{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:JMPDPGEKTMD3IH7EEPE5RXKIKD","short_pith_number":"pith:JMPDPGEK","schema_version":"1.0","canonical_sha256":"4b1e37988a9b07b41fe423c9d8dd4850e09e578ccb417674ff0c21ef39e35f41","source":{"kind":"arxiv","id":"1905.04256","version":3},"attestation_state":"computed","paper":{"title":"Plane bipolar orientations and quadrant walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"\\'Eric Fusy, Kilian Raschel, Mireille Bousquet-M\\'elou","submitted_at":"2019-05-10T16:57:23Z","abstract_excerpt":"Bipolar orientations of planar maps have recently attracted some interest in combinatorics, probability theory and theoretical physics. Plane bipolar orientations with $n$ edges are known to be counted by the $n$th Baxter number $b(n)$, which can be defined by a linear recurrence relation with polynomial coefficients. Equivalently, the associated generating function $\\sum_n b(n)t^n$ is D-finite. In this paper, we address a much refined enumeration problem, where we record for every $r$ the number of faces of degree $r$. When these degrees are bounded, we show that the associated generating fun"},"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":"1905.04256","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-05-10T16:57:23Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"b1c1d429d49cd1f82f5e744265bfa682a0099b2cc7feeba1b3e1058396704bc9","abstract_canon_sha256":"6b7f39508bd289379412194ca1acaa3f473197a45a69a61ce11a831fcac2bcfe"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:18:13.598691Z","signature_b64":"BMsqcVQGLP+w00F3kiuzd2My+ZXC8PUE/tNCn1SKKi/r5OhMLU9yQ2joRDQ0rjEkxCI7JNi/G2iYIL67toYJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4b1e37988a9b07b41fe423c9d8dd4850e09e578ccb417674ff0c21ef39e35f41","last_reissued_at":"2026-07-05T02:18:13.598119Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:18:13.598119Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Plane bipolar orientations and quadrant walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.CO","authors_text":"\\'Eric Fusy, Kilian Raschel, Mireille Bousquet-M\\'elou","submitted_at":"2019-05-10T16:57:23Z","abstract_excerpt":"Bipolar orientations of planar maps have recently attracted some interest in combinatorics, probability theory and theoretical physics. Plane bipolar orientations with $n$ edges are known to be counted by the $n$th Baxter number $b(n)$, which can be defined by a linear recurrence relation with polynomial coefficients. Equivalently, the associated generating function $\\sum_n b(n)t^n$ is D-finite. In this paper, we address a much refined enumeration problem, where we record for every $r$ the number of faces of degree $r$. When these degrees are bounded, we show that the associated generating fun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04256","kind":"arxiv","version":3},"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/1905.04256/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":"1905.04256","created_at":"2026-07-05T02:18:13.598181+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.04256v3","created_at":"2026-07-05T02:18:13.598181+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04256","created_at":"2026-07-05T02:18:13.598181+00:00"},{"alias_kind":"pith_short_12","alias_value":"JMPDPGEKTMD3","created_at":"2026-07-05T02:18:13.598181+00:00"},{"alias_kind":"pith_short_16","alias_value":"JMPDPGEKTMD3IH7E","created_at":"2026-07-05T02:18:13.598181+00:00"},{"alias_kind":"pith_short_8","alias_value":"JMPDPGEK","created_at":"2026-07-05T02:18:13.598181+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.09469","citing_title":"Precision measurements of Hausdorff dimensions in two-dimensional quantum gravity","ref_index":41,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JMPDPGEKTMD3IH7EEPE5RXKIKD","json":"https://pith.science/pith/JMPDPGEKTMD3IH7EEPE5RXKIKD.json","graph_json":"https://pith.science/api/pith-number/JMPDPGEKTMD3IH7EEPE5RXKIKD/graph.json","events_json":"https://pith.science/api/pith-number/JMPDPGEKTMD3IH7EEPE5RXKIKD/events.json","paper":"https://pith.science/paper/JMPDPGEK"},"agent_actions":{"view_html":"https://pith.science/pith/JMPDPGEKTMD3IH7EEPE5RXKIKD","download_json":"https://pith.science/pith/JMPDPGEKTMD3IH7EEPE5RXKIKD.json","view_paper":"https://pith.science/paper/JMPDPGEK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.04256&json=true","fetch_graph":"https://pith.science/api/pith-number/JMPDPGEKTMD3IH7EEPE5RXKIKD/graph.json","fetch_events":"https://pith.science/api/pith-number/JMPDPGEKTMD3IH7EEPE5RXKIKD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JMPDPGEKTMD3IH7EEPE5RXKIKD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JMPDPGEKTMD3IH7EEPE5RXKIKD/action/storage_attestation","attest_author":"https://pith.science/pith/JMPDPGEKTMD3IH7EEPE5RXKIKD/action/author_attestation","sign_citation":"https://pith.science/pith/JMPDPGEKTMD3IH7EEPE5RXKIKD/action/citation_signature","submit_replication":"https://pith.science/pith/JMPDPGEKTMD3IH7EEPE5RXKIKD/action/replication_record"}},"created_at":"2026-07-05T02:18:13.598181+00:00","updated_at":"2026-07-05T02:18:13.598181+00:00"}