{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:S26AGINOW5A2NOH4REEBSROC2S","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":"88f62c670bccd85f2755b98023af9346819db3ed32324b02a7f6130a20805fa7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-01-14T14:21:36Z","title_canon_sha256":"6c1a5c2c6437d97bf9f86df965e14d5fb4e3e177df6b7d26bcd2f7ec4f217bf1"},"schema_version":"1.0","source":{"id":"1801.07099","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.07099","created_at":"2026-05-18T00:25:22Z"},{"alias_kind":"arxiv_version","alias_value":"1801.07099v1","created_at":"2026-05-18T00:25:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.07099","created_at":"2026-05-18T00:25:22Z"},{"alias_kind":"pith_short_12","alias_value":"S26AGINOW5A2","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S26AGINOW5A2NOH4","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S26AGINO","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:32225ead828c3d1c86e78cff613ce00ced439a1b562c7a61fdae32d07cd7d6a4","target":"graph","created_at":"2026-05-18T00:25:22Z","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":"Given a finitely-connected bounded planar domain $\\Omega$, it is possible to define a {\\it divergence distance} $D(x,y)$ from $x\\in\\Omega$ to $y\\in\\Omega$, which takes into account the complex geometry of the domain. This distance function is based on the concept of $f$-divergence, a distance measure traditionally used to measure the difference between two probability distributions. The relevant probability distributions in our case are the Poisson kernels of the domain at $x$ and at $y$. We prove that for the $\\chi^2$-divergence distance, the gradient by $x$ of $D$ is opposite in direction to","authors_text":"Craig Gotsman, Kai Hormann, Renjie Chen","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-01-14T14:21:36Z","title":"On Divergence-based Distance Functions for Multiply-connected Domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.07099","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:e591f08eef00be4fc8b147fb492cb8a5aa44828ab8428a0e2cd8e32099eaf8e9","target":"record","created_at":"2026-05-18T00:25:22Z","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":"88f62c670bccd85f2755b98023af9346819db3ed32324b02a7f6130a20805fa7","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2018-01-14T14:21:36Z","title_canon_sha256":"6c1a5c2c6437d97bf9f86df965e14d5fb4e3e177df6b7d26bcd2f7ec4f217bf1"},"schema_version":"1.0","source":{"id":"1801.07099","kind":"arxiv","version":1}},"canonical_sha256":"96bc0321aeb741a6b8fc89081945c2d4bcbe7e7e1b04d6a45c336d4c8c5caad7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96bc0321aeb741a6b8fc89081945c2d4bcbe7e7e1b04d6a45c336d4c8c5caad7","first_computed_at":"2026-05-18T00:25:22.269501Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:22.269501Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O01u13iExA1HUR/t/87P9meD7T2RKUwhVGCRYutoZFOEH5Glhx3TsBS3DIhlyKGHBwuO9dDA+b4ewViEn/sMBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:22.270030Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.07099","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e591f08eef00be4fc8b147fb492cb8a5aa44828ab8428a0e2cd8e32099eaf8e9","sha256:32225ead828c3d1c86e78cff613ce00ced439a1b562c7a61fdae32d07cd7d6a4"],"state_sha256":"ab184a09b4d8432c13e1e2ea2e05c4ebafe09ee41abd5e5cf99e257a67312110"}