{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:TIALYAPB4ELI2Y3GPRLXUAP2LY","short_pith_number":"pith:TIALYAPB","schema_version":"1.0","canonical_sha256":"9a00bc01e1e1168d63667c577a01fa5e2dceb0fffcc86e6bf6c6fd20faf70771","source":{"kind":"arxiv","id":"2012.13797","version":3},"attestation_state":"computed","paper":{"title":"Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Simonetta Abenda","submitted_at":"2020-12-26T19:04:32Z","abstract_excerpt":"Maximal minors of Kasteleyn sign matrices on planar bipartite graphs in the disk count dimer configurations with prescribed boundary conditions, and the weighted version of such matrices provides a natural parametrization of the totally non--negative part of real Grassmannians (see Refs. [54,43,44,58,7]). In this paper we provide a geometric interpretation of such variant of Kasteleyn theorem: a signature is Kasteleyn if and only if it is geometric in the sense of Ref. [5]. We apply this geometric characterization to explicitly solve the associated system of relations and provide a new proof t"},"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":"2012.13797","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-12-26T19:04:32Z","cross_cats_sorted":["math.CO","math.MP","nlin.SI"],"title_canon_sha256":"b2eb5de94e48ec1f2d7cf1f52d347a8b6475b6933666aba5e1fc88557f7535cd","abstract_canon_sha256":"7ccc3d7945e1b087ed05975bfa907373336a6aa0c7b9e7c6524670c9f98c820e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:25:49.662498Z","signature_b64":"695wML+8IDFB9Wp3ArUFimYK0mjUVpHrp0BYzy05KwvtG3dZAyjPaTzz65Vi6/b9em6OFv/V3+ZmvhnaIRcKAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a00bc01e1e1168d63667c577a01fa5e2dceb0fffcc86e6bf6c6fd20faf70771","last_reissued_at":"2026-07-05T03:25:49.662003Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:25:49.662003Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kasteleyn theorem, geometric signatures and KP-II divisors on planar bipartite networks in the disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MP","nlin.SI"],"primary_cat":"math-ph","authors_text":"Simonetta Abenda","submitted_at":"2020-12-26T19:04:32Z","abstract_excerpt":"Maximal minors of Kasteleyn sign matrices on planar bipartite graphs in the disk count dimer configurations with prescribed boundary conditions, and the weighted version of such matrices provides a natural parametrization of the totally non--negative part of real Grassmannians (see Refs. [54,43,44,58,7]). In this paper we provide a geometric interpretation of such variant of Kasteleyn theorem: a signature is Kasteleyn if and only if it is geometric in the sense of Ref. [5]. We apply this geometric characterization to explicitly solve the associated system of relations and provide a new proof t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.13797","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/2012.13797/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":"2012.13797","created_at":"2026-07-05T03:25:49.662065+00:00"},{"alias_kind":"arxiv_version","alias_value":"2012.13797v3","created_at":"2026-07-05T03:25:49.662065+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2012.13797","created_at":"2026-07-05T03:25:49.662065+00:00"},{"alias_kind":"pith_short_12","alias_value":"TIALYAPB4ELI","created_at":"2026-07-05T03:25:49.662065+00:00"},{"alias_kind":"pith_short_16","alias_value":"TIALYAPB4ELI2Y3G","created_at":"2026-07-05T03:25:49.662065+00:00"},{"alias_kind":"pith_short_8","alias_value":"TIALYAPB","created_at":"2026-07-05T03:25:49.662065+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.07437","citing_title":"Edge vectors on plabic networks in the disk and amalgamation of totally non-negative Grassmannians","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/TIALYAPB4ELI2Y3GPRLXUAP2LY","json":"https://pith.science/pith/TIALYAPB4ELI2Y3GPRLXUAP2LY.json","graph_json":"https://pith.science/api/pith-number/TIALYAPB4ELI2Y3GPRLXUAP2LY/graph.json","events_json":"https://pith.science/api/pith-number/TIALYAPB4ELI2Y3GPRLXUAP2LY/events.json","paper":"https://pith.science/paper/TIALYAPB"},"agent_actions":{"view_html":"https://pith.science/pith/TIALYAPB4ELI2Y3GPRLXUAP2LY","download_json":"https://pith.science/pith/TIALYAPB4ELI2Y3GPRLXUAP2LY.json","view_paper":"https://pith.science/paper/TIALYAPB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2012.13797&json=true","fetch_graph":"https://pith.science/api/pith-number/TIALYAPB4ELI2Y3GPRLXUAP2LY/graph.json","fetch_events":"https://pith.science/api/pith-number/TIALYAPB4ELI2Y3GPRLXUAP2LY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TIALYAPB4ELI2Y3GPRLXUAP2LY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TIALYAPB4ELI2Y3GPRLXUAP2LY/action/storage_attestation","attest_author":"https://pith.science/pith/TIALYAPB4ELI2Y3GPRLXUAP2LY/action/author_attestation","sign_citation":"https://pith.science/pith/TIALYAPB4ELI2Y3GPRLXUAP2LY/action/citation_signature","submit_replication":"https://pith.science/pith/TIALYAPB4ELI2Y3GPRLXUAP2LY/action/replication_record"}},"created_at":"2026-07-05T03:25:49.662065+00:00","updated_at":"2026-07-05T03:25:49.662065+00:00"}