{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SPPVAZJZZNL3A5UOCAIBUN7YX5","short_pith_number":"pith:SPPVAZJZ","canonical_record":{"source":{"id":"1501.04545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-19T16:37:53Z","cross_cats_sorted":[],"title_canon_sha256":"d2a52758f2b649a4eff84c3d0dd0d87c18de209172393cae20b7cc439a1aaab1","abstract_canon_sha256":"bee387c0d910867f3d617a9d95bd742fca986fba5e5dfc236aa0f9f3653d9b91"},"schema_version":"1.0"},"canonical_sha256":"93df506539cb57b0768e10101a37f8bf69d743662c8d828c1a2df3194e42e3e1","source":{"kind":"arxiv","id":"1501.04545","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04545","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04545v1","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04545","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"pith_short_12","alias_value":"SPPVAZJZZNL3","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SPPVAZJZZNL3A5UO","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SPPVAZJZ","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SPPVAZJZZNL3A5UOCAIBUN7YX5","target":"record","payload":{"canonical_record":{"source":{"id":"1501.04545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-19T16:37:53Z","cross_cats_sorted":[],"title_canon_sha256":"d2a52758f2b649a4eff84c3d0dd0d87c18de209172393cae20b7cc439a1aaab1","abstract_canon_sha256":"bee387c0d910867f3d617a9d95bd742fca986fba5e5dfc236aa0f9f3653d9b91"},"schema_version":"1.0"},"canonical_sha256":"93df506539cb57b0768e10101a37f8bf69d743662c8d828c1a2df3194e42e3e1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:08.763939Z","signature_b64":"QkKooP5L0Lem0uA55vnFcrX3DuyffRNT/ZkAoBShhZsovPcVY61scUjyQEnkHw2pLoey9jM+sKBlESS1EM0TBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93df506539cb57b0768e10101a37f8bf69d743662c8d828c1a2df3194e42e3e1","last_reissued_at":"2026-05-18T02:29:08.763344Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:08.763344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.04545","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":"2026-05-18T02:29:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"29b9WL86AvDgPyMGfZnVyszJc73gIezekHSSkq1PGhRWC0XEFPgWM7EBz6ecuVgjiktHsigmwJodDgsrDZaaDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:03:17.452803Z"},"content_sha256":"2245607170951d54e6bdfb69eae42e6f134868346f3c3ecaa04fe8ccdcc66b95","schema_version":"1.0","event_id":"sha256:2245607170951d54e6bdfb69eae42e6f134868346f3c3ecaa04fe8ccdcc66b95"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SPPVAZJZZNL3A5UOCAIBUN7YX5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chordal generators and the hydrodynamic normalization for the unit ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Sebastian Schleissinger","submitted_at":"2015-01-19T16:37:53Z","abstract_excerpt":"Let $c\\geq0$ and denote by $\\mathcal{K}(\\mathbb{H},c)$ the set of all infinitesimal generators $G:\\mathbb{H}\\to\\mathbb{C}$ on the upper half-plane $\\mathbb{H}$ such that $\\limsup_{y\\to\\infty}y\\cdot |G(iy)|\\leq c.$ This class is related to univalent functions $f:\\mathbb{H}\\to\\mathbb{H}$ with hydrodynamic normalization and appears in the so called chordal Loewner equation. In this paper, we generalize the class $\\mathcal{K}(\\mathbb{H},c)$ and the hydrodynamic normalization to the Euclidean unit ball in $\\mathbb{C}^n$. The generalization is based on the observation that $G\\in\\mathcal{K}(\\mathbb{H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04545","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":"2026-05-18T02:29:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fAXYu0ov6yLVT7aMw5sMT9gKeUUx2Hr0KlCHVvt3KGjdeShq4Ro6gRFvFV/BSY2dLbCH8MC9XObnjL49ge8ADQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T20:03:17.453147Z"},"content_sha256":"ff9c00f7317c4e71a6a18f3c2d8fa3db78549de6955c328695c3a186e59112ed","schema_version":"1.0","event_id":"sha256:ff9c00f7317c4e71a6a18f3c2d8fa3db78549de6955c328695c3a186e59112ed"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SPPVAZJZZNL3A5UOCAIBUN7YX5/bundle.json","state