{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:TEMX47C665UUOLDI27A74Z2KFT","short_pith_number":"pith:TEMX47C6","schema_version":"1.0","canonical_sha256":"99197e7c5ef769472c68d7c1fe674a2ce2a4c8cb5c23e74e81cd9f84b752cd0b","source":{"kind":"arxiv","id":"1705.05781","version":1},"attestation_state":"computed","paper":{"title":"A Compact Representation for Modular Semilattices and its Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hiroshi Hirai, So Nakashima","submitted_at":"2017-05-15T08:13:25Z","abstract_excerpt":"A modular semilattice is a semilattice generalization of a modular lattice. We establish a Birkhoff-type representation theorem for modular semilattices, which says that every modular semilattice is isomorphic to the family of ideals in a certain poset with additional relations.This new poset structure, which we axiomatize in this paper, is called a PPIP (projective poset with inconsistent pairs). A PPIP is a common generalization of a PIP (poset with inconsistent pairs) and a projective ordered space. The former was introduced by Barth\\'elemy and Constantin for establishing Birkhoff-type theo"},"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":"1705.05781","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-15T08:13:25Z","cross_cats_sorted":[],"title_canon_sha256":"ebd97b8213ff40c5442c592a0d92e0a211c14852631316698ba8169071a4b1d0","abstract_canon_sha256":"f6f06e04b42f7842e026b5f29fd45bb0987a77b6ee0b89b0b4c31d006ab1fc48"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:20.186261Z","signature_b64":"KNN0NNWk7z6TtcBS35VSlrd3AMtb/hq8swKhIk44P30X7qa49zfIlBtDazDTvRQaTyqawSFsY3F1EMhA2MjpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"99197e7c5ef769472c68d7c1fe674a2ce2a4c8cb5c23e74e81cd9f84b752cd0b","last_reissued_at":"2026-05-18T00:44:20.185756Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:20.185756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Compact Representation for Modular Semilattices and its Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hiroshi Hirai, So Nakashima","submitted_at":"2017-05-15T08:13:25Z","abstract_excerpt":"A modular semilattice is a semilattice generalization of a modular lattice. We establish a Birkhoff-type representation theorem for modular semilattices, which says that every modular semilattice is isomorphic to the family of ideals in a certain poset with additional relations.This new poset structure, which we axiomatize in this paper, is called a PPIP (projective poset with inconsistent pairs). A PPIP is a common generalization of a PIP (poset with inconsistent pairs) and a projective ordered space. The former was introduced by Barth\\'elemy and Constantin for establishing Birkhoff-type theo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05781","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":"1705.05781","created_at":"2026-05-18T00:44:20.185831+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.05781v1","created_at":"2026-05-18T00:44:20.185831+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.05781","created_at":"2026-05-18T00:44:20.185831+00:00"},{"alias_kind":"pith_short_12","alias_value":"TEMX47C665UU","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_16","alias_value":"TEMX47C665UUOLDI","created_at":"2026-05-18T12:31:46.661854+00:00"},{"alias_kind":"pith_short_8","alias_value":"TEMX47C6","created_at":"2026-05-18T12:31:46.661854+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/TEMX47C665UUOLDI27A74Z2KFT","json":"https://pith.science/pith/TEMX47C665UUOLDI27A74Z2KFT.json","graph_json":"https://pith.science/api/pith-number/TEMX47C665UUOLDI27A74Z2KFT/graph.json","events_json":"https://pith.science/api/pith-number/TEMX47C665UUOLDI27A74Z2KFT/events.json","paper":"https://pith.science/paper/TEMX47C6"},"agent_actions":{"view_html":"https://pith.science/pith/TEMX47C665UUOLDI27A74Z2KFT","download_json":"https://pith.science/pith/TEMX47C665UUOLDI27A74Z2KFT.json","view_paper":"https://pith.science/paper/TEMX47C6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.05781&json=true","fetch_graph":"https://pith.science/api/pith-number/TEMX47C665UUOLDI27A74Z2KFT/graph.json","fetch_events":"https://pith.science/api/pith-number/TEMX47C665UUOLDI27A74Z2KFT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TEMX47C665UUOLDI27A74Z2KFT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TEMX47C665UUOLDI27A74Z2KFT/action/storage_attestation","attest_author":"https://pith.science/pith/TEMX47C665UUOLDI27A74Z2KFT/action/author_attestation","sign_citation":"https://pith.science/pith/TEMX47C665UUOLDI27A74Z2KFT/action/citation_signature","submit_replication":"https://pith.science/pith/TEMX47C665UUOLDI27A74Z2KFT/action/replication_record"}},"created_at":"2026-05-18T00:44:20.185831+00:00","updated_at":"2026-05-18T00:44:20.185831+00:00"}