{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZQWTC2434U63QZZLL3BUOCSQ4B","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":"7da881d36723f90fa964326d0a75cd8e6e4b9c943a126214958c31350ce26efb","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-09T04:52:31Z","title_canon_sha256":"3ac60389296e2d1021194472195f3baf8903b5d703ba0c352639d6475adef522"},"schema_version":"1.0","source":{"id":"1507.02375","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02375","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02375v2","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02375","created_at":"2026-05-18T00:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"ZQWTC2434U63","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZQWTC2434U63QZZL","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZQWTC243","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:32f5bc0a210492c1c91401828f6f10b11684aa961b6d51bb3087e7614211f567","target":"graph","created_at":"2026-05-18T00:29:39Z","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":"A metric projective structure is a manifold equipped with the unparametrised geodesics of some pseudo-Riemannian metric. We make acomprehensive treatment of such structures in the case that there is a projective Weyl curvature nullity condition. The analysis is simplified by a fundamental and canonical 2-tensor invariant that we discover. It leads to a new canonical tractor connection for these geometries which is defined on a rank $(n+1)$-bundle. We show this connection is linked to the metrisability equations that govern the existence of metrics compatible with the structure. The fundamental","authors_text":"A. Rod Gover, Vladimir S. Matveev","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-09T04:52:31Z","title":"Projectively related metrics, Weyl nullity, and metric projectively invariant equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02375","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":"sha256:702f752b0dc299984d43e778c585ce1195d2784dd1caaa84c6214ee85ee9826a","target":"record","created_at":"2026-05-18T00:29:39Z","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":"7da881d36723f90fa964326d0a75cd8e6e4b9c943a126214958c31350ce26efb","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-07-09T04:52:31Z","title_canon_sha256":"3ac60389296e2d1021194472195f3baf8903b5d703ba0c352639d6475adef522"},"schema_version":"1.0","source":{"id":"1507.02375","kind":"arxiv","version":2}},"canonical_sha256":"cc2d316b9be53db8672b5ec3470a50e054678544999519e391e2260503fa60f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc2d316b9be53db8672b5ec3470a50e054678544999519e391e2260503fa60f7","first_computed_at":"2026-05-18T00:29:39.757593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:39.757593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eSUamwUg5PehD2Pg/Ftei15wgVsysFwB8atEolQPGaZgiME4XABj8HoiSBw5H9vbkpy1wj68k/jgOzFOpy9GCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:39.758038Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02375","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:702f752b0dc299984d43e778c585ce1195d2784dd1caaa84c6214ee85ee9826a","sha256:32f5bc0a210492c1c91401828f6f10b11684aa961b6d51bb3087e7614211f567"],"state_sha256":"cadea297d6aa4a0903b3e70454ebdd909cb98a54340c5f0cc9632768e8a6c5fe"}