$ that tends to zero as $k\\to\\infty$."},"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":"1009.4626","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-23T14:57:01Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"8351eeb83618afa43dcd014690b0bb5471e7fd6776f19ccd60d211303e1ce253","abstract_canon_sha256":"a9882ec805b6ff9283e8d530e18f63cf30cb6474ac4d9a9afbbfc99ab7bfce41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:40:21.989784Z","signature_b64":"oCL4l9TtMnLDXd00aqKvmpHVK9GwyruHNhhltxuBoKpbax3dFUxnnSfGBlZR8Y1T+pTuCpQux2iH0HczCP4FCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"061d36aaccf84e72a4dbc3dccfc145931dd6af73114fa10940a341c9b217aa64","last_reissued_at":"2026-05-18T04:40:21.989207Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:40:21.989207Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Omnimosaics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"Anant P. 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We provide constructions of omnimosaics and show that for fixed $a$ the smallest possible size $\\omega(k,a)$ of an $O(n,k,a)$ omnimosaic satisfies \\[\\frac{ka^{k/2}}{e}\\le \\omega(k,a)\\le \\frac{ka^{k/2}}{e}(1+o(1))\\] for a well-specified function $o(1)$ that tends to zero as $k\\to\\infty$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4626","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":""},"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":"1009.4626","created_at":"2026-05-18T04:40:21.989291+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.4626v1","created_at":"2026-05-18T04:40:21.989291+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4626","created_at":"2026-05-18T04:40:21.989291+00:00"},{"alias_kind":"pith_short_12","alias_value":"AYOTNKWM7BHH","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"AYOTNKWM7BHHFJG3","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"AYOTNKWM","created_at":"2026-05-18T12:26:05.355336+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/AYOTNKWM7BHHFJG3YPOM7QKFSM","json":"https://pith.science/pith/AYOTNKWM7BHHFJG3YPOM7QKFSM.json","graph_json":"https://pith.science/api/pith-number/AYOTNKWM7BHHFJG3YPOM7QKFSM/graph.json","events_json":"https://pith.science/api/pith-number/AYOTNKWM7BHHFJG3YPOM7QKFSM/events.json","paper":"https://pith.science/paper/AYOTNKWM"},"agent_actions":{"view_html":"https://pith.science/pith/AYOTNKWM7BHHFJG3YPOM7QKFSM","download_json":"https://pith.science/pith/AYOTNKWM7BHHFJG3YPOM7QKFSM.json","view_paper":"https://pith.science/paper/AYOTNKWM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.4626&json=true","fetch_graph":"https://pith.science/api/pith-number/AYOTNKWM7BHHFJG3YPOM7QKFSM/graph.json","fetch_events":"https://pith.science/api/pith-number/AYOTNKWM7BHHFJG3YPOM7QKFSM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AYOTNKWM7BHHFJG3YPOM7QKFSM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AYOTNKWM7BHHFJG3YPOM7QKFSM/action/storage_attestation","attest_author":"https://pith.science/pith/AYOTNKWM7BHHFJG3YPOM7QKFSM/action/author_attestation","sign_citation":"https://pith.science/pith/AYOTNKWM7BHHFJG3YPOM7QKFSM/action/citation_signature","submit_replication":"https://pith.science/pith/AYOTNKWM7BHHFJG3YPOM7QKFSM/action/replication_record"}},"created_at":"2026-05-18T04:40:21.989291+00:00","updated_at":"2026-05-18T04:40:21.989291+00:00"}