{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FZH2JIFNXV7M5XQTJPHI5W5DZQ","short_pith_number":"pith:FZH2JIFN","schema_version":"1.0","canonical_sha256":"2e4fa4a0adbd7ecede134bce8edba3cc0ec97e9f731bad711d6498d9afbf087e","source":{"kind":"arxiv","id":"1708.06928","version":4},"attestation_state":"computed","paper":{"title":"Filling systems on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bidyut Sanki, Shiv Parsad","submitted_at":"2017-08-23T09:20:46Z","abstract_excerpt":"Let $F_g$ be a closed orientable surface of genus $g$. A set $\\Omega = \\{ \\gamma_1, \\dots, \\gamma_s\\}$ of pairwise non-homotopic simple closed curves on $F_g$ is called a \\emph{filling system} or simply a \\emph{filling} of $F_g$, if $F_g\\setminus \\Omega$ is a union of $b$ topological discs for some $b\\geq 1$. A filling system is called \\emph{minimal}, if $b=1$. The \\emph{size} of a filling is defined as the number of its elements. We prove that the maximum size of a filling of $F_g$ with $b$ complementary discs is $2g+b-1$. Next, we show that for $g\\geq 2, b\\geq 1\\text{ with }(g,b)\\neq (2,1)$ "},"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":"1708.06928","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2017-08-23T09:20:46Z","cross_cats_sorted":[],"title_canon_sha256":"7121654c7ab5faec95c2c611ecce4b938ff3241c29169c28fd5a08832e648937","abstract_canon_sha256":"4a2d5e46784574aafbb475cbc84e60bd70da4fedec2f65beab84f15ced95d992"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:47.114298Z","signature_b64":"eE6lQDbQSYkeGgtV74ueTDEgm0dhlSVxMdE1KrFcN7W2NeDUACmtMQ3hfUeiyzN0XmUtZLq7BB9Ngb/By9gEAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e4fa4a0adbd7ecede134bce8edba3cc0ec97e9f731bad711d6498d9afbf087e","last_reissued_at":"2026-05-18T00:15:47.113711Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:47.113711Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Filling systems on surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Bidyut Sanki, Shiv Parsad","submitted_at":"2017-08-23T09:20:46Z","abstract_excerpt":"Let $F_g$ be a closed orientable surface of genus $g$. A set $\\Omega = \\{ \\gamma_1, \\dots, \\gamma_s\\}$ of pairwise non-homotopic simple closed curves on $F_g$ is called a \\emph{filling system} or simply a \\emph{filling} of $F_g$, if $F_g\\setminus \\Omega$ is a union of $b$ topological discs for some $b\\geq 1$. A filling system is called \\emph{minimal}, if $b=1$. The \\emph{size} of a filling is defined as the number of its elements. We prove that the maximum size of a filling of $F_g$ with $b$ complementary discs is $2g+b-1$. Next, we show that for $g\\geq 2, b\\geq 1\\text{ with }(g,b)\\neq (2,1)$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.06928","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":"1708.06928","created_at":"2026-05-18T00:15:47.113787+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.06928v4","created_at":"2026-05-18T00:15:47.113787+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.06928","created_at":"2026-05-18T00:15:47.113787+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZH2JIFNXV7M","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZH2JIFNXV7M5XQT","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZH2JIFN","created_at":"2026-05-18T12:31:15.632608+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/FZH2JIFNXV7M5XQTJPHI5W5DZQ","json":"https://pith.science/pith/FZH2JIFNXV7M5XQTJPHI5W5DZQ.json","graph_json":"https://pith.science/api/pith-number/FZH2JIFNXV7M5XQTJPHI5W5DZQ/graph.json","events_json":"https://pith.science/api/pith-number/FZH2JIFNXV7M5XQTJPHI5W5DZQ/events.json","paper":"https://pith.science/paper/FZH2JIFN"},"agent_actions":{"view_html":"https://pith.science/pith/FZH2JIFNXV7M5XQTJPHI5W5DZQ","download_json":"https://pith.science/pith/FZH2JIFNXV7M5XQTJPHI5W5DZQ.json","view_paper":"https://pith.science/paper/FZH2JIFN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.06928&json=true","fetch_graph":"https://pith.science/api/pith-number/FZH2JIFNXV7M5XQTJPHI5W5DZQ/graph.json","fetch_events":"https://pith.science/api/pith-number/FZH2JIFNXV7M5XQTJPHI5W5DZQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZH2JIFNXV7M5XQTJPHI5W5DZQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZH2JIFNXV7M5XQTJPHI5W5DZQ/action/storage_attestation","attest_author":"https://pith.science/pith/FZH2JIFNXV7M5XQTJPHI5W5DZQ/action/author_attestation","sign_citation":"https://pith.science/pith/FZH2JIFNXV7M5XQTJPHI5W5DZQ/action/citation_signature","submit_replication":"https://pith.science/pith/FZH2JIFNXV7M5XQTJPHI5W5DZQ/action/replication_record"}},"created_at":"2026-05-18T00:15:47.113787+00:00","updated_at":"2026-05-18T00:15:47.113787+00:00"}