{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:T63UKJEKUGOPBASKP5S7O7GYXP","short_pith_number":"pith:T63UKJEK","canonical_record":{"source":{"id":"1509.01455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-09-04T14:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"f7a9fce3c6e55fecffbb451fe505c3c0af17db6e23428ef1ed499cae62ab716a","abstract_canon_sha256":"b7c0cfa436580115224ad80d14fd006db553eb0926d981df615c03cf3146afb1"},"schema_version":"1.0"},"canonical_sha256":"9fb745248aa19cf0824a7f65f77cd8bbe8952c8f16592fdd3d00a51fe68bb4ef","source":{"kind":"arxiv","id":"1509.01455","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01455","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01455v1","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01455","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"T63UKJEKUGOP","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T63UKJEKUGOPBASK","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T63UKJEK","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:T63UKJEKUGOPBASKP5S7O7GYXP","target":"record","payload":{"canonical_record":{"source":{"id":"1509.01455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-09-04T14:03:00Z","cross_cats_sorted":[],"title_canon_sha256":"f7a9fce3c6e55fecffbb451fe505c3c0af17db6e23428ef1ed499cae62ab716a","abstract_canon_sha256":"b7c0cfa436580115224ad80d14fd006db553eb0926d981df615c03cf3146afb1"},"schema_version":"1.0"},"canonical_sha256":"9fb745248aa19cf0824a7f65f77cd8bbe8952c8f16592fdd3d00a51fe68bb4ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:57.652832Z","signature_b64":"WYeHXXazPBZRha0vxQ3wc2tPMupQGYF68GrBFrjJwShoZQK0GSbNPXjf5p5JHQI6aFM73fBn1x2FWWeSbBY5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fb745248aa19cf0824a7f65f77cd8bbe8952c8f16592fdd3d00a51fe68bb4ef","last_reissued_at":"2026-05-18T01:33:57.652456Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:57.652456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.01455","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":"2026-05-18T01:33:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SXKqUoCympxolLq5BnUEkFb8Tyvc8l4I5Wt2S7l/4d57IlSwqCxJVVduhYoHjQW0/QzmhyKkOnk6bRjQ59g/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:33:14.922665Z"},"content_sha256":"8953068953247d2a4dd3c5b62bb42393688084034d4546dca02cc739e7133254","schema_version":"1.0","event_id":"sha256:8953068953247d2a4dd3c5b62bb42393688084034d4546dca02cc739e7133254"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:T63UKJEKUGOPBASKP5S7O7GYXP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\mathcal{N}_p$-type functions with Hadamard gaps in the unit ball","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Bingyang Hu, Songxiao Li","submitted_at":"2015-09-04T14:03:00Z","abstract_excerpt":"We study the holomorphic functions with Hadamard gaps in $\\mathcal{N}_p$-spaces on the unit ball of $\\mathbb{C}^n$ when $0<p \\le n$ and $p>n$. A corollary on analytic functions with Hadamard gaps on $\\mathcal{N}_p$-spaces on the unit disk is also given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01455","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":"2026-05-18T01:33:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8kTiLtpkzBqVmQUUkeDg3GI522UsJ71jOuZl8Rr4uFnvXYEjNwnFMlUVN7KnJI2+tiO9LW4bCbMJH0Q7szBZAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T06:33:14.923031Z"},"content_sha256":"0c50cf5fb79660e2fb6190610f656f442488725d9c2a1ecb5e6cac44c94b1909","schema_version":"1.0","event_id":"sha256:0c50cf5fb79660e2fb6190610f656f442488725d9c2a1ecb5e6cac44c94b1909"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T63UKJEKUGOPBASKP5S7O7GYXP/bundle.json","state_url":"https://pith.science/pith/T63UKJEKUGOPBASKP5S7O7GYXP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T63UKJEKUGOPBASKP5S7O7GYXP/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":"2026-05-30T06:33:14Z","links":{"resolver":"https://pith.science/pith/T63UKJEKUGOPBASKP5S7O7GYXP","bundle":"https://pith.science/pith/T63UKJEKUGOPBASKP5S7O7GYXP/bundle.json","state":"https://pith.science/pith/T63UKJEKUGOPBASKP5S7O7GYXP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T63UKJEKUGOPBASKP5S7O7GYXP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:T63UKJEKUGOPBASKP5S7O7GYXP","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":"b7c0cfa436580115224ad80d14fd006db553eb0926d981df615c03cf3146afb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-09-04T14:03:00Z","title_canon_sha256":"f7a9fce3c6e55fecffbb451fe505c3c0af17db6e23428ef1ed499cae62ab716a"},"schema_version":"1.0","source":{"id":"1509.01455","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.01455","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"arxiv_version","alias_value":"1509.01455v1","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.01455","created_at":"2026-05-18T01:33:57Z"},{"alias_kind":"pith_short_12","alias_value":"T63UKJEKUGOP","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"T63UKJEKUGOPBASK","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"T63UKJEK","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:0c50cf5fb79660e2fb6190610f656f442488725d9c2a1ecb5e6cac44c94b1909","target":"graph","created_at":"2026-05-18T01:33:57Z","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":"We study the holomorphic functions with Hadamard gaps in $\\mathcal{N}_p$-spaces on the unit ball of $\\mathbb{C}^n$ when $0<p \\le n$ and $p>n$. A corollary on analytic functions with Hadamard gaps on $\\mathcal{N}_p$-spaces on the unit disk is also given.","authors_text":"Bingyang Hu, Songxiao Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-09-04T14:03:00Z","title":"$\\mathcal{N}_p$-type functions with Hadamard gaps in the unit ball"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.01455","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":"sha256:8953068953247d2a4dd3c5b62bb42393688084034d4546dca02cc739e7133254","target":"record","created_at":"2026-05-18T01:33:57Z","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":"b7c0cfa436580115224ad80d14fd006db553eb0926d981df615c03cf3146afb1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-09-04T14:03:00Z","title_canon_sha256":"f7a9fce3c6e55fecffbb451fe505c3c0af17db6e23428ef1ed499cae62ab716a"},"schema_version":"1.0","source":{"id":"1509.01455","kind":"arxiv","version":1}},"canonical_sha256":"9fb745248aa19cf0824a7f65f77cd8bbe8952c8f16592fdd3d00a51fe68bb4ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fb745248aa19cf0824a7f65f77cd8bbe8952c8f16592fdd3d00a51fe68bb4ef","first_computed_at":"2026-05-18T01:33:57.652456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:57.652456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WYeHXXazPBZRha0vxQ3wc2tPMupQGYF68GrBFrjJwShoZQK0GSbNPXjf5p5JHQI6aFM73fBn1x2FWWeSbBY5AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:57.652832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.01455","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8953068953247d2a4dd3c5b62bb42393688084034d4546dca02cc739e7133254","sha256:0c50cf5fb79660e2fb6190610f656f442488725d9c2a1ecb5e6cac44c94b1909"],"state_sha256":"7021be8408088422e6c6f5b7829f01952e13c767834db075553b76aa88598f43"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RP/uwqF3NcGCqLtTQAROyEpMUgNmeortgdJHFEfDsY837qXrquXGvfvf3js9kEwRun8jtzcoF6ZkYcAGhBs2Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T06:33:14.928873Z","bundle_sha256":"eec4436caa2ceb5b63cee25f16b30ef4d31bf13fafee2381f0649f7a0081a14b"}}