{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:IWVOLIIL6Q2ZAJCZLRIMIHJF2B","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":"750addac68d163bc8dd6295e5015276360de073aa87b7beb56c2ed7fb2bfc6bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-25T15:56:29Z","title_canon_sha256":"cf88ea0ee94c84a2a09c05b77d07853fef5830d961fce8431b2e4ee2d6a0fb24"},"schema_version":"1.0","source":{"id":"1301.6075","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.6075","created_at":"2026-05-18T03:35:27Z"},{"alias_kind":"arxiv_version","alias_value":"1301.6075v1","created_at":"2026-05-18T03:35:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.6075","created_at":"2026-05-18T03:35:27Z"},{"alias_kind":"pith_short_12","alias_value":"IWVOLIIL6Q2Z","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"IWVOLIIL6Q2ZAJCZ","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"IWVOLIIL","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:bf6fb7ce28fd54fd0b74678b89abd5465a82992a7933dc784e598c0cf0a3c322","target":"graph","created_at":"2026-05-18T03:35:27Z","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 vector field s on a Riemannian manifold M is said to be harmonic if there exists a member of a 2-parameter family of generalised Cheeger-Gromoll metrics on TM with respect to which s is a harmonic section. If M is a simply-connected non-flat space form other than the 2-sphere, examples are obtained of conformal vector fields that are harmonic. In particular, the harmonic Killing fields and conformal gradient fields are classified, a loop of non-congruent harmonic conformal fields on the hyperbolic plane constructed, and the 2-dimensional classification achieved for conformal fields. A classi","authors_text":"C.M. Wood, E. Loubeau, M. Benyounes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-25T15:56:29Z","title":"Harmonic Vector Fields on Space Forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.6075","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":"sha256:4a62fa4c43d0cdc7512e0eb991e25ff96b601f571c047333e15e124fe651a02f","target":"record","created_at":"2026-05-18T03:35:27Z","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":"750addac68d163bc8dd6295e5015276360de073aa87b7beb56c2ed7fb2bfc6bf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-01-25T15:56:29Z","title_canon_sha256":"cf88ea0ee94c84a2a09c05b77d07853fef5830d961fce8431b2e4ee2d6a0fb24"},"schema_version":"1.0","source":{"id":"1301.6075","kind":"arxiv","version":1}},"canonical_sha256":"45aae5a10bf4359024595c50c41d25d05b19dfeb84d9f3cc26ed7eb808b12c82","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"45aae5a10bf4359024595c50c41d25d05b19dfeb84d9f3cc26ed7eb808b12c82","first_computed_at":"2026-05-18T03:35:27.199539Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:27.199539Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8VA3Nhlw+++VEFI0mMGyOwMV+2MNkCn/5u0COGKnYITPIzBVzVqCJEKfH0PCxsQfN0oI9/4L2LSgio4+0fGMDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:27.200202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.6075","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a62fa4c43d0cdc7512e0eb991e25ff96b601f571c047333e15e124fe651a02f","sha256:bf6fb7ce28fd54fd0b74678b89abd5465a82992a7933dc784e598c0cf0a3c322"],"state_sha256":"4f5826d59b4191e73e70bbc9651a2971fb695f5d130d62a4fb591b251d3e3890"}