{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QOOE5ERRSOCEFTA2XLK5VCWAL6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"56fbe9b6effc94e27ffc63e8dfdbda48d246be39492e65fa3268551419b863ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-06-08T19:07:38Z","title_canon_sha256":"98dedfe9f79e4e73c11ecdc0d1a537f6e58d347729a77acdfa1c1eee4969b4c2"},"schema_version":"1.0","source":{"id":"1106.1623","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.1623","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"arxiv_version","alias_value":"1106.1623v1","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.1623","created_at":"2026-05-18T04:20:22Z"},{"alias_kind":"pith_short_12","alias_value":"QOOE5ERRSOCE","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QOOE5ERRSOCEFTA2","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QOOE5ERR","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:9f7d3d4baa1cdec8a2e2eccf5d0b306065eb3d8676c68cec13a9f3b884c902d8","target":"graph","created_at":"2026-05-18T04:20:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Dusa McDuff, Susan Tolman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-06-08T19:07:38Z","title":"Polytopes with mass linear functions II: the 4-dimensional case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1623","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:0c4f60e65c51b6880377b0bad780b56c0ef97caad2ed095e3a5b5bbfe455b50b","target":"record","created_at":"2026-05-18T04:20:22Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"56fbe9b6effc94e27ffc63e8dfdbda48d246be39492e65fa3268551419b863ab","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2011-06-08T19:07:38Z","title_canon_sha256":"98dedfe9f79e4e73c11ecdc0d1a537f6e58d347729a77acdfa1c1eee4969b4c2"},"schema_version":"1.0","source":{"id":"1106.1623","kind":"arxiv","version":1}},"canonical_sha256":"839c4e9231938442cc1abad5da8ac05faa2b2e59ae9c6cfef6574f5b2faaf7b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"839c4e9231938442cc1abad5da8ac05faa2b2e59ae9c6cfef6574f5b2faaf7b2","first_computed_at":"2026-05-18T04:20:22.640142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:22.640142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fe+29UsVTFrAalGKXNeg6x/XRLwHv4YSV2TDEAND1hCMtaYAGYdYY4o0nqOv9ejZYKmVNMBcfMerYokJ6YE8BA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:22.640749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.1623","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c4f60e65c51b6880377b0bad780b56c0ef97caad2ed095e3a5b5bbfe455b50b","sha256:9f7d3d4baa1cdec8a2e2eccf5d0b306065eb3d8676c68cec13a9f3b884c902d8"],"state_sha256":"c4093c9920e06d076a088593ba9ee941c26294f54e189c5873d43b80d4264cbf"}