{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:HYFWHQ72HERKWMW7LSIFZ6IPFX","short_pith_number":"pith:HYFWHQ72","canonical_record":{"source":{"id":"1206.2676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-06-12T21:32:34Z","cross_cats_sorted":[],"title_canon_sha256":"7cf2c81173815e3bc3b32bce7637c80947f692b4abd48040fddbbd1bf5f38fd1","abstract_canon_sha256":"9c79c96279a83868bad43027091703169581e3a41c0a4c5f25cb33f34486d0d3"},"schema_version":"1.0"},"canonical_sha256":"3e0b63c3fa3922ab32df5c905cf90f2dc069ca3fabb0d22b7e394fdfdd1ef4ab","source":{"kind":"arxiv","id":"1206.2676","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2676","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2676v1","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2676","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"pith_short_12","alias_value":"HYFWHQ72HERK","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HYFWHQ72HERKWMW7","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HYFWHQ72","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:HYFWHQ72HERKWMW7LSIFZ6IPFX","target":"record","payload":{"canonical_record":{"source":{"id":"1206.2676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-06-12T21:32:34Z","cross_cats_sorted":[],"title_canon_sha256":"7cf2c81173815e3bc3b32bce7637c80947f692b4abd48040fddbbd1bf5f38fd1","abstract_canon_sha256":"9c79c96279a83868bad43027091703169581e3a41c0a4c5f25cb33f34486d0d3"},"schema_version":"1.0"},"canonical_sha256":"3e0b63c3fa3922ab32df5c905cf90f2dc069ca3fabb0d22b7e394fdfdd1ef4ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:43.352003Z","signature_b64":"T/5zneqzmLB6d+3KX2b/81dxA71YoGwv+ZdJj3zSPp7Sp8Fe3oN7z2W8XI3I3Mmr7KQKFuDXu16I5OH3Lno/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e0b63c3fa3922ab32df5c905cf90f2dc069ca3fabb0d22b7e394fdfdd1ef4ab","last_reissued_at":"2026-05-18T03:53:43.351603Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:43.351603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.2676","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":"2026-05-18T03:53:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0sAuklyzCk0tFCX27pQT1T1jV+Zd4K++8/sbuMiblBAXHXi2MjIqROt0/vaTsV9nx166sXOCRe00XB+aBojHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T10:44:49.109681Z"},"content_sha256":"135280247b1dca9d294cd2b38918b7f31cb2e3e16678f154966195b5a657eb6f","schema_version":"1.0","event_id":"sha256:135280247b1dca9d294cd2b38918b7f31cb2e3e16678f154966195b5a657eb6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:HYFWHQ72HERKWMW7LSIFZ6IPFX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the topology of monotone Lagrangian submanifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SG","authors_text":"Mihai Damian","submitted_at":"2012-06-12T21:32:34Z","abstract_excerpt":"We find new obstructions on the topology of monotone Lagrangian submanifolds of $C^{n}$ under some hypothesis on the homology of their universal cover. In particular we show that nontrivial connected sums of manifolds of odd dimensions do not admit monotone Lagrangian embeddings into $\\C^{n}$ whereas some of these examples are known to admit usual Lagrangian embeddings. In dimension three we get as a corollary that the only orientable Lagrangians in ${\\bf C}^{3}$ are products $S^{1}\\times \\Sigma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2676","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":"2026-05-18T03:53:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ycXtgo/ebELVNy6FbslDT0pLSdeB3hf02beFQdRi5qH93lX23KioJyJ39sJoI4VoGYWygLL6s9yYZlhs+GEKCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T10:44:49.110192Z"},"content_sha256":"52ab5dab21bbe3358091bcb3bd3f008a742ed045a8b920b9c4a120282eee30f6","schema_version":"1.0","event_id":"sha256:52ab5dab21bbe3358091bcb3bd3f008a742ed045a8b920b9c4a120282eee30f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HYFWHQ72HERKWMW7LSIFZ6IPFX/bundle.json","state_url":"https://pith.science