{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AJLEHVF7R22USE3DK7EHPJ2TCZ","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":"d0e5b3d529cdcecefdd0490173995e8d8aeac745b158d19542cfbb75aeb6adc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-05-26T16:03:29Z","title_canon_sha256":"a0463e9c9c1a1681971ff5c0b3c905e3c782ebb51515f70bdc736a0f7a33ac8c"},"schema_version":"1.0","source":{"id":"2605.27213","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.27213","created_at":"2026-05-27T02:05:48Z"},{"alias_kind":"arxiv_version","alias_value":"2605.27213v1","created_at":"2026-05-27T02:05:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.27213","created_at":"2026-05-27T02:05:48Z"},{"alias_kind":"pith_short_12","alias_value":"AJLEHVF7R22U","created_at":"2026-05-27T02:05:48Z"},{"alias_kind":"pith_short_16","alias_value":"AJLEHVF7R22USE3D","created_at":"2026-05-27T02:05:48Z"},{"alias_kind":"pith_short_8","alias_value":"AJLEHVF7","created_at":"2026-05-27T02:05:48Z"}],"graph_snapshots":[{"event_id":"sha256:96732158f39c0bc51df161ebbce4ef29720b74794b1060c3395070225286dbfd","target":"graph","created_at":"2026-05-27T02:05:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.27213/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We define metrics in space that are natural counterparts of the hyperbolic metric in plane domains, using the characterization of the hyperbolic metric due to Beardon and Pommerenke. We obtain inequalities for these metrics under quasiconformal homeomorphisms between domains in space that have at least two boundary points. We discuss the failure of the existence of such estimates for non-homeomorphic quasiregular mappings.","authors_text":"Aimo Hinkkanen, Poranee Khayo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-05-26T16:03:29Z","title":"Hyperbolic-type metrics in space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.27213","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:dd67a9cd61faab920d6e37cdf8cc3ad80be97ee0ad96b87976ff2cfa4d758681","target":"record","created_at":"2026-05-27T02:05:48Z","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":"d0e5b3d529cdcecefdd0490173995e8d8aeac745b158d19542cfbb75aeb6adc3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2026-05-26T16:03:29Z","title_canon_sha256":"a0463e9c9c1a1681971ff5c0b3c905e3c782ebb51515f70bdc736a0f7a33ac8c"},"schema_version":"1.0","source":{"id":"2605.27213","kind":"arxiv","version":1}},"canonical_sha256":"025643d4bf8eb549136357c877a75316560190dcf5a1d9d97784402f1f0b74f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"025643d4bf8eb549136357c877a75316560190dcf5a1d9d97784402f1f0b74f0","first_computed_at":"2026-05-27T02:05:48.375022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T02:05:48.375022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uhviEOO66ngkMfWpyQN3UsEb0xqLVOqXtWxKiRCH8yhhb++lncbOTufEKKvvv+xHywiPHsUmZXsM8w3XwjDcAA==","signature_status":"signed_v1","signed_at":"2026-05-27T02:05:48.375740Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.27213","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd67a9cd61faab920d6e37cdf8cc3ad80be97ee0ad96b87976ff2cfa4d758681","sha256:96732158f39c0bc51df161ebbce4ef29720b74794b1060c3395070225286dbfd"],"state_sha256":"fe70d274afc4a0cf8045323aac41d823d9856cde4faff5f3ad104e4ea42f27e2"}