{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ASZ43MWT574BFKV4R4L4GLYYQH","short_pith_number":"pith:ASZ43MWT","canonical_record":{"source":{"id":"1503.01519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-05T02:49:00Z","cross_cats_sorted":[],"title_canon_sha256":"ecc916d2caf5a5094dbe8f1e9b6c5c068ebb16f1e04721ff867f3dca510720bf","abstract_canon_sha256":"cf927476fc9df6a3a4fddc1c2da596e7c01174096e0fdbb9dfa3dd7690cb42e4"},"schema_version":"1.0"},"canonical_sha256":"04b3cdb2d3eff812aabc8f17c32f1881ef8380c754ad212e56ab23f32b5fb2e6","source":{"kind":"arxiv","id":"1503.01519","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01519","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01519v1","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01519","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"pith_short_12","alias_value":"ASZ43MWT574B","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ASZ43MWT574BFKV4","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ASZ43MWT","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ASZ43MWT574BFKV4R4L4GLYYQH","target":"record","payload":{"canonical_record":{"source":{"id":"1503.01519","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-05T02:49:00Z","cross_cats_sorted":[],"title_canon_sha256":"ecc916d2caf5a5094dbe8f1e9b6c5c068ebb16f1e04721ff867f3dca510720bf","abstract_canon_sha256":"cf927476fc9df6a3a4fddc1c2da596e7c01174096e0fdbb9dfa3dd7690cb42e4"},"schema_version":"1.0"},"canonical_sha256":"04b3cdb2d3eff812aabc8f17c32f1881ef8380c754ad212e56ab23f32b5fb2e6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:33.474370Z","signature_b64":"O4MsuZIEMqPLAMh3UK8ntckvJYV7PBuw8WjXBkcAlMl1kfn8fDDW+HLjUVPLIwESKY2WYOM/sJJCC9ew12SrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04b3cdb2d3eff812aabc8f17c32f1881ef8380c754ad212e56ab23f32b5fb2e6","last_reissued_at":"2026-05-18T02:25:33.473936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:33.473936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.01519","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":"2026-05-18T02:25:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FaDHge2A6Uj+ZPE3sM1ekDkMai18mH++Xr6Idy0CvXddh9yajvjUV0D0oPTFaPvJ4JYFghExo6tSkBK6SKS8Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:22:27.855940Z"},"content_sha256":"b015a34b94ac236d325c67e3ff4b6039b63d12004dca4141cb95402ad7416f57","schema_version":"1.0","event_id":"sha256:b015a34b94ac236d325c67e3ff4b6039b63d12004dca4141cb95402ad7416f57"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ASZ43MWT574BFKV4R4L4GLYYQH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spherical density of hyperbolic metric and uniform perfectness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Toshiyuki Sugawa","submitted_at":"2015-03-05T02:49:00Z","abstract_excerpt":"It is well known that a hyperbolic domain in the complex plane has uniformly perfect boundary precisely when the product of its hyperbolic density and the distance function to its boundary has a positive lower bound. We extend this characterization to a hyperbolic domain in the Riemann sphere in terms of the spherical metric."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01519","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":"2026-05-18T02:25:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q4apjNdjLbABvFfJtGULGYFltX5QzCsmijJztzWo8/9o9AIIwdV5GFN4rkFEEqeVE2puevszvhafPPs3sezqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T03:22:27.856292Z"},"content_sha256":"8cb690392073c6a04d039c40d77593742ace79b9db7a826fdd5e79ceececc0b5","schema_version":"1.0","event_id":"sha256:8cb690392073c6a04d039c40d77593742ace79b9db7a826fdd5e79ceececc0b5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ASZ43MWT574BFKV4R4L4GLYYQH/bundle.json","state_url":"https://pith.science/pith/ASZ43MWT574BFKV4R4L4GLYYQH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ASZ43MWT574BFKV4R4L4GLYYQH/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":"2026-06-23T03:22:27Z","links":{"resolver":"https://pith.science/pith/ASZ43MWT574BFKV4R4L4GLYYQH","bundle":"https://pith.science/pith/ASZ43MWT574BFKV4R4L4GLYYQH/bundle.json","state":"https://pith.science/pith/ASZ43MWT574BFKV4R4L4GLYYQH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ASZ43MWT574BFKV4R4L4GLYYQH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ASZ43MWT574BFKV4R4L4GLYYQH","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":"cf927476fc9df6a3a4fddc1c2da596e7c01174096e0fdbb9dfa3dd7690cb42e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-05T02:49:00Z","title_canon_sha256":"ecc916d2caf5a5094dbe8f1e9b6c5c068ebb16f1e04721ff867f3dca510720bf"},"schema_version":"1.0","source":{"id":"1503.01519","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.01519","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"arxiv_version","alias_value":"1503.01519v1","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01519","created_at":"2026-05-18T02:25:33Z"},{"alias_kind":"pith_short_12","alias_value":"ASZ43MWT574B","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ASZ43MWT574BFKV4","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ASZ43MWT","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:8cb690392073c6a04d039c40d77593742ace79b9db7a826fdd5e79ceececc0b5","target":"graph","created_at":"2026-05-18T02:25:33Z","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":"It is well known that a hyperbolic domain in the complex plane has uniformly perfect boundary precisely when the product of its hyperbolic density and the distance function to its boundary has a positive lower bound. We extend this characterization to a hyperbolic domain in the Riemann sphere in terms of the spherical metric.","authors_text":"Toshiyuki Sugawa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-05T02:49:00Z","title":"Spherical density of hyperbolic metric and uniform perfectness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01519","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:b015a34b94ac236d325c67e3ff4b6039b63d12004dca4141cb95402ad7416f57","target":"record","created_at":"2026-05-18T02:25:33Z","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":"cf927476fc9df6a3a4fddc1c2da596e7c01174096e0fdbb9dfa3dd7690cb42e4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-03-05T02:49:00Z","title_canon_sha256":"ecc916d2caf5a5094dbe8f1e9b6c5c068ebb16f1e04721ff867f3dca510720bf"},"schema_version":"1.0","source":{"id":"1503.01519","kind":"arxiv","version":1}},"canonical_sha256":"04b3cdb2d3eff812aabc8f17c32f1881ef8380c754ad212e56ab23f32b5fb2e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"04b3cdb2d3eff812aabc8f17c32f1881ef8380c754ad212e56ab23f32b5fb2e6","first_computed_at":"2026-05-18T02:25:33.473936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:33.473936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O4MsuZIEMqPLAMh3UK8ntckvJYV7PBuw8WjXBkcAlMl1kfn8fDDW+HLjUVPLIwESKY2WYOM/sJJCC9ew12SrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:33.474370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.01519","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b015a34b94ac236d325c67e3ff4b6039b63d12004dca4141cb95402ad7416f57","sha256:8cb690392073c6a04d039c40d77593742ace79b9db7a826fdd5e79ceececc0b5"],"state_sha256":"d6dd9fc96f9fef7c976de9bc1b82c8f55f361123392a4e172e62b3e1891ddc1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"faWjFvbEV1Jz7rYPWeJz5i/6yAYPEIpabcejtrAqa7W0GgyUjBMMZowSMXKVlMW7ndwSKxkya/TomO3QmoIMAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T03:22:27.858242Z","bundle_sha256":"f93006db94a30eb3f36cbe650c5d9467700e12c7338b1e68fef14b883ec3faf6"}}