{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OECWQ3F4LNCUH3VIAJGHOHJG6S","short_pith_number":"pith:OECWQ3F4","canonical_record":{"source":{"id":"1510.05844","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-20T11:49:51Z","cross_cats_sorted":[],"title_canon_sha256":"a03385c08ce757711d4a13084bb12e3dedf6f3063c021ba7f226376a107d7dc8","abstract_canon_sha256":"6ff41fa99f4bab9cb447b1c755286a2ec416dbb69f77c4c9cb0051729a9e7cde"},"schema_version":"1.0"},"canonical_sha256":"7105686cbc5b4543eea8024c771d26f4af274115dee1914fde3e87578c7ed445","source":{"kind":"arxiv","id":"1510.05844","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05844","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05844v1","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05844","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"OECWQ3F4LNCU","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OECWQ3F4LNCUH3VI","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OECWQ3F4","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OECWQ3F4LNCUH3VIAJGHOHJG6S","target":"record","payload":{"canonical_record":{"source":{"id":"1510.05844","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-20T11:49:51Z","cross_cats_sorted":[],"title_canon_sha256":"a03385c08ce757711d4a13084bb12e3dedf6f3063c021ba7f226376a107d7dc8","abstract_canon_sha256":"6ff41fa99f4bab9cb447b1c755286a2ec416dbb69f77c4c9cb0051729a9e7cde"},"schema_version":"1.0"},"canonical_sha256":"7105686cbc5b4543eea8024c771d26f4af274115dee1914fde3e87578c7ed445","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:39.541832Z","signature_b64":"5giVdC4rCDgUv6EtkwyaZ+55kQD77mS54Yl97l0f40MoXmORVBLDb0FCjGolHUjzO2ROEkuNxN/QoJ63HJU8DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7105686cbc5b4543eea8024c771d26f4af274115dee1914fde3e87578c7ed445","last_reissued_at":"2026-05-18T01:29:39.541271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:39.541271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.05844","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":"2026-05-18T01:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Z+22nZvKNJQiuZdkK8iRl3tl/EiGF5NN6m8jldPK1mGuttmWZ+QjGD59am0EEfObjIr9o0hbxo8K7cnlb5PAAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:07:34.581689Z"},"content_sha256":"05dcf0ec6ae4e0fd9885a68fd4e0369c9aa49b9ae25fb0a1686dc69b303eb6cf","schema_version":"1.0","event_id":"sha256:05dcf0ec6ae4e0fd9885a68fd4e0369c9aa49b9ae25fb0a1686dc69b303eb6cf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OECWQ3F4LNCUH3VIAJGHOHJG6S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strongly regular sequences and proximate orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Javier Jim\\'enez-Garrido, Javier Sanz","submitted_at":"2015-10-20T11:49:51Z","abstract_excerpt":"Summability methods for ultraholomorphic classes in sectors, defined in terms of a strongly regular sequence $\\mathbb{M}=(M_p)_{p\\in\\mathbb{N}_0}$, have been put forward by A. Lastra, S. Malek and the second author (Summability in general Carleman ultraholomorphic classes, J. Math. Anal. Appl. 430 (2015), 1175--1206). We study several open questions related to the existence of kernels of summability constructed by means of analytic proximate orders. In particular, we give a simple condition that allows us to associate a proximate order with a strongly regular sequence. Under this assumption, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05844","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":"2026-05-18T01:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ezhV4SrAmoFA6pMkRcyX4Jtc1HZUMV4sGdAYEZXMBJiA4FMXSLO5tBySzJc6gCLD9ruuWXy1l/IEnd1wRZiyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:07:34.582449Z"},"content_sha256":"8000a42b3acd936c1025844d0748b584910a2b2bea5b2327f5ce6f1d7f14af26","schema_version":"1.0","event_id":"sha256:8000a42b3acd936c1025844d0748b584910a2b2bea5b2327f5ce6f1d7f14af26"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OECWQ3F4LNCUH3VIAJGHOHJG6S/bundle.json","state_url":"https://pith.science/pith/