{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:DH5GJ3B4J65YFEXUCHBDHAH2QG","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":"110e20168e41b2178ed38843fb25b85e2f96d0acfb5ed00ecdb5e1d830cba225","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-11-17T22:43:50Z","title_canon_sha256":"3a607b7c3be5bba204f6f737a0c542618b442af27a4d40c31b23bddd27fe3d3e"},"schema_version":"1.0","source":{"id":"0811.2819","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.2819","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"arxiv_version","alias_value":"0811.2819v5","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.2819","created_at":"2026-05-18T04:19:32Z"},{"alias_kind":"pith_short_12","alias_value":"DH5GJ3B4J65Y","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"DH5GJ3B4J65YFEXU","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"DH5GJ3B4","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:e48c8dc00477f4562cb4a8f178f1d849ef6d1396195a53c18b0ce09a1e0af7ca","target":"graph","created_at":"2026-05-18T04:19:32Z","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":"In this note it is shown that the Maslov Index for pairs of Lagrangian Paths as introduced by Cappell, Lee and Miller appears by parallel transporting elements of (a certain complex line-subbundle of) the symplectic spinorbundle over Euclidean space, when pulled back to an (embedded) Lagrangian submanifold $L$, along closed or non-closed paths therein. In especially, the CLM-Index mod 4 determines the holonomy group of this line bundle w.r.t. the Levi-Civita-connection on $L$, hence its vanishing mod 4 is equivalent to the existence of a trivializing parallel section. Moreover, it is shown tha","authors_text":"Andreas Klein","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-11-17T22:43:50Z","title":"Symplectic Spinors, Holonomy and Maslov Index"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.2819","kind":"arxiv","version":5},"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:b19be9cc19b5a841ef4e2b5b8653018f0937466c7c4f4056138353b278270601","target":"record","created_at":"2026-05-18T04:19:32Z","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":"110e20168e41b2178ed38843fb25b85e2f96d0acfb5ed00ecdb5e1d830cba225","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2008-11-17T22:43:50Z","title_canon_sha256":"3a607b7c3be5bba204f6f737a0c542618b442af27a4d40c31b23bddd27fe3d3e"},"schema_version":"1.0","source":{"id":"0811.2819","kind":"arxiv","version":5}},"canonical_sha256":"19fa64ec3c4fbb8292f411c23380fa81a4eb2f1788129277365e51e876a5ba7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19fa64ec3c4fbb8292f411c23380fa81a4eb2f1788129277365e51e876a5ba7b","first_computed_at":"2026-05-18T04:19:32.718032Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:32.718032Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tsa/5stuhVo4Btf1hPianIMtANx7Qh0noLMaReXFBCnCM9C/KaT18ydih3+Tb0zMmf4ldI2B1oUmcaaJXwkDAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:32.718439Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.2819","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b19be9cc19b5a841ef4e2b5b8653018f0937466c7c4f4056138353b278270601","sha256:e48c8dc00477f4562cb4a8f178f1d849ef6d1396195a53c18b0ce09a1e0af7ca"],"state_sha256":"aa58ed7fccfb61efae83b84b2aa6143dcbc8057b7eda2bacfa809c9a05f6eb1a"}