{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:NNF7BG2IOMONOUAKXKWPTMZWYC","short_pith_number":"pith:NNF7BG2I","schema_version":"1.0","canonical_sha256":"6b4bf09b48731cd7500abaacf9b336c087d615f38237f93e1d7411efc6b365f0","source":{"kind":"arxiv","id":"2606.19032","version":1},"attestation_state":"computed","paper":{"title":"Peripheral \\texorpdfstring{$\\Theta$}{Theta}-classes and forbidden partial cube-minors of daisy cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guangfu Wang","submitted_at":"2026-06-17T12:58:29Z","abstract_excerpt":"Daisy cubes are partial cubes whose vertices can be represented by a down-set of a Boolean lattice. This paper gives a label-free characterization: a finite partial cube is a daisy cube if and only if every Djokovi\\'c--Winkler $\\Theta$-class is peripheral. The proof orients each $\\Theta$-class toward a peripheral halfspace and shows that the resulting $\\Theta$-coordinate labels are closed downward. The characterization turns recognition into a condition on the halfspace structure and gives an exact obstruction formulation: the minimal forbidden pc-minors for daisy cubes are precisely the pc-mi"},"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":"2606.19032","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2026-06-17T12:58:29Z","cross_cats_sorted":[],"title_canon_sha256":"ce72ff40b1644040c54299419ff554fe1bd4ddddc7e316b959787888b1718b5d","abstract_canon_sha256":"9b8d34f2aa9196bd07c02570865b95c9f8e71818ae87b88a0eee6975c738f608"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-19T16:11:54.938026Z","signature_b64":"Y/ZAQ+rGYB/rz6ZVNnUbBvdtv4Vb2yiXXfJ4Gn647ZtDCfmukJT3GedsQ15SSuHZ6kkImzipKtqoj9/Y58KFAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b4bf09b48731cd7500abaacf9b336c087d615f38237f93e1d7411efc6b365f0","last_reissued_at":"2026-06-19T16:11:54.937686Z","signature_status":"signed_v1","first_computed_at":"2026-06-19T16:11:54.937686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Peripheral \\texorpdfstring{$\\Theta$}{Theta}-classes and forbidden partial cube-minors of daisy cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guangfu Wang","submitted_at":"2026-06-17T12:58:29Z","abstract_excerpt":"Daisy cubes are partial cubes whose vertices can be represented by a down-set of a Boolean lattice. This paper gives a label-free characterization: a finite partial cube is a daisy cube if and only if every Djokovi\\'c--Winkler $\\Theta$-class is peripheral. The proof orients each $\\Theta$-class toward a peripheral halfspace and shows that the resulting $\\Theta$-coordinate labels are closed downward. The characterization turns recognition into a condition on the halfspace structure and gives an exact obstruction formulation: the minimal forbidden pc-minors for daisy cubes are precisely the pc-mi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.19032","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/2606.19032/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":"2606.19032","created_at":"2026-06-19T16:11:54.937747+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.19032v1","created_at":"2026-06-19T16:11:54.937747+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.19032","created_at":"2026-06-19T16:11:54.937747+00:00"},{"alias_kind":"pith_short_12","alias_value":"NNF7BG2IOMON","created_at":"2026-06-19T16:11:54.937747+00:00"},{"alias_kind":"pith_short_16","alias_value":"NNF7BG2IOMONOUAK","created_at":"2026-06-19T16:11:54.937747+00:00"},{"alias_kind":"pith_short_8","alias_value":"NNF7BG2I","created_at":"2026-06-19T16:11:54.937747+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/NNF7BG2IOMONOUAKXKWPTMZWYC","json":"https://pith.science/pith/NNF7BG2IOMONOUAKXKWPTMZWYC.json","graph_json":"https://pith.science/api/pith-number/NNF7BG2IOMONOUAKXKWPTMZWYC/graph.json","events_json":"https://pith.science/api/pith-number/NNF7BG2IOMONOUAKXKWPTMZWYC/events.json","paper":"https://pith.science/paper/NNF7BG2I"},"agent_actions":{"view_html":"https://pith.science/pith/NNF7BG2IOMONOUAKXKWPTMZWYC","download_json":"https://pith.science/pith/NNF7BG2IOMONOUAKXKWPTMZWYC.json","view_paper":"https://pith.science/paper/NNF7BG2I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.19032&json=true","fetch_graph":"https://pith.science/api/pith-number/NNF7BG2IOMONOUAKXKWPTMZWYC/graph.json","fetch_events":"https://pith.science/api/pith-number/NNF7BG2IOMONOUAKXKWPTMZWYC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NNF7BG2IOMONOUAKXKWPTMZWYC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NNF7BG2IOMONOUAKXKWPTMZWYC/action/storage_attestation","attest_author":"https://pith.science/pith/NNF7BG2IOMONOUAKXKWPTMZWYC/action/author_attestation","sign_citation":"https://pith.science/pith/NNF7BG2IOMONOUAKXKWPTMZWYC/action/citation_signature","submit_replication":"https://pith.science/pith/NNF7BG2IOMONOUAKXKWPTMZWYC/action/replication_record"}},"created_at":"2026-06-19T16:11:54.937747+00:00","updated_at":"2026-06-19T16:11:54.937747+00:00"}