{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QTTOWKVERN3C5PIUPMN7OEKYJI","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":"c1335746cb248bdc280bf76a183447c5f0ecf68bf6518cd60952f0b0026eeeef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-05-04T10:27:37Z","title_canon_sha256":"125f9b29b09ecc78cc8f71c36e595e6bfbe0f140ccb813b4c4cc83fd99204b43"},"schema_version":"1.0","source":{"id":"0905.0345","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.0345","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"arxiv_version","alias_value":"0905.0345v2","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.0345","created_at":"2026-05-18T04:31:51Z"},{"alias_kind":"pith_short_12","alias_value":"QTTOWKVERN3C","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QTTOWKVERN3C5PIU","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QTTOWKVE","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:78b8a088693be505f02acae35e1306eb9ab0c29b9e178b5ce0448c34ad2bd6a8","target":"graph","created_at":"2026-05-18T04:31:51Z","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 study focal points and Maslov index of a horizontal geodesic $\\gamma:I\\to M$ in the total space of a semi-Riemannian submersion $\\pi:M\\to B$ by determining an explicit relation with the corresponding objects along the projected geodesic $\\pi\\circ\\gamma:I\\to B$ in the base space. We use this result to calculate the focal Maslov index of a (spacelike) geodesic in a stationary space-time which is orthogonal to a timelike Killing vector field.","authors_text":"Erasmo Caponio, Miguel Angel Javaloyes, Paolo Piccione","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-05-04T10:27:37Z","title":"Maslov index in semi-Riemannian submersions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.0345","kind":"arxiv","version":2},"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":"sha256:4af3b65a54a92b70290bd062e1a81d285bd4a5ac971653fbc85756d456d4eb57","target":"record","created_at":"2026-05-18T04:31:51Z","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":"c1335746cb248bdc280bf76a183447c5f0ecf68bf6518cd60952f0b0026eeeef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-05-04T10:27:37Z","title_canon_sha256":"125f9b29b09ecc78cc8f71c36e595e6bfbe0f140ccb813b4c4cc83fd99204b43"},"schema_version":"1.0","source":{"id":"0905.0345","kind":"arxiv","version":2}},"canonical_sha256":"84e6eb2aa48b762ebd147b1bf711584a28f1a15880f13e14345602329bcd7a8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"84e6eb2aa48b762ebd147b1bf711584a28f1a15880f13e14345602329bcd7a8e","first_computed_at":"2026-05-18T04:31:51.243464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:51.243464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gdBidBZd+BegMeDngXsXvXAuvj670GO6gZk5LoiTzAyRWn+PLukWshHsrtwKJIUdCWA65vI6uRvQ8LsuHXLMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:51.244112Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.0345","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4af3b65a54a92b70290bd062e1a81d285bd4a5ac971653fbc85756d456d4eb57","sha256:78b8a088693be505f02acae35e1306eb9ab0c29b9e178b5ce0448c34ad2bd6a8"],"state_sha256":"0ee194a6d8d1af10477d032382b86bbc9eba90d80141ac35a30c9db91b3de2e8"}