{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UJCCNLLMA3YDRJEMFV3P2WYOVS","short_pith_number":"pith:UJCCNLLM","canonical_record":{"source":{"id":"1404.3352","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-04-13T07:29:52Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"37e7b0ae13026aeafe3caedc33d838754d10a5877e0087a9ebefdaa1c0d283fe","abstract_canon_sha256":"b1238a58ce651ad1af4790e377683ec04bde6a7eac75cf88d1188a4d7d24b1c0"},"schema_version":"1.0"},"canonical_sha256":"a24426ad6c06f038a48c2d76fd5b0eac9121a625eea6c8e9098a1654b6743db1","source":{"kind":"arxiv","id":"1404.3352","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3352","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3352v2","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3352","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"UJCCNLLMA3YD","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UJCCNLLMA3YDRJEM","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UJCCNLLM","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UJCCNLLMA3YDRJEMFV3P2WYOVS","target":"record","payload":{"canonical_record":{"source":{"id":"1404.3352","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-04-13T07:29:52Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"37e7b0ae13026aeafe3caedc33d838754d10a5877e0087a9ebefdaa1c0d283fe","abstract_canon_sha256":"b1238a58ce651ad1af4790e377683ec04bde6a7eac75cf88d1188a4d7d24b1c0"},"schema_version":"1.0"},"canonical_sha256":"a24426ad6c06f038a48c2d76fd5b0eac9121a625eea6c8e9098a1654b6743db1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:07.962192Z","signature_b64":"ShCYZtqEMWTEDdTc7hJ7RvbdYSfHbMogDhMsueZwdeEm6X05ZF0w/mzMpR0fUSA2hy9WXZJzSiqe/pdYOQPBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a24426ad6c06f038a48c2d76fd5b0eac9121a625eea6c8e9098a1654b6743db1","last_reissued_at":"2026-05-18T02:51:07.961807Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:07.961807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.3352","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:51:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1qz7iTS/UR2jPM6EaoU3QTSteFOhg/GvP98rCRVaG4h9rbsnVuGlTAtcZZV/uxhmDvtTbmfTc6pR6nlxtCEFCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:36:59.776590Z"},"content_sha256":"9d95989d631c69bec4dcd744b3f9b20bc49bc78b99fa9ad697932116a74fb2df","schema_version":"1.0","event_id":"sha256:9d95989d631c69bec4dcd744b3f9b20bc49bc78b99fa9ad697932116a74fb2df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UJCCNLLMA3YDRJEMFV3P2WYOVS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Boundary interpolation for slice hyperholomorphic Schur functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CV","authors_text":"D. Alpay, D. P. Kimsey, F. Colombo, I. Sabadini, K. Abu-Ghanem","submitted_at":"2014-04-13T07:29:52Z","abstract_excerpt":"A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers $\\kappa_1, \\ldots, \\kappa_N$, quaternions $p_1, \\ldots, p_N$ all of modulus $1$, so that the $2$-spheres determined by each point do not intersect and $p_u \\neq 1$ for $u = 1,\\ldots, N$, and quaternions $s_1, \\ldots, s_N$, we wish to find a slice hyperholomorphic Schur function $s$ so that $$\\lim_{\\substack{r\\rightarrow 1\\\\ r\\in(0,1)}} s(r p_u) = s_u\\quad {\\rm for} \\quad u=1,\\ldots, N,$$ and $$\\lim_{\\substack{r\\rightarrow 1\\\\ r\\in(0,1)}}\\frac{1-s(rp_u)\\overline{s_u}}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3352","kind":"arxiv","version":2},"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":"2026-05-18T02:51:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d5yVEyz0vMayd+8Fso64KsDVbau6/XEt9PcAxLA3wwaD80Nt3vkgnPPg2lmTHEeqiaf2qS797ddZrGlqNwDTBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T07:36:59.776936Z"},"content_sha256":"54359d95c43b631a8aa6b40ee09008e72c8974aa4c4555fb1b10de5449c8efd5","schema_version":"1.0","event_id":"sha256:54359d95c43b631a8aa6b40ee09008e72c8974aa4c4555fb1b10de5449c8efd5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UJCCNLLMA3YDRJEMFV3P2WYOVS/bundle.json","state_url":"https://pith.science/pith/UJCCNLLMA3YDRJEMFV3P2WYOVS