{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:UB3Q55RXKI663AR7GSLGY5OAIC","short_pith_number":"pith:UB3Q55RX","canonical_record":{"source":{"id":"1401.1594","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-08T07:58:37Z","cross_cats_sorted":[],"title_canon_sha256":"c0280cd37dbc4ec416ad219f7ae5458ebdc4a9ebf82fa94de99477f4d1e6a78a","abstract_canon_sha256":"88fd0b0e71233ad58cdc2961e05d9c0c98244d93e3630ccc4aa2b998f02bae53"},"schema_version":"1.0"},"canonical_sha256":"a0770ef637523ded823f34966c75c0409189a34ed80c95afd7112e2eaaaf1377","source":{"kind":"arxiv","id":"1401.1594","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1594","created_at":"2026-05-18T03:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1594v1","created_at":"2026-05-18T03:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1594","created_at":"2026-05-18T03:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"UB3Q55RXKI66","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UB3Q55RXKI663AR7","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UB3Q55RX","created_at":"2026-05-18T12:28:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:UB3Q55RXKI663AR7GSLGY5OAIC","target":"record","payload":{"canonical_record":{"source":{"id":"1401.1594","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-08T07:58:37Z","cross_cats_sorted":[],"title_canon_sha256":"c0280cd37dbc4ec416ad219f7ae5458ebdc4a9ebf82fa94de99477f4d1e6a78a","abstract_canon_sha256":"88fd0b0e71233ad58cdc2961e05d9c0c98244d93e3630ccc4aa2b998f02bae53"},"schema_version":"1.0"},"canonical_sha256":"a0770ef637523ded823f34966c75c0409189a34ed80c95afd7112e2eaaaf1377","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:02:58.476466Z","signature_b64":"eNvCLoZhBkGbP/GsoQXYZ8jVMnsMrHfghnavvB92yYQHLebOaYaSGLOkPrhwNUO7NwbuVBMMzp0KIyqdUSXfCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0770ef637523ded823f34966c75c0409189a34ed80c95afd7112e2eaaaf1377","last_reissued_at":"2026-05-18T03:02:58.475786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:02:58.475786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.1594","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":"2026-05-18T03:02:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PtLiRBxfbpH+TeQBods0LmpdyhnhHiQN9VIb0w6SNEIPB1AJWMx2FyKNxJMi5c3AbRAimgaK4ttLwcdRfHL2Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:16:44.482959Z"},"content_sha256":"8dad442871c6db5cd173bc98ee8f7eb486f1518927b3f51b6fb9f0fbe77e8851","schema_version":"1.0","event_id":"sha256:8dad442871c6db5cd173bc98ee8f7eb486f1518927b3f51b6fb9f0fbe77e8851"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:UB3Q55RXKI663AR7GSLGY5OAIC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized universal series","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Augustin Mouze (LPP), St\\'ephane Charpentier (LATP), Vincent Munnier","submitted_at":"2014-01-08T07:58:37Z","abstract_excerpt":"We unify the recently developed abstract theories of universal series and extended universal series to include sums of the form  $\\sum_{k=0}^n a_k x_{n,k}$ for given sequences of vectors $(x_{n,k})_{n\\geq k\\geq 0}$ in a topological vector space X. The algebraic and topological genericity as well as the spaceability are discussed. Then we provide various examples of such generalized universal series which do not proceed from the classical theory. In particular, we build universal series involving Bernstein's polynomials, we obtain a universal series version of MacLane's Theorem, and we extend a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1594","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":"2026-05-18T03:02:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jht9r5HC+sUJJFYHV++N6BAmPjuiZSFOpsyfxnfp469h9fuVWg3zxs9SvymKDVrNJEN81g7IUqlC1WgghpzDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T16:16:44.483714Z"},"content_sha256":"c6a817b66e3a4cf904d9770510ce93003744be1e94080150654c29a28b4acc95","schema_version":"1.0","event_id":"sha256:c6a817b66e3a4cf904d9770510ce93003744be1e94080150654c29a28b4acc95"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UB3Q55RXKI663AR7GSLGY5OAIC/bundle.json","state_url":"https://