{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EDRHD3BKRQBM65BJT6YCD3GNHV","short_pith_number":"pith:EDRHD3BK","canonical_record":{"source":{"id":"1512.01757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-06T07:51:26Z","cross_cats_sorted":[],"title_canon_sha256":"3e2c2bce3d9b6c38157b525d5b00608c3bf7921b00d9b491d7f3536a85a21373","abstract_canon_sha256":"7cc70f52c05934817ed70b2298da2560731ddac7f6fe1fd515b0ecb2010c7634"},"schema_version":"1.0"},"canonical_sha256":"20e271ec2a8c02cf74299fb021eccd3d58fa3c79597f90caa55704e13a4b4a23","source":{"kind":"arxiv","id":"1512.01757","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01757","created_at":"2026-05-18T01:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01757v1","created_at":"2026-05-18T01:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01757","created_at":"2026-05-18T01:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"EDRHD3BKRQBM","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EDRHD3BKRQBM65BJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EDRHD3BK","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EDRHD3BKRQBM65BJT6YCD3GNHV","target":"record","payload":{"canonical_record":{"source":{"id":"1512.01757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-06T07:51:26Z","cross_cats_sorted":[],"title_canon_sha256":"3e2c2bce3d9b6c38157b525d5b00608c3bf7921b00d9b491d7f3536a85a21373","abstract_canon_sha256":"7cc70f52c05934817ed70b2298da2560731ddac7f6fe1fd515b0ecb2010c7634"},"schema_version":"1.0"},"canonical_sha256":"20e271ec2a8c02cf74299fb021eccd3d58fa3c79597f90caa55704e13a4b4a23","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:10.427976Z","signature_b64":"N8eYG0SwCjnnQAVtQBKw36nGvUT8fXAe8eLM7DOc/N/mYIITFUID796LslhDMPP6plK+KaV7MxPuuE1AbqxHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20e271ec2a8c02cf74299fb021eccd3d58fa3c79597f90caa55704e13a4b4a23","last_reissued_at":"2026-05-18T01:25:10.427407Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:10.427407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.01757","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":"2026-05-18T01:25:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e0fv4EGxDl/SJmfCIDFsg70vzN0AyxjPz54S1IfpmvJsy/StP1W9Nvs6Qv+0ddkVlMzwfua6R1SL5UhBLJfMBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:10:35.220629Z"},"content_sha256":"0e24697b8a51abab3216c4b064895e408731c7e66995812f486d925769bd8b8a","schema_version":"1.0","event_id":"sha256:0e24697b8a51abab3216c4b064895e408731c7e66995812f486d925769bd8b8a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EDRHD3BKRQBM65BJT6YCD3GNHV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On strongly separately continuous functions on sequence spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Olena Karlova, Tom\\'a\\v{s} Visnyai","submitted_at":"2015-12-06T07:51:26Z","abstract_excerpt":"We study strongly separately continuous real-valued function defined on the Banach spaces $\\ell_p$. Determining sets for the class of strongly separately continuous functions on $\\ell_p$ are characterized. We prove that for every $1\\le \\alpha<\\omega_1$ there exists a strongly separately continuous function which belongs the $(\\alpha+1)$'th Baire class and does not belong to the $\\alpha$'th Baire class on $\\ell_p$. We show that any open set in $\\ell_p$ is the set of discontinuities of a strongly separately continuous real-valued function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01757","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":"2026-05-18T01:25:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yegNBt4lsw5y5IjZU0tfrfBPTLuSO1teIC/3th7PV+h2z1b9eRKDhEI5cNLF1cb6icg4QGg2e8oaSkF7Si2dDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:10:35.220971Z"},"content_sha256":"a216a729363aa7eb247771d5cdee186674006ddbca60430f0dd2fc035592e2ce","schema_version":"1.0","event_id":"sha256:a216a729363aa7eb247771d5cdee186674006ddbca60430f0dd2fc035592e2ce"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EDRHD3BKRQBM65BJT6YCD3GNHV/bundle.json","state_url":"https://pith.science/pith/EDRHD3BKRQBM65BJT6YCD3GNHV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EDRHD3BKRQBM65BJT6YCD3GNHV/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":"2026-06-26T00:10:35Z","links":{"resolver":"https://pith.science/pith/EDRHD3BKRQBM65BJT6YCD3GNHV","bundle":"https://pith.science/pith/EDRHD3BKRQBM65BJT6YCD3GNHV/bundle.json","state":"https://pith.science/pith/EDRHD3BKRQBM65BJT6YCD3GNHV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EDRHD3BKRQBM65BJT6YCD3GNHV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EDRHD3BKRQBM65BJT6YCD3GNHV","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":"7cc70f52c05934817ed70b2298da2560731ddac7f6fe1fd515b0ecb2010c7634","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-06T07:51:26Z","title_canon_sha256":"3e2c2bce3d9b6c38157b525d5b00608c3bf7921b00d9b491d7f3536a85a21373"},"schema_version":"1.0","source":{"id":"1512.01757","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.01757","created_at":"2026-05-18T01:25:10Z"},{"alias_kind":"arxiv_version","alias_value":"1512.01757v1","created_at":"2026-05-18T01:25:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.01757","created_at":"2026-05-18T01:25:10Z"},{"alias_kind":"pith_short_12","alias_value":"EDRHD3BKRQBM","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EDRHD3BKRQBM65BJ","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EDRHD3BK","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:a216a729363aa7eb247771d5cdee186674006ddbca60430f0dd2fc035592e2ce","target":"graph","created_at":"2026-05-18T01:25:10Z","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 strongly separately continuous real-valued function defined on the Banach spaces $\\ell_p$. Determining sets for the class of strongly separately continuous functions on $\\ell_p$ are characterized. We prove that for every $1\\le \\alpha<\\omega_1$ there exists a strongly separately continuous function which belongs the $(\\alpha+1)$'th Baire class and does not belong to the $\\alpha$'th Baire class on $\\ell_p$. We show that any open set in $\\ell_p$ is the set of discontinuities of a strongly separately continuous real-valued function.","authors_text":"Olena Karlova, Tom\\'a\\v{s} Visnyai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-06T07:51:26Z","title":"On strongly separately continuous functions on sequence spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01757","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":"sha256:0e24697b8a51abab3216c4b064895e408731c7e66995812f486d925769bd8b8a","target":"record","created_at":"2026-05-18T01:25:10Z","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":"7cc70f52c05934817ed70b2298da2560731ddac7f6fe1fd515b0ecb2010c7634","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2015-12-06T07:51:26Z","title_canon_sha256":"3e2c2bce3d9b6c38157b525d5b00608c3bf7921b00d9b491d7f3536a85a21373"},"schema_version":"1.0","source":{"id":"1512.01757","kind":"arxiv","version":1}},"canonical_sha256":"20e271ec2a8c02cf74299fb021eccd3d58fa3c79597f90caa55704e13a4b4a23","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20e271ec2a8c02cf74299fb021eccd3d58fa3c79597f90caa55704e13a4b4a23","first_computed_at":"2026-05-18T01:25:10.427407Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:10.427407Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N8eYG0SwCjnnQAVtQBKw36nGvUT8fXAe8eLM7DOc/N/mYIITFUID796LslhDMPP6plK+KaV7MxPuuE1AbqxHCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:10.427976Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.01757","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e24697b8a51abab3216c4b064895e408731c7e66995812f486d925769bd8b8a","sha256:a216a729363aa7eb247771d5cdee186674006ddbca60430f0dd2fc035592e2ce"],"state_sha256":"cb639e348e2b7263c4479634ff6d5f7b162be9b628c39f3a1bb52c9016da6a7b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"auTWYR/sWl4DmfGKT2jeOCEhfHw5oct6clO7vS+etMYidIqi/idK7KdY9tvfNHT7C1QQumLt5skgPP1+n4sZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:10:35.223043Z","bundle_sha256":"231a60e8a951a8c98a4dedd69153df5c776ebbf104bd4fbc11a6e0c995d3f867"}}