{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:4R5YVRM2KIJG3KNOHGKRZHBSDS","short_pith_number":"pith:4R5YVRM2","schema_version":"1.0","canonical_sha256":"e47b8ac59a52126da9ae39951c9c321c959de035f024759c37911bf6a9341ecb","source":{"kind":"arxiv","id":"1406.0154","version":1},"attestation_state":"computed","paper":{"title":"On the Galois Lattice of Bipartite Distance Hereditary Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Massimiliano Caramia, Nicola Apollonio, Paolo Giulio Franciosa","submitted_at":"2014-06-01T11:02:12Z","abstract_excerpt":"We give a complete characterization of bipartite graphs having tree-like Galois lattices. We prove that the poset obtained by deleting bottom and top elements from the Galois lattice of a bipartite graph is tree-like if and only if the graph is a Bipartite Distance Hereditary graph. By relying on the interplay between bipartite distance hereditary graphs and series-parallel graphs, we show that the lattice can be realized as the containment relation among directed paths in an arborescence. Moreover, a compact encoding of Bipartite Distance Hereditary graphs is proposed, that allows optimal tim"},"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":"1406.0154","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2014-06-01T11:02:12Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"440dd3712a346d5c1bdaf48ab8fc18eb5434bdc166642a9b06594cdfa69d8bd9","abstract_canon_sha256":"df509e997f9e408c66bb120b002f707ff448f20df3e69e5ca78a89529a485594"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:41.641674Z","signature_b64":"i25aDHqeBcu3BXYx1Gd2Vs57gTrahGYbURt9Dapmd9JUPo6f9duqEBMs5JQzbFJL1Sv1RRqhqEsxNIZ2taesDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e47b8ac59a52126da9ae39951c9c321c959de035f024759c37911bf6a9341ecb","last_reissued_at":"2026-05-18T02:50:41.641103Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:41.641103Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Galois Lattice of Bipartite Distance Hereditary Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Massimiliano Caramia, Nicola Apollonio, Paolo Giulio Franciosa","submitted_at":"2014-06-01T11:02:12Z","abstract_excerpt":"We give a complete characterization of bipartite graphs having tree-like Galois lattices. We prove that the poset obtained by deleting bottom and top elements from the Galois lattice of a bipartite graph is tree-like if and only if the graph is a Bipartite Distance Hereditary graph. By relying on the interplay between bipartite distance hereditary graphs and series-parallel graphs, we show that the lattice can be realized as the containment relation among directed paths in an arborescence. Moreover, a compact encoding of Bipartite Distance Hereditary graphs is proposed, that allows optimal tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.0154","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":"1406.0154","created_at":"2026-05-18T02:50:41.641181+00:00"},{"alias_kind":"arxiv_version","alias_value":"1406.0154v1","created_at":"2026-05-18T02:50:41.641181+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.0154","created_at":"2026-05-18T02:50:41.641181+00:00"},{"alias_kind":"pith_short_12","alias_value":"4R5YVRM2KIJG","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4R5YVRM2KIJG3KNO","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4R5YVRM2","created_at":"2026-05-18T12:28:14.216126+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/4R5YVRM2KIJG3KNOHGKRZHBSDS","json":"https://pith.science/pith/4R5YVRM2KIJG3KNOHGKRZHBSDS.json","graph_json":"https://pith.science/api/pith-number/4R5YVRM2KIJG3KNOHGKRZHBSDS/graph.json","events_json":"https://pith.science/api/pith-number/4R5YVRM2KIJG3KNOHGKRZHBSDS/events.json","paper":"https://pith.science/paper/4R5YVRM2"},"agent_actions":{"view_html":"https://pith.science/pith/4R5YVRM2KIJG3KNOHGKRZHBSDS","download_json":"https://pith.science/pith/4R5YVRM2KIJG3KNOHGKRZHBSDS.json","view_paper":"https://pith.science/paper/4R5YVRM2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1406.0154&json=true","fetch_graph":"https://pith.science/api/pith-number/4R5YVRM2KIJG3KNOHGKRZHBSDS/graph.json","fetch_events":"https://pith.science/api/pith-number/4R5YVRM2KIJG3KNOHGKRZHBSDS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4R5YVRM2KIJG3KNOHGKRZHBSDS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4R5YVRM2KIJG3KNOHGKRZHBSDS/action/storage_attestation","attest_author":"https://pith.science/pith/4R5YVRM2KIJG3KNOHGKRZHBSDS/action/author_attestation","sign_citation":"https://pith.science/pith/4R5YVRM2KIJG3KNOHGKRZHBSDS/action/citation_signature","submit_replication":"https://pith.science/pith/4R5YVRM2KIJG3KNOHGKRZHBSDS/action/replication_record"}},"created_at":"2026-05-18T02:50:41.641181+00:00","updated_at":"2026-05-18T02:50:41.641181+00:00"}