{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AWCD5XISSTJGW3YR4HEN4Q745W","short_pith_number":"pith:AWCD5XIS","canonical_record":{"source":{"id":"1212.4394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-12-18T15:44:10Z","cross_cats_sorted":[],"title_canon_sha256":"9dfd98436fbafb72d0d76f4577f967e1547257821f4159954bccdafa050b1d99","abstract_canon_sha256":"ad263a81870a45b06fdb7c2541c9bcc31fcc35a0de8377d28e01adcaa913575c"},"schema_version":"1.0"},"canonical_sha256":"05843edd1294d26b6f11e1c8de43fced8ffa0585258ceaeac42230a9220f342e","source":{"kind":"arxiv","id":"1212.4394","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4394","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4394v1","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4394","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"AWCD5XISSTJG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AWCD5XISSTJGW3YR","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AWCD5XIS","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AWCD5XISSTJGW3YR4HEN4Q745W","target":"record","payload":{"canonical_record":{"source":{"id":"1212.4394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-12-18T15:44:10Z","cross_cats_sorted":[],"title_canon_sha256":"9dfd98436fbafb72d0d76f4577f967e1547257821f4159954bccdafa050b1d99","abstract_canon_sha256":"ad263a81870a45b06fdb7c2541c9bcc31fcc35a0de8377d28e01adcaa913575c"},"schema_version":"1.0"},"canonical_sha256":"05843edd1294d26b6f11e1c8de43fced8ffa0585258ceaeac42230a9220f342e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:38:13.174884Z","signature_b64":"Zd2Van3SOO3ZvXD5zoRP4sMaF3yWnf9CjAXh9yoDx19VUzUpmCGUdmCFL7VQzvkwZAJLGr/4poMafgrfKrx0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05843edd1294d26b6f11e1c8de43fced8ffa0585258ceaeac42230a9220f342e","last_reissued_at":"2026-05-18T03:38:13.174268Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:38:13.174268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.4394","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":"2026-05-18T03:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DTUPZ8/bUZ4uE5FR2SAuT2t1dYt4qb+jaamoQrqSTyZFC7WdLWvwmV+W481R5ruxApAsebXg4G46u+ytW0b+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T10:15:51.331106Z"},"content_sha256":"5bdf88899268d063245b734a324a6f729c3a01b9f2ecd5184a5d7232520043ae","schema_version":"1.0","event_id":"sha256:5bdf88899268d063245b734a324a6f729c3a01b9f2ecd5184a5d7232520043ae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AWCD5XISSTJGW3YR4HEN4Q745W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pad\\'{e} Approximants, density of rational functions in $\\bbb{A^\\infty(\\OO)}$ and smoothness of the integration operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ilias Zadik, Vassili Nestoridis","submitted_at":"2012-12-18T15:44:10Z","abstract_excerpt":"First we establish some generic universalities for Pad\\'{e} approximants in the closure $X^\\infty(\\OO)$ in $A^\\infty(\\OO)$ of all rational functions with poles off $\\oO$, the closure taken in $\\C$ of the domain $\\OO\\subset\\C$.\\ Next we give sufficient conditions on $\\OO$ so that $X^\\infty(\\OO)=A^\\infty(\\OO)$.\\ Some of these conditions imply that, even if the boundary $\\partial\\OO$ of a Jordan domain $\\OO$ has infinite length, the integration operator on $\\OO$ preserves $H^\\infty(\\OO)$ and $A(\\OO)$ as well.\\ We also give an example of a Jordan domain $\\OO$ and a function $f\\in A(\\OO)$, such tha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4394","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":"2026-05-18T03:38:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4683zXw5xC4gtIkP3WzU/k33HaM2tFm4d0YmVR2nfgmYvXyBQGha+dvNsTAMA/iwSS7mh7vRran4+6q77icGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T10:15:51.331459Z"},"content_sha256":"1e98127da367e5a567101dca67791b1aa12d5005073dd9000b1eddbb18c719f3","schema_version":"1.0","event_id":"sha256:1e98127da367e5a567101dca67791b1aa12d5005073dd9000b1eddbb18c719f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AWCD5XISSTJGW3YR4HEN4Q745W/bundle.json","state_url":"https://pith.science/pith/AWCD5XISSTJGW3YR4HEN4Q745W