{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QOOE5ERRSOCEFTA2XLK5VCWAL6","short_pith_number":"pith:QOOE5ERR","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"},"canonical_sha256":"839c4e9231938442cc1abad5da8ac05faa2b2e59ae9c6cfef6574f5b2faaf7b2","source":{"kind":"arxiv","id":"1106.1623","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QOOE5ERRSOCEFTA2XLK5VCWAL6","target":"record","payload":{"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"},"canonical_sha256":"839c4e9231938442cc1abad5da8ac05faa2b2e59ae9c6cfef6574f5b2faaf7b2","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"},"source_kind":"arxiv","source_id":"1106.1623","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Lv3H7WrVEe18vThiHCrWq3Gd9pIlgc8UNXewt8ugV3zrrtR1E4Ed6R0Hsx4m88ne4P2bIUiuAV/07d7tj2sAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:42:50.093606Z"},"content_sha256":"0c4f60e65c51b6880377b0bad780b56c0ef97caad2ed095e3a5b5bbfe455b50b","schema_version":"1.0","event_id":"sha256:0c4f60e65c51b6880377b0bad780b56c0ef97caad2ed095e3a5b5bbfe455b50b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QOOE5ERRSOCEFTA2XLK5VCWAL6","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:20:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gbmHpc/aaRzyUR4jhevFw3gbZMeLGXBpMN11K9R/jo/pcUnSDPpiPz2arVhHgPnvJHNISQp+Wv9rWk6nbMAlCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T20:42:50.093968Z"},"content_sha256":"9f7d3d4baa1cdec8a2e2eccf5d0b306065eb3d8676c68cec13a9f3b884c902d8","schema_version":"1.0","event_id":"sha256:9f7d3d4baa1cdec8a2e2eccf5d0b306065eb3d8676c68cec13a9f3b884c902d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6/bundle.json","state_url":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T20:42:50Z","links":{"resolver":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6","bundle":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6/bundle.json","state":"https://pith.science/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QOOE5ERRSOCEFTA2XLK5VCWAL6/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ggu1pIrt3iub84ePQJ75Rs6IEICt9H9ytKhhy6Y8y9wZVh91v+6BpBsYCaEAKP0eFBXR+j0e+srQfzvpp9qxAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T20:42:50.095933Z","bundle_sha256":"e7263fc3a5690f4b2847480516c60e1797ec954acada94c7bc9dc671bb3b8aff"}}