{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:Z7O65HJAZ6BA4ZVWBB5BXYMXFV","short_pith_number":"pith:Z7O65HJA","schema_version":"1.0","canonical_sha256":"cfddee9d20cf820e66b6087a1be1972d74768acef02762075f623272c6461d1d","source":{"kind":"arxiv","id":"2009.05608","version":1},"attestation_state":"computed","paper":{"title":"Lifting Arc Diagrams Under Branched Covers: An Inverse Problem and its Solution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Cyrus Peterpaul","submitted_at":"2020-09-11T18:49:41Z","abstract_excerpt":"A branched covering map of surfaces induces a map in the opposite direction between their arc complexes. We represent a branched covering map combinatorially using what we call a lifting picture, and use this representation to computably solve the membership problem of the set of weighted arc diagrams on a given surface which can be obtained by lifting a weighted arc diagram on a bigon. We provide a brute force solution in the general case, and an efficient solution when the input arc diagram is a triangulation."},"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":"2009.05608","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2020-09-11T18:49:41Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"193ad89dad5ea9009bde15e4ad0ad8e1f3059a745dbf25287384cf12b27a8016","abstract_canon_sha256":"9828feccd80ca568f8f57ef29936dac6122f1ec2f729cfb80ec6907020e0ac7f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:34:59.261678Z","signature_b64":"LME+iJCp7MHm+5AToRN0KJn2uDo0EI2wfiRIelqIjOy11pqHRk47a9CiQygHqOYvowwI/dEeAkInSv/oMpomCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfddee9d20cf820e66b6087a1be1972d74768acef02762075f623272c6461d1d","last_reissued_at":"2026-07-05T01:34:59.261336Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:34:59.261336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Lifting Arc Diagrams Under Branched Covers: An Inverse Problem and its Solution","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CO","authors_text":"Cyrus Peterpaul","submitted_at":"2020-09-11T18:49:41Z","abstract_excerpt":"A branched covering map of surfaces induces a map in the opposite direction between their arc complexes. We represent a branched covering map combinatorially using what we call a lifting picture, and use this representation to computably solve the membership problem of the set of weighted arc diagrams on a given surface which can be obtained by lifting a weighted arc diagram on a bigon. We provide a brute force solution in the general case, and an efficient solution when the input arc diagram is a triangulation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.05608","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/2009.05608/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":"2009.05608","created_at":"2026-07-05T01:34:59.261395+00:00"},{"alias_kind":"arxiv_version","alias_value":"2009.05608v1","created_at":"2026-07-05T01:34:59.261395+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.05608","created_at":"2026-07-05T01:34:59.261395+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z7O65HJAZ6BA","created_at":"2026-07-05T01:34:59.261395+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z7O65HJAZ6BA4ZVW","created_at":"2026-07-05T01:34:59.261395+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z7O65HJA","created_at":"2026-07-05T01:34:59.261395+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2606.27272","citing_title":"MLC for parabolically bounded primitive renormalization","ref_index":38,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z7O65HJAZ6BA4ZVWBB5BXYMXFV","json":"https://pith.science/pith/Z7O65HJAZ6BA4ZVWBB5BXYMXFV.json","graph_json":"https://pith.science/api/pith-number/Z7O65HJAZ6BA4ZVWBB5BXYMXFV/graph.json","events_json":"https://pith.science/api/pith-number/Z7O65HJAZ6BA4ZVWBB5BXYMXFV/events.json","paper":"https://pith.science/paper/Z7O65HJA"},"agent_actions":{"view_html":"https://pith.science/pith/Z7O65HJAZ6BA4ZVWBB5BXYMXFV","download_json":"https://pith.science/pith/Z7O65HJAZ6BA4ZVWBB5BXYMXFV.json","view_paper":"https://pith.science/paper/Z7O65HJA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2009.05608&json=true","fetch_graph":"https://pith.science/api/pith-number/Z7O65HJAZ6BA4ZVWBB5BXYMXFV/graph.json","fetch_events":"https://pith.science/api/pith-number/Z7O65HJAZ6BA4ZVWBB5BXYMXFV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z7O65HJAZ6BA4ZVWBB5BXYMXFV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z7O65HJAZ6BA4ZVWBB5BXYMXFV/action/storage_attestation","attest_author":"https://pith.science/pith/Z7O65HJAZ6BA4ZVWBB5BXYMXFV/action/author_attestation","sign_citation":"https://pith.science/pith/Z7O65HJAZ6BA4ZVWBB5BXYMXFV/action/citation_signature","submit_replication":"https://pith.science/pith/Z7O65HJAZ6BA4ZVWBB5BXYMXFV/action/replication_record"}},"created_at":"2026-07-05T01:34:59.261395+00:00","updated_at":"2026-07-05T01:34:59.261395+00:00"}