/pith/HYFWHQ72HERKWMW7LSIFZ6IPFX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HYFWHQ72HERKWMW7LSIFZ6IPFX/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":"2026-05-20T10:44:49Z","links":{"resolver":"https://pith.science/pith/HYFWHQ72HERKWMW7LSIFZ6IPFX","bundle":"https://pith.science/pith/HYFWHQ72HERKWMW7LSIFZ6IPFX/bundle.json","state":"https://pith.science/pith/HYFWHQ72HERKWMW7LSIFZ6IPFX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HYFWHQ72HERKWMW7LSIFZ6IPFX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HYFWHQ72HERKWMW7LSIFZ6IPFX","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":"9c79c96279a83868bad43027091703169581e3a41c0a4c5f25cb33f34486d0d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-06-12T21:32:34Z","title_canon_sha256":"7cf2c81173815e3bc3b32bce7637c80947f692b4abd48040fddbbd1bf5f38fd1"},"schema_version":"1.0","source":{"id":"1206.2676","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2676","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2676v1","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2676","created_at":"2026-05-18T03:53:43Z"},{"alias_kind":"pith_short_12","alias_value":"HYFWHQ72HERK","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HYFWHQ72HERKWMW7","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HYFWHQ72","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:52ab5dab21bbe3358091bcb3bd3f008a742ed045a8b920b9c4a120282eee30f6","target":"graph","created_at":"2026-05-18T03:53:43Z","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":"We find new obstructions on the topology of monotone Lagrangian submanifolds of $C^{n}$ under some hypothesis on the homology of their universal cover. In particular we show that nontrivial connected sums of manifolds of odd dimensions do not admit monotone Lagrangian embeddings into $\\C^{n}$ whereas some of these examples are known to admit usual Lagrangian embeddings. In dimension three we get as a corollary that the only orientable Lagrangians in ${\\bf C}^{3}$ are products $S^{1}\\times \\Sigma$.","authors_text":"Mihai Damian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-06-12T21:32:34Z","title":"On the topology of monotone Lagrangian submanifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2676","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":"sha256:135280247b1dca9d294cd2b38918b7f31cb2e3e16678f154966195b5a657eb6f","target":"record","created_at":"2026-05-18T03:53:43Z","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":"9c79c96279a83868bad43027091703169581e3a41c0a4c5f25cb33f34486d0d3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2012-06-12T21:32:34Z","title_canon_sha256":"7cf2c81173815e3bc3b32bce7637c80947f692b4abd48040fddbbd1bf5f38fd1"},"schema_version":"1.0","source":{"id":"1206.2676","kind":"arxiv","version":1}},"canonical_sha256":"3e0b63c3fa3922ab32df5c905cf90f2dc069ca3fabb0d22b7e394fdfdd1ef4ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e0b63c3fa3922ab32df5c905cf90f2dc069ca3fabb0d22b7e394fdfdd1ef4ab","first_computed_at":"2026-05-18T03:53:43.351603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:43.351603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T/5zneqzmLB6d+3KX2b/81dxA71YoGwv+ZdJj3zSPp7Sp8Fe3oN7z2W8XI3I3Mmr7KQKFuDXu16I5OH3Lno/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:43.352003Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2676","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:135280247b1dca9d294cd2b38918b7f31cb2e3e16678f154966195b5a657eb6f","sha256:52ab5dab21bbe3358091bcb3bd3f008a742ed045a8b920b9c4a120282eee30f6"],"state_sha256":"4aa0d6b93ec41649e16c8d5677e09ebc8b3efaf3e9a2318efd833c0ce4606f58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vVmldRKgIbp6aorot1I37mwbUMu/6seSbOQnKVDUrW4GaItlKAGSSso2IO4JxUhDSdCa4EcUDqRo6KngcHSfDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T10:44:49.112347Z","bundle_sha256":"062b7b9f36fe5174d39fc43b09d98d47e447aca9beb18dafdf8534bc86baa245"}}