{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LNKGASECM7267YZBUWPIKJVFRY","short_pith_number":"pith:LNKGASEC","canonical_record":{"source":{"id":"1304.7994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-30T13:41:26Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"835abf68b0442fd4b17b85e3344153bc3a79120cf95d63542b2443c1a93342fa","abstract_canon_sha256":"586eba6411ac3fec917d9dbc7860eb307a9e5128e88be423522a421a2d02dff5"},"schema_version":"1.0"},"canonical_sha256":"5b5460488267f5efe321a59e8526a58e22fbde05190b803da27d5c7e6076fddc","source":{"kind":"arxiv","id":"1304.7994","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7994","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7994v1","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7994","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"LNKGASECM726","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LNKGASECM7267YZB","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LNKGASEC","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LNKGASECM7267YZBUWPIKJVFRY","target":"record","payload":{"canonical_record":{"source":{"id":"1304.7994","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-30T13:41:26Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"835abf68b0442fd4b17b85e3344153bc3a79120cf95d63542b2443c1a93342fa","abstract_canon_sha256":"586eba6411ac3fec917d9dbc7860eb307a9e5128e88be423522a421a2d02dff5"},"schema_version":"1.0"},"canonical_sha256":"5b5460488267f5efe321a59e8526a58e22fbde05190b803da27d5c7e6076fddc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:51.242893Z","signature_b64":"n1WuzEH9Sr2MbzeDniRHe3gXXaEeqPb6ri+0is2btX3DXEKTbGetfUhKza1WmVH1Gk9AMGKHi0UVmoY4pwyEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b5460488267f5efe321a59e8526a58e22fbde05190b803da27d5c7e6076fddc","last_reissued_at":"2026-05-18T03:26:51.242333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:51.242333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.7994","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:26:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MHfyBLw9xU5cTukKzD16pN2WbD3Of7hDKcr9Av/DPRnMZvHjezekPd+Zvi0JD0VfaX16mx2hULHTe704t8hUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:25:51.205976Z"},"content_sha256":"60ca13e89866e01617c3917d2db0ce7b74ee836b51bbac000593adfcf15a6fb0","schema_version":"1.0","event_id":"sha256:60ca13e89866e01617c3917d2db0ce7b74ee836b51bbac000593adfcf15a6fb0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LNKGASECM7267YZBUWPIKJVFRY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lipschitz conditions and the distance ratio metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.MG","authors_text":"Matti Vuorinen, Slavko Simi\\'c","submitted_at":"2013-04-30T13:41:26Z","abstract_excerpt":"We give study the Lipschitz continuity of M\\\"obius transformations of a punctured disk onto another punctured disk with respect to the distance ratio metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7994","kind":"arxiv","version":1},"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":"2026-05-18T03:26:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DMfbl8jPgANkIZeHMlXg5FluOTHTeqbmqKK7tHk4Fx4t5ptmh1Wd4ccdf7WSa/dlDqNI0ePpgy9/Z1R+ufhSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:25:51.206310Z"},"content_sha256":"748f841fc76e59759165805306ed616e3ba7a33bcece4b737432e0f1aa1810aa","schema_version":"1.0","event_id":"sha256:748f841fc76e59759165805306ed616e3ba7a33bcece4b737432e0f1aa1810aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LNKGASECM7267YZBUWPIKJVFRY/bundle.json","state_url":"https://pith.science/pith/LNKGASECM7267YZBUWPIKJVFRY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LNKGASECM7267YZBUWPIKJVFRY/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":"2026-06-21T08:25:51Z","links":{"resolver":"https://pith.science/pith/LNKGASECM7267YZBUWPIKJVFRY","bundle":"https://pith.science/pith/LNKGASECM7267YZBUWPIKJVFRY/bundle.json","state":"https://pith.science/pith/LNKGASECM7267YZBUWPIKJVFRY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LNKGASECM7267YZBUWPIKJVFRY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LNKGASECM7267YZBUWPIKJVFRY","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":"586eba6411ac3fec917d9dbc7860eb307a9e5128e88be423522a421a2d02dff5","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-30T13:41:26Z","title_canon_sha256":"835abf68b0442fd4b17b85e3344153bc3a79120cf95d63542b2443c1a93342fa"},"schema_version":"1.0","source":{"id":"1304.7994","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.7994","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"arxiv_version","alias_value":"1304.7994v1","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7994","created_at":"2026-05-18T03:26:51Z"},{"alias_kind":"pith_short_12","alias_value":"LNKGASECM726","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LNKGASECM7267YZB","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LNKGASEC","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:748f841fc76e59759165805306ed616e3ba7a33bcece4b737432e0f1aa1810aa","target":"graph","created_at":"2026-05-18T03:26:51Z","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":"We give study the Lipschitz continuity of M\\\"obius transformations of a punctured disk onto another punctured disk with respect to the distance ratio metric.","authors_text":"Matti Vuorinen, Slavko Simi\\'c","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-30T13:41:26Z","title":"Lipschitz conditions and the distance ratio metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7994","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":"sha256:60ca13e89866e01617c3917d2db0ce7b74ee836b51bbac000593adfcf15a6fb0","target":"record","created_at":"2026-05-18T03:26:51Z","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":"586eba6411ac3fec917d9dbc7860eb307a9e5128e88be423522a421a2d02dff5","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-04-30T13:41:26Z","title_canon_sha256":"835abf68b0442fd4b17b85e3344153bc3a79120cf95d63542b2443c1a93342fa"},"schema_version":"1.0","source":{"id":"1304.7994","kind":"arxiv","version":1}},"canonical_sha256":"5b5460488267f5efe321a59e8526a58e22fbde05190b803da27d5c7e6076fddc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b5460488267f5efe321a59e8526a58e22fbde05190b803da27d5c7e6076fddc","first_computed_at":"2026-05-18T03:26:51.242333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:51.242333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n1WuzEH9Sr2MbzeDniRHe3gXXaEeqPb6ri+0is2btX3DXEKTbGetfUhKza1WmVH1Gk9AMGKHi0UVmoY4pwyEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:51.242893Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.7994","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60ca13e89866e01617c3917d2db0ce7b74ee836b51bbac000593adfcf15a6fb0","sha256:748f841fc76e59759165805306ed616e3ba7a33bcece4b737432e0f1aa1810aa"],"state_sha256":"37e04d76b0360bac9368da426e819397bedd109c749eabe95251cd512d873a22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fP3t+l1/QyUWZclO2L3GhOm6H/RtecoR7l4DND8sR4WPxxGp/hcHX/6aghzYA2ERXI5Ai9pJg/c92/WQpcsADg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T08:25:51.208123Z","bundle_sha256":"c84a76121f40ec4dea4297593297b95afe294dc63d4048f37e8a61e728661fd4"}}