{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YXJWJG3XQ6434MEAQ26D772F2F","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":"23428f27a54e33871fcc6e77b83d233b495c77f028970e5059fa796588ac04e0","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T16:38:53Z","title_canon_sha256":"b2e0687ea6a20445704a72fc41aad15b97d0b367a8077ad0029ba0c2bd6cd034"},"schema_version":"1.0","source":{"id":"1709.06520","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06520","created_at":"2026-05-18T00:10:19Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06520v2","created_at":"2026-05-18T00:10:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06520","created_at":"2026-05-18T00:10:19Z"},{"alias_kind":"pith_short_12","alias_value":"YXJWJG3XQ643","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YXJWJG3XQ6434MEA","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YXJWJG3X","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:56b1f0ec6721619ff7852acccd413bdb0b1da1504acd9d5cffb84a515da1e034","target":"graph","created_at":"2026-05-18T00:10:19Z","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 prove the global existence of Dirac-wave maps with curvature term with small initial data on globally hyperbolic manifolds of arbitrary dimension which satisfy a suitable growth condition. In addition, we also prove a global existence result for wave maps under similar assumptions.","authors_text":"Klaus Kroencke, Volker Branding","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T16:38:53Z","title":"Global existence of Dirac-wave maps with curvature term on expanding spacetimes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06520","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":"sha256:7727ec70d31e4281dd137e4ccc2b61459f830207db1588539a47fa04d93c7325","target":"record","created_at":"2026-05-18T00:10:19Z","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":"23428f27a54e33871fcc6e77b83d233b495c77f028970e5059fa796588ac04e0","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"math.DG","submitted_at":"2017-09-19T16:38:53Z","title_canon_sha256":"b2e0687ea6a20445704a72fc41aad15b97d0b367a8077ad0029ba0c2bd6cd034"},"schema_version":"1.0","source":{"id":"1709.06520","kind":"arxiv","version":2}},"canonical_sha256":"c5d3649b7787b9be308086bc3fff45d164bde5c661c04b1975aaee2af5ade10e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5d3649b7787b9be308086bc3fff45d164bde5c661c04b1975aaee2af5ade10e","first_computed_at":"2026-05-18T00:10:19.244806Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:19.244806Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nJfa7co2bJWL2vSfe5S8MY+hYmdV6OtRKq4Gx4VijLPsdqkb0u1PfkFmy9iIdag30wnYRFm+MKOa8Q7cUp1mDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:19.245290Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06520","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7727ec70d31e4281dd137e4ccc2b61459f830207db1588539a47fa04d93c7325","sha256:56b1f0ec6721619ff7852acccd413bdb0b1da1504acd9d5cffb84a515da1e034"],"state_sha256":"99fabcb90c43ce0c3a80907b190f98874a4ec40a536166f3e869f7b8294da033"}