{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DMK2YZ4DIFYQNBRGV3OWC6N42X","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":"a4f5a5c7457ceaab2c3615003b68ef45d2b4d89a302abee2bf26a4b4b9f9ad56","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-12-12T16:16:03Z","title_canon_sha256":"aaa2e07434e03bc90c998a52d9bf2aaf502963d733c429a27cc378e74a8f88e8"},"schema_version":"1.0","source":{"id":"1412.4035","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.4035","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"arxiv_version","alias_value":"1412.4035v2","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.4035","created_at":"2026-05-18T01:27:46Z"},{"alias_kind":"pith_short_12","alias_value":"DMK2YZ4DIFYQ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DMK2YZ4DIFYQNBRG","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DMK2YZ4D","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:47a0fd5fbec3c29e5531cbc42466ff8f5c900713e92e2e95ff80ad5dc5e4e548","target":"graph","created_at":"2026-05-18T01:27:46Z","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":"The Cassinian metric and its inner metric have been studied for subdomains of the $n$-dimensional Euclidean space $\\mathbb{R}^n$ ($n\\ge 2$) by the first named author. In this paper we obtain various inequalities between the Cassinian metric and other related metrics in some specific subdomains of $\\mathbb{R}^n$. Also, a sharp distortion property of the Cassinian metric under M\\\"obius transformations of the unit ball is obtained.","authors_text":"Manas Ranjan Mohapatra, Swadesh Kumar Sahoo, Xiaohui Zhang, Zair Ibragimov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-12-12T16:16:03Z","title":"Geometry of the Cassinian metric and its inner metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.4035","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":"sha256:638384a2bb96e32afb90bfc6700b98153e330a452bcee76c745f80a98a97427e","target":"record","created_at":"2026-05-18T01:27:46Z","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":"a4f5a5c7457ceaab2c3615003b68ef45d2b4d89a302abee2bf26a4b4b9f9ad56","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-12-12T16:16:03Z","title_canon_sha256":"aaa2e07434e03bc90c998a52d9bf2aaf502963d733c429a27cc378e74a8f88e8"},"schema_version":"1.0","source":{"id":"1412.4035","kind":"arxiv","version":2}},"canonical_sha256":"1b15ac67834171068626aedd6179bcd5c1f1748e0ee980104adbf6b22a47d7bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b15ac67834171068626aedd6179bcd5c1f1748e0ee980104adbf6b22a47d7bc","first_computed_at":"2026-05-18T01:27:46.439058Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:46.439058Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IpI4gFQNG3ZZB0j9azHQe4QEqfKFCS7tkiFS/tSFPT+aQAmZN6aJYUisHsdYA8QEcWSN1dT86itcK3GTOOVUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:46.439727Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.4035","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:638384a2bb96e32afb90bfc6700b98153e330a452bcee76c745f80a98a97427e","sha256:47a0fd5fbec3c29e5531cbc42466ff8f5c900713e92e2e95ff80ad5dc5e4e548"],"state_sha256":"b06654e02bcd60961ae331e1ba2c95ce3bb98d205a52d1e802473c345f84548c"}