{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:44KENFSQRWCGNBIL4DHFHM6IAG","short_pith_number":"pith:44KENFSQ","schema_version":"1.0","canonical_sha256":"e7144696508d8466850be0ce53b3c801a1b0607248ab6fa565480053c4fe722f","source":{"kind":"arxiv","id":"0908.3448","version":2},"attestation_state":"computed","paper":{"title":"Buchstaber invariants of skeleta of a simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Mikiya Masuda, Yukiko Fukukawa","submitted_at":"2009-08-24T14:29:19Z","abstract_excerpt":"A moment-angle complex $\\mathcal{Z}_K$ is a compact topological space associated with a finite simplicial complex $K$. It is realized as a subspace of a polydisk $(D^2)^m$, where $m$ is the number of vertices in $K$ and $D^2$ is the unit disk of the complex numbers $\\C$, and the natural action of a torus $(S^1)^m$ on $(D^2)^m$ leaves $\\mathcal{Z}_K$ invariant. The Buchstaber invariant $s(K)$ of $K$ is the maximum integer for which there is a subtorus of rank $s(K)$ acting on $\\mathcal{Z}_K$ freely.\n  The story above goes over the real numbers $\\R$ in place of $\\C$ and a real analogue of the Bu"},"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":"0908.3448","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2009-08-24T14:29:19Z","cross_cats_sorted":[],"title_canon_sha256":"8508c809bec94f2389b69bdf62a96ec90c0fa685474689e7870a3b85f6145d41","abstract_canon_sha256":"8ba460a1aa6dbc7d6a45c8e4493eee0e9a7db46e42c77790eedeb1ebecece81b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:18:33.287585Z","signature_b64":"qvs5P2gq/7inVtvLgEzqkfDcnfmiMGhAhwbjFZjnQee85Um+05kXbd1cNgkOOhTJi6wK0ZklhexYBnGsGYRRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7144696508d8466850be0ce53b3c801a1b0607248ab6fa565480053c4fe722f","last_reissued_at":"2026-05-18T04:18:33.287159Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:18:33.287159Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Buchstaber invariants of skeleta of a simplex","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Mikiya Masuda, Yukiko Fukukawa","submitted_at":"2009-08-24T14:29:19Z","abstract_excerpt":"A moment-angle complex $\\mathcal{Z}_K$ is a compact topological space associated with a finite simplicial complex $K$. It is realized as a subspace of a polydisk $(D^2)^m$, where $m$ is the number of vertices in $K$ and $D^2$ is the unit disk of the complex numbers $\\C$, and the natural action of a torus $(S^1)^m$ on $(D^2)^m$ leaves $\\mathcal{Z}_K$ invariant. The Buchstaber invariant $s(K)$ of $K$ is the maximum integer for which there is a subtorus of rank $s(K)$ acting on $\\mathcal{Z}_K$ freely.\n  The story above goes over the real numbers $\\R$ in place of $\\C$ and a real analogue of the Bu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.3448","kind":"arxiv","version":2},"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":"0908.3448","created_at":"2026-05-18T04:18:33.287213+00:00"},{"alias_kind":"arxiv_version","alias_value":"0908.3448v2","created_at":"2026-05-18T04:18:33.287213+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0908.3448","created_at":"2026-05-18T04:18:33.287213+00:00"},{"alias_kind":"pith_short_12","alias_value":"44KENFSQRWCG","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"44KENFSQRWCGNBIL","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"44KENFSQ","created_at":"2026-05-18T12:25:58.018023+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/44KENFSQRWCGNBIL4DHFHM6IAG","json":"https://pith.science/pith/44KENFSQRWCGNBIL4DHFHM6IAG.json","graph_json":"https://pith.science/api/pith-number/44KENFSQRWCGNBIL4DHFHM6IAG/graph.json","events_json":"https://pith.science/api/pith-number/44KENFSQRWCGNBIL4DHFHM6IAG/events.json","paper":"https://pith.science/paper/44KENFSQ"},"agent_actions":{"view_html":"https://pith.science/pith/44KENFSQRWCGNBIL4DHFHM6IAG","download_json":"https://pith.science/pith/44KENFSQRWCGNBIL4DHFHM6IAG.json","view_paper":"https://pith.science/paper/44KENFSQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0908.3448&json=true","fetch_graph":"https://pith.science/api/pith-number/44KENFSQRWCGNBIL4DHFHM6IAG/graph.json","fetch_events":"https://pith.science/api/pith-number/44KENFSQRWCGNBIL4DHFHM6IAG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/44KENFSQRWCGNBIL4DHFHM6IAG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/44KENFSQRWCGNBIL4DHFHM6IAG/action/storage_attestation","attest_author":"https://pith.science/pith/44KENFSQRWCGNBIL4DHFHM6IAG/action/author_attestation","sign_citation":"https://pith.science/pith/44KENFSQRWCGNBIL4DHFHM6IAG/action/citation_signature","submit_replication":"https://pith.science/pith/44KENFSQRWCGNBIL4DHFHM6IAG/action/replication_record"}},"created_at":"2026-05-18T04:18:33.287213+00:00","updated_at":"2026-05-18T04:18:33.287213+00:00"}