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UJCCNLLMA3YDRJEMFV3P2WYOVS/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":"2026-05-30T07:36:59Z","links":{"resolver":"https://pith.science/pith/UJCCNLLMA3YDRJEMFV3P2WYOVS","bundle":"https://pith.science/pith/UJCCNLLMA3YDRJEMFV3P2WYOVS/bundle.json","state":"https://pith.science/pith/UJCCNLLMA3YDRJEMFV3P2WYOVS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UJCCNLLMA3YDRJEMFV3P2WYOVS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UJCCNLLMA3YDRJEMFV3P2WYOVS","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":"b1238a58ce651ad1af4790e377683ec04bde6a7eac75cf88d1188a4d7d24b1c0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-04-13T07:29:52Z","title_canon_sha256":"37e7b0ae13026aeafe3caedc33d838754d10a5877e0087a9ebefdaa1c0d283fe"},"schema_version":"1.0","source":{"id":"1404.3352","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3352","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3352v2","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3352","created_at":"2026-05-18T02:51:07Z"},{"alias_kind":"pith_short_12","alias_value":"UJCCNLLMA3YD","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UJCCNLLMA3YDRJEM","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UJCCNLLM","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:54359d95c43b631a8aa6b40ee09008e72c8974aa4c4555fb1b10de5449c8efd5","target":"graph","created_at":"2026-05-18T02:51:07Z","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":"A boundary Nevanlinna-Pick interpolation problem is posed and solved in the quaternionic setting. Given nonnegative real numbers $\\kappa_1, \\ldots, \\kappa_N$, quaternions $p_1, \\ldots, p_N$ all of modulus $1$, so that the $2$-spheres determined by each point do not intersect and $p_u \\neq 1$ for $u = 1,\\ldots, N$, and quaternions $s_1, \\ldots, s_N$, we wish to find a slice hyperholomorphic Schur function $s$ so that $$\\lim_{\\substack{r\\rightarrow 1\\\\ r\\in(0,1)}} s(r p_u) = s_u\\quad {\\rm for} \\quad u=1,\\ldots, N,$$ and $$\\lim_{\\substack{r\\rightarrow 1\\\\ r\\in(0,1)}}\\frac{1-s(rp_u)\\overline{s_u}}","authors_text":"D. Alpay, D. P. Kimsey, F. Colombo, I. Sabadini, K. Abu-Ghanem","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-04-13T07:29:52Z","title":"Boundary interpolation for slice hyperholomorphic Schur functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3352","kind":"arxiv","version":2},"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":"sha256:9d95989d631c69bec4dcd744b3f9b20bc49bc78b99fa9ad697932116a74fb2df","target":"record","created_at":"2026-05-18T02:51:07Z","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":"b1238a58ce651ad1af4790e377683ec04bde6a7eac75cf88d1188a4d7d24b1c0","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2014-04-13T07:29:52Z","title_canon_sha256":"37e7b0ae13026aeafe3caedc33d838754d10a5877e0087a9ebefdaa1c0d283fe"},"schema_version":"1.0","source":{"id":"1404.3352","kind":"arxiv","version":2}},"canonical_sha256":"a24426ad6c06f038a48c2d76fd5b0eac9121a625eea6c8e9098a1654b6743db1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a24426ad6c06f038a48c2d76fd5b0eac9121a625eea6c8e9098a1654b6743db1","first_computed_at":"2026-05-18T02:51:07.961807Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:07.961807Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ShCYZtqEMWTEDdTc7hJ7RvbdYSfHbMogDhMsueZwdeEm6X05ZF0w/mzMpR0fUSA2hy9WXZJzSiqe/pdYOQPBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:07.962192Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.3352","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d95989d631c69bec4dcd744b3f9b20bc49bc78b99fa9ad697932116a74fb2df","sha256:54359d95c43b631a8aa6b40ee09008e72c8974aa4c4555fb1b10de5449c8efd5"],"state_sha256":"bc73e045dca0228a3e738f5126bd3b02c8a6394c7a60d4ba62e4600da383f3a2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K/O8LEosdPb9USs5Gy+JuN47NzuQG5AU58+B31CWVAPRymrUm3fmiVtTHt/UNaMaTc2koSy+uZObjKRVTtddCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T07:36:59.779117Z","bundle_sha256":"455a799f86fb71223b5cc9a8ac00623a262115bfb7b370bc7c8b6a2c85234e07"}}