{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:QOOE5ERRSOCEFTA2XLK5VCWAL6","short_pith_number":"pith:QOOE5ERR","schema_version":"1.0","canonical_sha256":"839c4e9231938442cc1abad5da8ac05faa2b2e59ae9c6cfef6574f5b2faaf7b2","source":{"kind":"arxiv","id":"1106.1623","version":1},"attestation_state":"computed","paper":{"title":"Polytopes with mass linear functions II: the 4-dimensional case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dusa McDuff, Susan Tolman","submitted_at":"2011-06-08T19:07:38Z","abstract_excerpt":"This paper continues the analysis begun in {\\it Polytopes with mass linear functions, Part I} of the structure of smooth moment polytopes $\\Delta\\subset \\ft^*$ that support a mass linear function $H \\in \\ft$. As explained there, besides its purely combinatorial interest, this question is relevant to the study of the homomorphism $\\pi_1(T^n)\\to \\pi_1(\\Symp(M_\\Delta, \\omega_\\Delta))$ from the fundamental group of the torus $T^n$ to that of the group of symplectomorphisms of the $2n$-dimensional symplectic toric manifold $(M_\\Delta, \\omega_\\Delta)$ associated to $\\Delta$. In Part I, we made a gen"},"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":"1106.1623","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-06-08T19:07:38Z","cross_cats_sorted":[],"title_canon_sha256":"98dedfe9f79e4e73c11ecdc0d1a537f6e58d347729a77acdfa1c1eee4969b4c2","abstract_canon_sha256":"56fbe9b6effc94e27ffc63e8dfdbda48d246be39492e65fa3268551419b863ab"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:20:22.640749Z","signature_b64":"fe+29UsVTFrAalGKXNeg6x/XRLwHv4YSV2TDEAND1hCMtaYAGYdYY4o0nqOv9ejZYKmVNMBcfMerYokJ6YE8BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"839c4e9231938442cc1abad5da8ac05faa2b2e59ae9c6cfef6574f5b2faaf7b2","last_reissued_at":"2026-05-18T04:20:22.640142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:20:22.640142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Polytopes with mass linear functions II: the 4-dimensional case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Dusa McDuff, Susan Tolman","submitted_at":"2011-06-08T19:07:38Z","abstract_excerpt":"This paper continues the analysis begun in {\\it Polytopes with mass linear functions, Part I} of the structure of smooth moment polytopes $\\Delta\\subset \\ft^*$ that support a mass linear function $H \\in \\ft$. As explained there, besides its purely combinatorial interest, this question is relevant to the study of the homomorphism $\\pi_1(T^n)\\to \\pi_1(\\Symp(M_\\Delta, \\omega_\\Delta))$ from the fundamental group of the torus $T^n$ to that of the group of symplectomorphisms of the $2n$-dimensional symplectic toric manifold $(M_\\Delta, \\omega_\\Delta)$ associated to $\\Delta$. In Part I, we made a gen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1623","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":"1106.1623","created_at":"2026-05-18T04:20:22.640245+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.1623v1","created_at":"2026-05-18T04:20:22.640245+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1623","created_at":"2026-05-18T04:20:22.640245+00:00"},{"alias_kind":"pith_short_12","alias_value":"QOOE5ERRSOCE","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_16","alias_value":"QOOE5ERRSOCEFTA2","created_at":"2026-05-18T12:26:39.201973+00:00"},{"alias_kind":"pith_short_8","alias_value":"QOOE5ERR","created_at":"2026-05-18T12:26:39.201973+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/QOOE5ERRSOCEFTA2XLK5VCWAL6","json":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6.json","graph_json":"https://pith.science/api/pith-number/QOOE5ERRSOCEFTA2XLK5VCWAL6/graph.json","events_json":"https://pith.science/api/pith-number/QOOE5ERRSOCEFTA2XLK5VCWAL6/events.json","paper":"https://pith.science/paper/QOOE5ERR"},"agent_actions":{"view_html":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6","download_json":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6.json","view_paper":"https://pith.science/paper/QOOE5ERR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.1623&json=true","fetch_graph":"https://pith.science/api/pith-number/QOOE5ERRSOCEFTA2XLK5VCWAL6/graph.json","fetch_events":"https://pith.science/api/pith-number/QOOE5ERRSOCEFTA2XLK5VCWAL6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6/action/storage_attestation","attest_author":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6/action/author_attestation","sign_citation":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6/action/citation_signature","submit_replication":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6/action/replication_record"}},"created_at":"2026-05-18T04:20:22.640245+00:00","updated_at":"2026-05-18T04:20:22.640245+00:00"}