{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:7UFSWRLJDIPBRDZ2CWPAONV7YK","short_pith_number":"pith:7UFSWRLJ","canonical_record":{"source":{"id":"1411.2747","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-11T10:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"d2833b84964f32efc61fe52d43a2ec0e2545edacbbc93d67f53f28f483ee288a","abstract_canon_sha256":"97db6b1d9177a326d87ec7199125e2805df7801713541d11f525a61bb5e708b0"},"schema_version":"1.0"},"canonical_sha256":"fd0b2b45691a1e188f3a159e0736bfc28a9327abb2908391cc08b83f7aa834b2","source":{"kind":"arxiv","id":"1411.2747","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2747","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2747v4","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2747","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"pith_short_12","alias_value":"7UFSWRLJDIPB","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7UFSWRLJDIPBRDZ2","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7UFSWRLJ","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:7UFSWRLJDIPBRDZ2CWPAONV7YK","target":"record","payload":{"canonical_record":{"source":{"id":"1411.2747","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-11T10:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"d2833b84964f32efc61fe52d43a2ec0e2545edacbbc93d67f53f28f483ee288a","abstract_canon_sha256":"97db6b1d9177a326d87ec7199125e2805df7801713541d11f525a61bb5e708b0"},"schema_version":"1.0"},"canonical_sha256":"fd0b2b45691a1e188f3a159e0736bfc28a9327abb2908391cc08b83f7aa834b2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:06.062121Z","signature_b64":"YfGNRn18nxoDGoki1hKzpYqeJ6JTaf0L1p3e3wPqISEQoswQ6NvlC3q2JsIEHINW7hDBiFw0nImIoFbr6DpOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd0b2b45691a1e188f3a159e0736bfc28a9327abb2908391cc08b83f7aa834b2","last_reissued_at":"2026-05-18T00:25:06.061648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:06.061648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.2747","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6Lojg8XJ3pJMO0o8iV4Edw7YM7fpN9oIBaKZpqDJxx+lHBbk0PddjCExpTZByValatQDSVvC10gPFhJN9OWSBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T07:21:59.400649Z"},"content_sha256":"9df501fca93e16bde8c5049c7bc25e0fa5d87062cfd549d9402523509403cf35","schema_version":"1.0","event_id":"sha256:9df501fca93e16bde8c5049c7bc25e0fa5d87062cfd549d9402523509403cf35"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:7UFSWRLJDIPBRDZ2CWPAONV7YK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Inequalities and bilipschitz conditions for triangular ratio metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Matti Vuorinen, Parisa Hariri, Xiaohui Zhang","submitted_at":"2014-11-11T10:00:31Z","abstract_excerpt":"Let $G \\subsetneq \\mathbb{R}^n$ be a domain and let $d_1$ and $d_2$ be two metrics on $G$. We compare the geometries defined by the two metrics to each other for several pairs of metrics. The metrics we study include the distance ratio metric, the triangular ratio metric and the visual angle metric. Finally we apply our results to study Lipschitz maps with respect to these metrics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2747","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:25:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"caDXwlhcIYAIoHnHqqkvdu+Up1zxrBVB2qPPCXvA4rafexVPHCk+pn2pbF47kWuDMTrXKEGq/rOK2Mk5iBcuBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T07:21:59.400983Z"},"content_sha256":"6406157d8ba33dcd54357b4683da87ce496d705f16ca52afb4994dc02089013b","schema_version":"1.0","event_id":"sha256:6406157d8ba33dcd54357b4683da87ce496d705f16ca52afb4994dc02089013b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UFSWRLJDIPBRDZ2CWPAONV7YK/bundle.json","state_url":"https://pith.science/pith/7UFSWRLJDIPBRDZ2CWPAONV7YK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UFSWRLJDIPBRDZ2CWPAONV7YK/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-21T07:21:59Z","links":{"resolver":"https://pith.science/pith/7UFSWRLJDIPBRDZ2CWPAONV7YK","bundle":"https://pith.science/pith/7UFSWRLJDIPBRDZ2CWPAONV7YK/bundle.json","state":"https://pith.science/pith/7UFSWRLJDIPBRDZ2CWPAONV7YK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UFSWRLJDIPBRDZ2CWPAONV7YK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:7UFSWRLJDIPBRDZ2CWPAONV7YK","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":"97db6b1d9177a326d87ec7199125e2805df7801713541d11f525a61bb5e708b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-11T10:00:31Z","title_canon_sha256":"d2833b84964f32efc61fe52d43a2ec0e2545edacbbc93d67f53f28f483ee288a"},"schema_version":"1.0","source":{"id":"1411.2747","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.2747","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"arxiv_version","alias_value":"1411.2747v4","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.2747","created_at":"2026-05-18T00:25:06Z"},{"alias_kind":"pith_short_12","alias_value":"7UFSWRLJDIPB","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"7UFSWRLJDIPBRDZ2","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"7UFSWRLJ","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:6406157d8ba33dcd54357b4683da87ce496d705f16ca52afb4994dc02089013b","target":"graph","created_at":"2026-05-18T00:25:06Z","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":"Let $G \\subsetneq \\mathbb{R}^n$ be a domain and let $d_1$ and $d_2$ be two metrics on $G$. We compare the geometries defined by the two metrics to each other for several pairs of metrics. The metrics we study include the distance ratio metric, the triangular ratio metric and the visual angle metric. Finally we apply our results to study Lipschitz maps with respect to these metrics.","authors_text":"Matti Vuorinen, Parisa Hariri, Xiaohui Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-11T10:00:31Z","title":"Inequalities and bilipschitz conditions for triangular ratio metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.2747","kind":"arxiv","version":4},"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":"sha256:9df501fca93e16bde8c5049c7bc25e0fa5d87062cfd549d9402523509403cf35","target":"record","created_at":"2026-05-18T00:25:06Z","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":"97db6b1d9177a326d87ec7199125e2805df7801713541d11f525a61bb5e708b0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2014-11-11T10:00:31Z","title_canon_sha256":"d2833b84964f32efc61fe52d43a2ec0e2545edacbbc93d67f53f28f483ee288a"},"schema_version":"1.0","source":{"id":"1411.2747","kind":"arxiv","version":4}},"canonical_sha256":"fd0b2b45691a1e188f3a159e0736bfc28a9327abb2908391cc08b83f7aa834b2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd0b2b45691a1e188f3a159e0736bfc28a9327abb2908391cc08b83f7aa834b2","first_computed_at":"2026-05-18T00:25:06.061648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:06.061648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YfGNRn18nxoDGoki1hKzpYqeJ6JTaf0L1p3e3wPqISEQoswQ6NvlC3q2JsIEHINW7hDBiFw0nImIoFbr6DpOBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:06.062121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.2747","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9df501fca93e16bde8c5049c7bc25e0fa5d87062cfd549d9402523509403cf35","sha256:6406157d8ba33dcd54357b4683da87ce496d705f16ca52afb4994dc02089013b"],"state_sha256":"a56eb0f8054e6fe813b6d15046e08fe51096046c79b74b19abf416420d7b3fe2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"By407aNjN23qseJfxqThbRjJE6IOExxJDxVs5eoqlrNMVVqw8cKxonV3GPWmVUur90fuD1L8u5sE2zrXh1f9Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T07:21:59.402922Z","bundle_sha256":"08b4e2bd3ce5c077672d5e9908c22e80b15aaeeb2369071b124e65cdc0ba975b"}}