{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:FZX35MZHBLJFRE6CO7TNWWNTP7","short_pith_number":"pith:FZX35MZH","canonical_record":{"source":{"id":"1209.2060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-10T16:59:22Z","cross_cats_sorted":[],"title_canon_sha256":"ac14710245973a4b7dda9d54d68a6a9e927b951465c653fa0ca6d7fc1da055fc","abstract_canon_sha256":"4af3c39ed0758ff603ce0c583cf8a3bb8f9acf2dc87d766074a072b6d9cc7480"},"schema_version":"1.0"},"canonical_sha256":"2e6fbeb3270ad25893c277e6db59b37fd83ad954c3a88dcf64b8b1f3b4c580fd","source":{"kind":"arxiv","id":"1209.2060","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2060","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2060v1","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2060","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"pith_short_12","alias_value":"FZX35MZHBLJF","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FZX35MZHBLJFRE6C","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FZX35MZH","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:FZX35MZHBLJFRE6CO7TNWWNTP7","target":"record","payload":{"canonical_record":{"source":{"id":"1209.2060","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-10T16:59:22Z","cross_cats_sorted":[],"title_canon_sha256":"ac14710245973a4b7dda9d54d68a6a9e927b951465c653fa0ca6d7fc1da055fc","abstract_canon_sha256":"4af3c39ed0758ff603ce0c583cf8a3bb8f9acf2dc87d766074a072b6d9cc7480"},"schema_version":"1.0"},"canonical_sha256":"2e6fbeb3270ad25893c277e6db59b37fd83ad954c3a88dcf64b8b1f3b4c580fd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:34:02.936705Z","signature_b64":"jbhpoRsDcxHHLe+9aPJ52MF7kbLW9Y546yrMvwg+BG66tonqqBnX95G567WQZD90l52MdQQS5U1FkOsdMlToDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e6fbeb3270ad25893c277e6db59b37fd83ad954c3a88dcf64b8b1f3b4c580fd","last_reissued_at":"2026-05-18T03:34:02.936088Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:34:02.936088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.2060","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":"2026-05-18T03:34:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G8mZKAn6QGR347B1F0+DcjacEBarEVBRTGP5ERQerUE9rAh8vECAafwF4L0umruZcVYsQKmVqKcjOtnhbVuXCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:38:44.604957Z"},"content_sha256":"d9aa6cc02f9f48ec7cce6dfead23f3e77cad364571ee5f73ead6ee32fe1fabf8","schema_version":"1.0","event_id":"sha256:d9aa6cc02f9f48ec7cce6dfead23f3e77cad364571ee5f73ead6ee32fe1fabf8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:FZX35MZHBLJFRE6CO7TNWWNTP7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Schwarz-Pick lemma for slice regular functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Caterina Stoppato, Cinzia Bisi","submitted_at":"2012-09-10T16:59:22Z","abstract_excerpt":"The celebrated Schwarz-Pick lemma for the complex unit disk is the basis for the study of hyperbolic geometry in one and in several complex variables. In the present paper, we turn our attention to the quaternionic unit ball B. We prove a version of the Schwarz-Pick lemma for self-maps of B that are slice regular, according to the definition of Gentili and Struppa. The lemma has interesting applications in the fixed-point case, and it generalizes to the case of vanishing higher order derivatives."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2060","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":"2026-05-18T03:34:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B/pnHIkg76ygnZYzbcZdDEtL4WVvGPrCWy49gaVIliQk3G3OMrWiWbUg0S9/XxdRQMjtEki7x2s23WkUizgJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T12:38:44.605437Z"},"content_sha256":"3abe94b51161d993fec9e08f55a0fba82e18ea7272fe0162ec6781122fc50df4","schema_version":"1.0","event_id":"sha256:3abe94b51161d993fec9e08f55a0fba82e18ea7272fe0162ec6781122fc50df4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FZX35MZHBLJFRE6CO7TNWWNTP7/bundle.json","state_url":"https://pith.science