pith.science/pith/UB3Q55RXKI663AR7GSLGY5OAIC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UB3Q55RXKI663AR7GSLGY5OAIC/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":"2026-06-10T16:16:44Z","links":{"resolver":"https://pith.science/pith/UB3Q55RXKI663AR7GSLGY5OAIC","bundle":"https://pith.science/pith/UB3Q55RXKI663AR7GSLGY5OAIC/bundle.json","state":"https://pith.science/pith/UB3Q55RXKI663AR7GSLGY5OAIC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UB3Q55RXKI663AR7GSLGY5OAIC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UB3Q55RXKI663AR7GSLGY5OAIC","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":"88fd0b0e71233ad58cdc2961e05d9c0c98244d93e3630ccc4aa2b998f02bae53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-08T07:58:37Z","title_canon_sha256":"c0280cd37dbc4ec416ad219f7ae5458ebdc4a9ebf82fa94de99477f4d1e6a78a"},"schema_version":"1.0","source":{"id":"1401.1594","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.1594","created_at":"2026-05-18T03:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"1401.1594v1","created_at":"2026-05-18T03:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.1594","created_at":"2026-05-18T03:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"UB3Q55RXKI66","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UB3Q55RXKI663AR7","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UB3Q55RX","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:c6a817b66e3a4cf904d9770510ce93003744be1e94080150654c29a28b4acc95","target":"graph","created_at":"2026-05-18T03:02:58Z","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 unify the recently developed abstract theories of universal series and extended universal series to include sums of the form  $\\sum_{k=0}^n a_k x_{n,k}$ for given sequences of vectors $(x_{n,k})_{n\\geq k\\geq 0}$ in a topological vector space X. The algebraic and topological genericity as well as the spaceability are discussed. Then we provide various examples of such generalized universal series which do not proceed from the classical theory. In particular, we build universal series involving Bernstein's polynomials, we obtain a universal series version of MacLane's Theorem, and we extend a","authors_text":"Augustin Mouze (LPP), St\\'ephane Charpentier (LATP), Vincent Munnier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-08T07:58:37Z","title":"Generalized universal series"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1594","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":"sha256:8dad442871c6db5cd173bc98ee8f7eb486f1518927b3f51b6fb9f0fbe77e8851","target":"record","created_at":"2026-05-18T03:02:58Z","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":"88fd0b0e71233ad58cdc2961e05d9c0c98244d93e3630ccc4aa2b998f02bae53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-08T07:58:37Z","title_canon_sha256":"c0280cd37dbc4ec416ad219f7ae5458ebdc4a9ebf82fa94de99477f4d1e6a78a"},"schema_version":"1.0","source":{"id":"1401.1594","kind":"arxiv","version":1}},"canonical_sha256":"a0770ef637523ded823f34966c75c0409189a34ed80c95afd7112e2eaaaf1377","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0770ef637523ded823f34966c75c0409189a34ed80c95afd7112e2eaaaf1377","first_computed_at":"2026-05-18T03:02:58.475786Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:02:58.475786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eNvCLoZhBkGbP/GsoQXYZ8jVMnsMrHfghnavvB92yYQHLebOaYaSGLOkPrhwNUO7NwbuVBMMzp0KIyqdUSXfCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:02:58.476466Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.1594","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8dad442871c6db5cd173bc98ee8f7eb486f1518927b3f51b6fb9f0fbe77e8851","sha256:c6a817b66e3a4cf904d9770510ce93003744be1e94080150654c29a28b4acc95"],"state_sha256":"3f89c4739720f45736e9272997e911bc81bf184a83a9512700819a9b5520db9d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Cs5CFhRi9xBN3QSv6Ai9kv2HzfFYIViMfQD6hqgHpz+PaBt2iilyj8zH9XvX5mh67CDqQBIk9ye/9yrbE6TbAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T16:16:44.487574Z","bundle_sha256":"5551b4ea6a560306a3c2298683aade0664728ba57f8aed18c0051e4f40d403f8"}}