{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XQ42LHQOY6V2FTCEQB6OXCUT6T","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":"8d8dd4bb4ff8ea8457aaea633db81f2a23a7d979dabbe6abb83b23177b5effc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-14T01:56:57Z","title_canon_sha256":"95445d2a35af44712a0f913404b00c8defd044c615f830ec85a3d20e3770c433"},"schema_version":"1.0","source":{"id":"1609.04109","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.04109","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"arxiv_version","alias_value":"1609.04109v1","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04109","created_at":"2026-05-18T01:04:38Z"},{"alias_kind":"pith_short_12","alias_value":"XQ42LHQOY6V2","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XQ42LHQOY6V2FTCE","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XQ42LHQO","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:64ecb72c8bc0012dc5ec9a7f1fe8a394dc904327fc042b4323158a42c7f44945","target":"graph","created_at":"2026-05-18T01:04:38Z","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 paper, the Douglas curvature of (\\alpha,\\beta)-metrics, a special class of Finsler metrics defined by a Riemannian metric \\alpha and a 1-form \\beta, is studied. These metrics with vanishing Douglas curvature in dimension n\\geq3 are classified by using a new class of metrical deformations called \\beta-deformations. The result shows that conformal 1-forms of Riemannian metrics play a key role, and an effective way to construct such 1-forms is provided also by \\beta-deformations.","authors_text":"Changtao Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-14T01:56:57Z","title":"Douglas metrics of (\\alpha,\\beta) type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04109","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:baee71e4f77a141f9b8150fa9e329620c6e18d5ec50f80318560988977e04658","target":"record","created_at":"2026-05-18T01:04:38Z","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":"8d8dd4bb4ff8ea8457aaea633db81f2a23a7d979dabbe6abb83b23177b5effc8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-09-14T01:56:57Z","title_canon_sha256":"95445d2a35af44712a0f913404b00c8defd044c615f830ec85a3d20e3770c433"},"schema_version":"1.0","source":{"id":"1609.04109","kind":"arxiv","version":1}},"canonical_sha256":"bc39a59e0ec7aba2cc44807ceb8a93f4fe494cf3b227848726f91af07075faf1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc39a59e0ec7aba2cc44807ceb8a93f4fe494cf3b227848726f91af07075faf1","first_computed_at":"2026-05-18T01:04:38.969671Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:38.969671Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H2CcXN+S+0mq6jnrukLI2L55ZSHbCnk79GYR9nD2t/QOYAlrXEU8jUKmnFyC8YJ+UjrGN4r/KhJ5pzVLLumyDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:38.970286Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.04109","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baee71e4f77a141f9b8150fa9e329620c6e18d5ec50f80318560988977e04658","sha256:64ecb72c8bc0012dc5ec9a7f1fe8a394dc904327fc042b4323158a42c7f44945"],"state_sha256":"081b6a68c5c1cd49a54dcfdf54243a6317d27a5cb5287528d048e4afe8a231f5"}