OECWQ3F4LNCUH3VIAJGHOHJG6S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OECWQ3F4LNCUH3VIAJGHOHJG6S/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":"2026-06-09T10:07:34Z","links":{"resolver":"https://pith.science/pith/OECWQ3F4LNCUH3VIAJGHOHJG6S","bundle":"https://pith.science/pith/OECWQ3F4LNCUH3VIAJGHOHJG6S/bundle.json","state":"https://pith.science/pith/OECWQ3F4LNCUH3VIAJGHOHJG6S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OECWQ3F4LNCUH3VIAJGHOHJG6S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OECWQ3F4LNCUH3VIAJGHOHJG6S","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":"6ff41fa99f4bab9cb447b1c755286a2ec416dbb69f77c4c9cb0051729a9e7cde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-20T11:49:51Z","title_canon_sha256":"a03385c08ce757711d4a13084bb12e3dedf6f3063c021ba7f226376a107d7dc8"},"schema_version":"1.0","source":{"id":"1510.05844","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05844","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05844v1","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05844","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"OECWQ3F4LNCU","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OECWQ3F4LNCUH3VI","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OECWQ3F4","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:8000a42b3acd936c1025844d0748b584910a2b2bea5b2327f5ce6f1d7f14af26","target":"graph","created_at":"2026-05-18T01:29:39Z","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":"Summability methods for ultraholomorphic classes in sectors, defined in terms of a strongly regular sequence $\\mathbb{M}=(M_p)_{p\\in\\mathbb{N}_0}$, have been put forward by A. Lastra, S. Malek and the second author (Summability in general Carleman ultraholomorphic classes, J. Math. Anal. Appl. 430 (2015), 1175--1206). We study several open questions related to the existence of kernels of summability constructed by means of analytic proximate orders. In particular, we give a simple condition that allows us to associate a proximate order with a strongly regular sequence. Under this assumption, a","authors_text":"Javier Jim\\'enez-Garrido, Javier Sanz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-20T11:49:51Z","title":"Strongly regular sequences and proximate orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05844","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":"sha256:05dcf0ec6ae4e0fd9885a68fd4e0369c9aa49b9ae25fb0a1686dc69b303eb6cf","target":"record","created_at":"2026-05-18T01:29:39Z","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":"6ff41fa99f4bab9cb447b1c755286a2ec416dbb69f77c4c9cb0051729a9e7cde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2015-10-20T11:49:51Z","title_canon_sha256":"a03385c08ce757711d4a13084bb12e3dedf6f3063c021ba7f226376a107d7dc8"},"schema_version":"1.0","source":{"id":"1510.05844","kind":"arxiv","version":1}},"canonical_sha256":"7105686cbc5b4543eea8024c771d26f4af274115dee1914fde3e87578c7ed445","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7105686cbc5b4543eea8024c771d26f4af274115dee1914fde3e87578c7ed445","first_computed_at":"2026-05-18T01:29:39.541271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:39.541271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5giVdC4rCDgUv6EtkwyaZ+55kQD77mS54Yl97l0f40MoXmORVBLDb0FCjGolHUjzO2ROEkuNxN/QoJ63HJU8DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:39.541832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05844","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05dcf0ec6ae4e0fd9885a68fd4e0369c9aa49b9ae25fb0a1686dc69b303eb6cf","sha256:8000a42b3acd936c1025844d0748b584910a2b2bea5b2327f5ce6f1d7f14af26"],"state_sha256":"440e07b42bc294bdd6ceec726844f1faa20899e25dd31c526c5c8bff6d3dfdff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IBHKgyipXDlOCocdH7bNlJRajgyKjoMSNNvcolU98EuqeCGm5wrDKZ8y6PXJJ3RAPJ9C/iYNpA6rBS7TJfLmCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:07:34.586472Z","bundle_sha256":"d622a2a19e9fd9d5c85fe6d747281ff8f58dd6c1dc0d550b747d0ad1dabd651e"}}