/pith/FZX35MZHBLJFRE6CO7TNWWNTP7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FZX35MZHBLJFRE6CO7TNWWNTP7/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":"2026-06-23T12:38:44Z","links":{"resolver":"https://pith.science/pith/FZX35MZHBLJFRE6CO7TNWWNTP7","bundle":"https://pith.science/pith/FZX35MZHBLJFRE6CO7TNWWNTP7/bundle.json","state":"https://pith.science/pith/FZX35MZHBLJFRE6CO7TNWWNTP7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FZX35MZHBLJFRE6CO7TNWWNTP7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FZX35MZHBLJFRE6CO7TNWWNTP7","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":"4af3c39ed0758ff603ce0c583cf8a3bb8f9acf2dc87d766074a072b6d9cc7480","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-10T16:59:22Z","title_canon_sha256":"ac14710245973a4b7dda9d54d68a6a9e927b951465c653fa0ca6d7fc1da055fc"},"schema_version":"1.0","source":{"id":"1209.2060","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2060","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2060v1","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2060","created_at":"2026-05-18T03:34:02Z"},{"alias_kind":"pith_short_12","alias_value":"FZX35MZHBLJF","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FZX35MZHBLJFRE6C","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FZX35MZH","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:3abe94b51161d993fec9e08f55a0fba82e18ea7272fe0162ec6781122fc50df4","target":"graph","created_at":"2026-05-18T03:34:02Z","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":"The celebrated Schwarz-Pick lemma for the complex unit disk is the basis for the study of hyperbolic geometry in one and in several complex variables. In the present paper, we turn our attention to the quaternionic unit ball B. We prove a version of the Schwarz-Pick lemma for self-maps of B that are slice regular, according to the definition of Gentili and Struppa. The lemma has interesting applications in the fixed-point case, and it generalizes to the case of vanishing higher order derivatives.","authors_text":"Caterina Stoppato, Cinzia Bisi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-10T16:59:22Z","title":"The Schwarz-Pick lemma for slice regular functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2060","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:d9aa6cc02f9f48ec7cce6dfead23f3e77cad364571ee5f73ead6ee32fe1fabf8","target":"record","created_at":"2026-05-18T03:34:02Z","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":"4af3c39ed0758ff603ce0c583cf8a3bb8f9acf2dc87d766074a072b6d9cc7480","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-09-10T16:59:22Z","title_canon_sha256":"ac14710245973a4b7dda9d54d68a6a9e927b951465c653fa0ca6d7fc1da055fc"},"schema_version":"1.0","source":{"id":"1209.2060","kind":"arxiv","version":1}},"canonical_sha256":"2e6fbeb3270ad25893c277e6db59b37fd83ad954c3a88dcf64b8b1f3b4c580fd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e6fbeb3270ad25893c277e6db59b37fd83ad954c3a88dcf64b8b1f3b4c580fd","first_computed_at":"2026-05-18T03:34:02.936088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:34:02.936088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jbhpoRsDcxHHLe+9aPJ52MF7kbLW9Y546yrMvwg+BG66tonqqBnX95G567WQZD90l52MdQQS5U1FkOsdMlToDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:34:02.936705Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2060","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d9aa6cc02f9f48ec7cce6dfead23f3e77cad364571ee5f73ead6ee32fe1fabf8","sha256:3abe94b51161d993fec9e08f55a0fba82e18ea7272fe0162ec6781122fc50df4"],"state_sha256":"fae85dbb31c895671fa2593c4b46a3536e0f275c8e230365002bfe06a808c458"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B6bXJWw1mkl7C0TUYIujcMVuSL1K/cYGoVV/Q7FEB6c1J9UzMhEJlS0za01XKZQjK7xiH0ItmvSsLhtJoNDWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T12:38:44.607891Z","bundle_sha256":"3b0ffd09e2fe7d146a243ca0565c172ce7825dca410f83a0a3f76657048f70aa"}}