_url":"https://pith.science/pith/SPPVAZJZZNL3A5UOCAIBUN7YX5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SPPVAZJZZNL3A5UOCAIBUN7YX5/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":"2026-06-02T20:03:17Z","links":{"resolver":"https://pith.science/pith/SPPVAZJZZNL3A5UOCAIBUN7YX5","bundle":"https://pith.science/pith/SPPVAZJZZNL3A5UOCAIBUN7YX5/bundle.json","state":"https://pith.science/pith/SPPVAZJZZNL3A5UOCAIBUN7YX5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SPPVAZJZZNL3A5UOCAIBUN7YX5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SPPVAZJZZNL3A5UOCAIBUN7YX5","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":"bee387c0d910867f3d617a9d95bd742fca986fba5e5dfc236aa0f9f3653d9b91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-19T16:37:53Z","title_canon_sha256":"d2a52758f2b649a4eff84c3d0dd0d87c18de209172393cae20b7cc439a1aaab1"},"schema_version":"1.0","source":{"id":"1501.04545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04545","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04545v1","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04545","created_at":"2026-05-18T02:29:08Z"},{"alias_kind":"pith_short_12","alias_value":"SPPVAZJZZNL3","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SPPVAZJZZNL3A5UO","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SPPVAZJZ","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:ff9c00f7317c4e71a6a18f3c2d8fa3db78549de6955c328695c3a186e59112ed","target":"graph","created_at":"2026-05-18T02:29:08Z","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":"Let $c\\geq0$ and denote by $\\mathcal{K}(\\mathbb{H},c)$ the set of all infinitesimal generators $G:\\mathbb{H}\\to\\mathbb{C}$ on the upper half-plane $\\mathbb{H}$ such that $\\limsup_{y\\to\\infty}y\\cdot |G(iy)|\\leq c.$ This class is related to univalent functions $f:\\mathbb{H}\\to\\mathbb{H}$ with hydrodynamic normalization and appears in the so called chordal Loewner equation. In this paper, we generalize the class $\\mathcal{K}(\\mathbb{H},c)$ and the hydrodynamic normalization to the Euclidean unit ball in $\\mathbb{C}^n$. The generalization is based on the observation that $G\\in\\mathcal{K}(\\mathbb{H","authors_text":"Sebastian Schleissinger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-19T16:37:53Z","title":"Chordal generators and the hydrodynamic normalization for the unit ball"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04545","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":"sha256:2245607170951d54e6bdfb69eae42e6f134868346f3c3ecaa04fe8ccdcc66b95","target":"record","created_at":"2026-05-18T02:29:08Z","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":"bee387c0d910867f3d617a9d95bd742fca986fba5e5dfc236aa0f9f3653d9b91","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-01-19T16:37:53Z","title_canon_sha256":"d2a52758f2b649a4eff84c3d0dd0d87c18de209172393cae20b7cc439a1aaab1"},"schema_version":"1.0","source":{"id":"1501.04545","kind":"arxiv","version":1}},"canonical_sha256":"93df506539cb57b0768e10101a37f8bf69d743662c8d828c1a2df3194e42e3e1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93df506539cb57b0768e10101a37f8bf69d743662c8d828c1a2df3194e42e3e1","first_computed_at":"2026-05-18T02:29:08.763344Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:08.763344Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QkKooP5L0Lem0uA55vnFcrX3DuyffRNT/ZkAoBShhZsovPcVY61scUjyQEnkHw2pLoey9jM+sKBlESS1EM0TBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:08.763939Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2245607170951d54e6bdfb69eae42e6f134868346f3c3ecaa04fe8ccdcc66b95","sha256:ff9c00f7317c4e71a6a18f3c2d8fa3db78549de6955c328695c3a186e59112ed"],"state_sha256":"9bfb62654ec188f34b5acc982e2119c59b4521fc090378009216ad03b3dc6d9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WvyvtCo18W3p8uwHFIIKiANDb/hoGkIuKGIsrNGsyJ3eAZbt/RcCRoy80nfoMP6N4SLBg4PZPJiQ/8hccnf4AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T20:03:17.455179Z","bundle_sha256":"72eabea9f2761a35bb2059ce706acf7bbf2fe1a36103e3f575ac67c42c493fed"}}