{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GT54ZJPDUKPQW3RONNRODMEFWQ","short_pith_number":"pith:GT54ZJPD","canonical_record":{"source":{"id":"1603.06818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-22T15:07:01Z","cross_cats_sorted":[],"title_canon_sha256":"3d457f1ebc23187f77b20653fbd5d8e1865323a6958c2e705bd4e59fba0f89ae","abstract_canon_sha256":"56de62c54dab8a77faddab6fb6c8dcabe40d2c050c0b4cc909d9c46bc2c6317f"},"schema_version":"1.0"},"canonical_sha256":"34fbcca5e3a29f0b6e2e6b62e1b085b4098bc7d66a9aabfc427d998a412894c9","source":{"kind":"arxiv","id":"1603.06818","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06818","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06818v1","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06818","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"GT54ZJPDUKPQ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GT54ZJPDUKPQW3RO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GT54ZJPD","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GT54ZJPDUKPQW3RONNRODMEFWQ","target":"record","payload":{"canonical_record":{"source":{"id":"1603.06818","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-22T15:07:01Z","cross_cats_sorted":[],"title_canon_sha256":"3d457f1ebc23187f77b20653fbd5d8e1865323a6958c2e705bd4e59fba0f89ae","abstract_canon_sha256":"56de62c54dab8a77faddab6fb6c8dcabe40d2c050c0b4cc909d9c46bc2c6317f"},"schema_version":"1.0"},"canonical_sha256":"34fbcca5e3a29f0b6e2e6b62e1b085b4098bc7d66a9aabfc427d998a412894c9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:34.634934Z","signature_b64":"AszXSfBzxN8tonrm2gSjCfqVCix/UoosOnzwpnyPjOAyENshC8xYwcfxuTAMIBHT+gMomHNHkHZBvXVo/MEWDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"34fbcca5e3a29f0b6e2e6b62e1b085b4098bc7d66a9aabfc427d998a412894c9","last_reissued_at":"2026-05-18T01:18:34.634332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:34.634332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.06818","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":"2026-05-18T01:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iudKIh5wuuoWtb83br6IvC0YUUCgiZyWeEgEdMU83jQPJkSx3C1Zc9P0pFeshcsGm3zqsMFOugUatCYIFR6qAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:55:02.286114Z"},"content_sha256":"0c05a17a3ede0741814d4500e148ec5a08d4f03ef38a502a1c1a22f32a3c96a1","schema_version":"1.0","event_id":"sha256:0c05a17a3ede0741814d4500e148ec5a08d4f03ef38a502a1c1a22f32a3c96a1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GT54ZJPDUKPQW3RONNRODMEFWQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strong submultiplicativity of the Poincare metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Daniela Kraus, Oliver Roth","submitted_at":"2016-03-22T15:07:01Z","abstract_excerpt":"We give a direct proof of an important result of Solynin which says that the Poincar\\'e metric is a strongly submultiplicative domain function. This result is then used to define a new capacity for compact subsets of the complex plane $\\mathbb{C}$, which might be called Poincar\\'e capacity. If the compact set $K \\subseteq \\mathbb{C}$ is connected, then the Poincar\\'e capacity of $K$ is the same as the logarithmic capacity of $K$. In this special case, the submultiplicativity is well--known and can be stated as an inequality for the normalized conformal map onto the complement of $K$. Using the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06818","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":"2026-05-18T01:18:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oxETRFjbUWKAxh/in3T+UuDsaRtriVksASTrrermpZ+/vTx2lrIGtY5UKUB4JK4kDXEOLfCIWTz5LF+2sCPHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:55:02.286475Z"},"content_sha256":"af01f02c3bb9bc520352078f812312634a5b2edcc16fd7d880bb55443093f9b7","schema_version":"1.0","event_id":"sha256:af01f02c3bb9bc520352078f812312634a5b2edcc16fd7d880bb55443093f9b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GT54ZJPDUKPQW3RONNRODMEFWQ/bundle.json","state_url":"https://pith.science/pith/GT54ZJPDUKPQW3RONNRODMEFWQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GT54ZJPDUKPQW3RONNRODMEFWQ/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":"2026-06-02T15:55:02Z","links":{"resolver":"https://pith.science/pith/GT54ZJPDUKPQW3RONNRODMEFWQ","bundle":"https://pith.science/pith/GT54ZJPDUKPQW3RONNRODMEFWQ/bundle.json","state":"https://pith.science/pith/GT54ZJPDUKPQW3RONNRODMEFWQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GT54ZJPDUKPQW3RONNRODMEFWQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GT54ZJPDUKPQW3RONNRODMEFWQ","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":"56de62c54dab8a77faddab6fb6c8dcabe40d2c050c0b4cc909d9c46bc2c6317f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-22T15:07:01Z","title_canon_sha256":"3d457f1ebc23187f77b20653fbd5d8e1865323a6958c2e705bd4e59fba0f89ae"},"schema_version":"1.0","source":{"id":"1603.06818","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06818","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06818v1","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06818","created_at":"2026-05-18T01:18:34Z"},{"alias_kind":"pith_short_12","alias_value":"GT54ZJPDUKPQ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GT54ZJPDUKPQW3RO","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GT54ZJPD","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:af01f02c3bb9bc520352078f812312634a5b2edcc16fd7d880bb55443093f9b7","target":"graph","created_at":"2026-05-18T01:18:34Z","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 a direct proof of an important result of Solynin which says that the Poincar\\'e metric is a strongly submultiplicative domain function. This result is then used to define a new capacity for compact subsets of the complex plane $\\mathbb{C}$, which might be called Poincar\\'e capacity. If the compact set $K \\subseteq \\mathbb{C}$ is connected, then the Poincar\\'e capacity of $K$ is the same as the logarithmic capacity of $K$. In this special case, the submultiplicativity is well--known and can be stated as an inequality for the normalized conformal map onto the complement of $K$. Using the","authors_text":"Daniela Kraus, Oliver Roth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-22T15:07:01Z","title":"Strong submultiplicativity of the Poincare metric"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06818","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":"sha256:0c05a17a3ede0741814d4500e148ec5a08d4f03ef38a502a1c1a22f32a3c96a1","target":"record","created_at":"2026-05-18T01:18:34Z","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":"56de62c54dab8a77faddab6fb6c8dcabe40d2c050c0b4cc909d9c46bc2c6317f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2016-03-22T15:07:01Z","title_canon_sha256":"3d457f1ebc23187f77b20653fbd5d8e1865323a6958c2e705bd4e59fba0f89ae"},"schema_version":"1.0","source":{"id":"1603.06818","kind":"arxiv","version":1}},"canonical_sha256":"34fbcca5e3a29f0b6e2e6b62e1b085b4098bc7d66a9aabfc427d998a412894c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34fbcca5e3a29f0b6e2e6b62e1b085b4098bc7d66a9aabfc427d998a412894c9","first_computed_at":"2026-05-18T01:18:34.634332Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:34.634332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AszXSfBzxN8tonrm2gSjCfqVCix/UoosOnzwpnyPjOAyENshC8xYwcfxuTAMIBHT+gMomHNHkHZBvXVo/MEWDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:34.634934Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06818","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0c05a17a3ede0741814d4500e148ec5a08d4f03ef38a502a1c1a22f32a3c96a1","sha256:af01f02c3bb9bc520352078f812312634a5b2edcc16fd7d880bb55443093f9b7"],"state_sha256":"a9ef1ff4071280dfe65304af5976faad5885ffd7a0e5d6d29b77da29986396ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g43gvgHlkURF31HuCyFuSTrz/3iigLsMNwaXlfWsbkkerFZ2qWGMtaRUsrvMytUl2sfNl3461F57aAgb+yW+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:55:02.288368Z","bundle_sha256":"fe044370c9ffa049b13bcdb882a4506687d8f0f4baeffa6e4a218aba348d4233"}}