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AWCD5XISSTJGW3YR4HEN4Q745W/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":"2026-07-04T10:15:51Z","links":{"resolver":"https://pith.science/pith/AWCD5XISSTJGW3YR4HEN4Q745W","bundle":"https://pith.science/pith/AWCD5XISSTJGW3YR4HEN4Q745W/bundle.json","state":"https://pith.science/pith/AWCD5XISSTJGW3YR4HEN4Q745W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AWCD5XISSTJGW3YR4HEN4Q745W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AWCD5XISSTJGW3YR4HEN4Q745W","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":"ad263a81870a45b06fdb7c2541c9bcc31fcc35a0de8377d28e01adcaa913575c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-12-18T15:44:10Z","title_canon_sha256":"9dfd98436fbafb72d0d76f4577f967e1547257821f4159954bccdafa050b1d99"},"schema_version":"1.0","source":{"id":"1212.4394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.4394","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"arxiv_version","alias_value":"1212.4394v1","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.4394","created_at":"2026-05-18T03:38:13Z"},{"alias_kind":"pith_short_12","alias_value":"AWCD5XISSTJG","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AWCD5XISSTJGW3YR","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AWCD5XIS","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:1e98127da367e5a567101dca67791b1aa12d5005073dd9000b1eddbb18c719f3","target":"graph","created_at":"2026-05-18T03:38:13Z","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":"First we establish some generic universalities for Pad\\'{e} approximants in the closure $X^\\infty(\\OO)$ in $A^\\infty(\\OO)$ of all rational functions with poles off $\\oO$, the closure taken in $\\C$ of the domain $\\OO\\subset\\C$.\\ Next we give sufficient conditions on $\\OO$ so that $X^\\infty(\\OO)=A^\\infty(\\OO)$.\\ Some of these conditions imply that, even if the boundary $\\partial\\OO$ of a Jordan domain $\\OO$ has infinite length, the integration operator on $\\OO$ preserves $H^\\infty(\\OO)$ and $A(\\OO)$ as well.\\ We also give an example of a Jordan domain $\\OO$ and a function $f\\in A(\\OO)$, such tha","authors_text":"Ilias Zadik, Vassili Nestoridis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-12-18T15:44:10Z","title":"Pad\\'{e} Approximants, density of rational functions in $\\bbb{A^\\infty(\\OO)}$ and smoothness of the integration operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4394","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":"sha256:5bdf88899268d063245b734a324a6f729c3a01b9f2ecd5184a5d7232520043ae","target":"record","created_at":"2026-05-18T03:38:13Z","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":"ad263a81870a45b06fdb7c2541c9bcc31fcc35a0de8377d28e01adcaa913575c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2012-12-18T15:44:10Z","title_canon_sha256":"9dfd98436fbafb72d0d76f4577f967e1547257821f4159954bccdafa050b1d99"},"schema_version":"1.0","source":{"id":"1212.4394","kind":"arxiv","version":1}},"canonical_sha256":"05843edd1294d26b6f11e1c8de43fced8ffa0585258ceaeac42230a9220f342e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05843edd1294d26b6f11e1c8de43fced8ffa0585258ceaeac42230a9220f342e","first_computed_at":"2026-05-18T03:38:13.174268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:13.174268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zd2Van3SOO3ZvXD5zoRP4sMaF3yWnf9CjAXh9yoDx19VUzUpmCGUdmCFL7VQzvkwZAJLGr/4poMafgrfKrx0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:13.174884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.4394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bdf88899268d063245b734a324a6f729c3a01b9f2ecd5184a5d7232520043ae","sha256:1e98127da367e5a567101dca67791b1aa12d5005073dd9000b1eddbb18c719f3"],"state_sha256":"39202f4004ae6fe9a7f65b58fa89fa4c0249172e0f016829da87651a3fecf471"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g2Oha+sUX4slSGvFvu1NMe2OrbhFWSfMVYSs1Pqn7BHCgL/KBsC+jALXIGUHhfd/FVgYDV9YA62tGwCdtIRsDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T10:15:51.333451Z","bundle_sha256":"f8a0efce3219e30d67e40cfd872d50ca6137ae60d937b6fe5250080f73473af1"}}