{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LRSL5FGUISJ5HKPVML3454LZJE","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":"70385355f99ab4331f18872f1a69d68984f04cf4b44ea23dfd5d69f835df750c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-30T01:44:42Z","title_canon_sha256":"2fc6aa7a64f21be2a187e5b872c6252302c41b6dc82f47ca26b07da3d0d640d4"},"schema_version":"1.0","source":{"id":"1710.00135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00135","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00135v1","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00135","created_at":"2026-05-17T23:43:18Z"},{"alias_kind":"pith_short_12","alias_value":"LRSL5FGUISJ5","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LRSL5FGUISJ5HKPV","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LRSL5FGU","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:f489c06983c55f518c2dd7f3501b279d2e152dca53b6dc2d35630da24cc6658d","target":"graph","created_at":"2026-05-17T23:43:18Z","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, we study the sharp constants of quantitative Hardy and Rellich inequalities on nonreversible Finsler manifolds equipped with arbitrary measures. In particular, these inequalities can be globally refined by adding remainder terms like the Brezis-V\\'azquez improvement, if Finsler manifolds are of strictly negative flag curvature, vanishing S-curvature and finite uniformity constant. Furthermore, these results remain valid when Finsler metrics are reversible.","authors_text":"Lixia Yuan, Wei Zhao, Yibing Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-30T01:44:42Z","title":"Improved Hardy and Rellich inequalities on nonreversible Finsler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00135","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:ca70bd4d09f7cc7321d797deecb6ccc44c9d8c373dbcf799c7f527a38502e3a1","target":"record","created_at":"2026-05-17T23:43:18Z","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":"70385355f99ab4331f18872f1a69d68984f04cf4b44ea23dfd5d69f835df750c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-09-30T01:44:42Z","title_canon_sha256":"2fc6aa7a64f21be2a187e5b872c6252302c41b6dc82f47ca26b07da3d0d640d4"},"schema_version":"1.0","source":{"id":"1710.00135","kind":"arxiv","version":1}},"canonical_sha256":"5c64be94d44493d3a9f562f7cef179492a4ce2fbe72a0ee873265f473761c6b7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c64be94d44493d3a9f562f7cef179492a4ce2fbe72a0ee873265f473761c6b7","first_computed_at":"2026-05-17T23:43:18.471128Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:18.471128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9vxnsj2JkmeaEChGKHSNpWiD81wXgk4Bc84Piv2q7ePmpWE405DKTPgn54hDhBvTtjlKgF0o6MLkbJ1ja8cdCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:18.471737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca70bd4d09f7cc7321d797deecb6ccc44c9d8c373dbcf799c7f527a38502e3a1","sha256:f489c06983c55f518c2dd7f3501b279d2e152dca53b6dc2d35630da24cc6658d"],"state_sha256":"5dcd6095a6b1efe1f947dd98e53a6597891f51cda3e81ac09adc0a20fb74bf6b"}