{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3FUSAVRQUAU7JNO2LPO47SYC25","short_pith_number":"pith:3FUSAVRQ","canonical_record":{"source":{"id":"1510.08801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-29T17:57:31Z","cross_cats_sorted":[],"title_canon_sha256":"d5586c39a1f761c82c4123bc71f463752c02abb0b4b2fb3e969a86391bf45a95","abstract_canon_sha256":"3cb04cc49a526a5f9c32a3df54ebedb5554ffdd03e605d4a244030d129e3cc63"},"schema_version":"1.0"},"canonical_sha256":"d969205630a029f4b5da5bddcfcb02d76393ae9741270850f0838b75a9b32b4b","source":{"kind":"arxiv","id":"1510.08801","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08801","created_at":"2026-05-18T01:28:26Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08801v1","created_at":"2026-05-18T01:28:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08801","created_at":"2026-05-18T01:28:26Z"},{"alias_kind":"pith_short_12","alias_value":"3FUSAVRQUAU7","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3FUSAVRQUAU7JNO2","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3FUSAVRQ","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3FUSAVRQUAU7JNO2LPO47SYC25","target":"record","payload":{"canonical_record":{"source":{"id":"1510.08801","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-29T17:57:31Z","cross_cats_sorted":[],"title_canon_sha256":"d5586c39a1f761c82c4123bc71f463752c02abb0b4b2fb3e969a86391bf45a95","abstract_canon_sha256":"3cb04cc49a526a5f9c32a3df54ebedb5554ffdd03e605d4a244030d129e3cc63"},"schema_version":"1.0"},"canonical_sha256":"d969205630a029f4b5da5bddcfcb02d76393ae9741270850f0838b75a9b32b4b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:26.686391Z","signature_b64":"9v8NQzKuNZOrcSMAyczY3wpCmCk6f5VLJUBZF5rb5phXjnCqu0/bXs39f9i2e84QzH7FcbpkzFXyNOmSVPooCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d969205630a029f4b5da5bddcfcb02d76393ae9741270850f0838b75a9b32b4b","last_reissued_at":"2026-05-18T01:28:26.685803Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:26.685803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.08801","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":"2026-05-18T01:28:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gde7Xo15y356jkTBaufMXC9cjMX1r7bLNDZnU0sOqFDqkYkK+r0YF63pztuh74s9yGD7+9bkzGL4TR0kmRgLDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T16:46:05.594156Z"},"content_sha256":"c52e2ee78ff5cb62f42782eaffe6dbdab494fdb64df2035e7dd1ebbe9303fa2c","schema_version":"1.0","event_id":"sha256:c52e2ee78ff5cb62f42782eaffe6dbdab494fdb64df2035e7dd1ebbe9303fa2c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3FUSAVRQUAU7JNO2LPO47SYC25","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Riemann integrability versus weak continuity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gonzalo Mart\\'inez-Cervantes","submitted_at":"2015-10-29T17:57:31Z","abstract_excerpt":"In this paper we focus on the relation between Riemann integrability and weak continuity. A Banach space $X$ is said to have the weak Lebesgue property if every Riemann integrable function from $[0,1]$ into $X$ is weakly continuous almost everywhere. We prove that the weak Lebesgue property is stable under $\\ell_1$-sums and obtain new examples of Banach spaces with and without this property. Furthermore, we characterize Dunford-Pettis operators in terms of Riemann integrability and provide a quantitative result about the size of the set of $\\tau$-continuous non Riemann integrable functions, wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08801","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":"2026-05-18T01:28:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qNVbu3lNQjRpdoOpsvjM3RJcOYh/DHQOmS8h2Vax6VbZdWjXFo12SXwQKmRzOgCVZ80r2g9SiCaQjHjDJJrRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T16:46:05.594499Z"},"content_sha256":"7d062ef4b60445a1558437d202562e06a656d063d198bc6ec5d7b1797505bff4","schema_version":"1.0","event_id":"sha256:7d062ef4b60445a1558437d202562e06a656d063d198bc6ec5d7b1797505bff4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3FUSAVRQUAU7JNO2LPO47SYC25/bundle.json","state_url":"https://pith.science/pith/3FUSAVRQUAU7JNO2LPO47SYC25/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3FUSAVRQUAU7JNO2LPO47SYC25/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":"2026-06-20T16:46:05Z","links":{"resolver":"https://pith.science/pith/3FUSAVRQUAU7JNO2LPO47SYC25","bundle":"https://pith.science/pith/3FUSAVRQUAU7JNO2LPO47SYC25/bundle.json","state":"https://pith.science/pith/3FUSAVRQUAU7JNO2LPO47SYC25/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3FUSAVRQUAU7JNO2LPO47SYC25/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3FUSAVRQUAU7JNO2LPO47SYC25","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":"3cb04cc49a526a5f9c32a3df54ebedb5554ffdd03e605d4a244030d129e3cc63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-29T17:57:31Z","title_canon_sha256":"d5586c39a1f761c82c4123bc71f463752c02abb0b4b2fb3e969a86391bf45a95"},"schema_version":"1.0","source":{"id":"1510.08801","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.08801","created_at":"2026-05-18T01:28:26Z"},{"alias_kind":"arxiv_version","alias_value":"1510.08801v1","created_at":"2026-05-18T01:28:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.08801","created_at":"2026-05-18T01:28:26Z"},{"alias_kind":"pith_short_12","alias_value":"3FUSAVRQUAU7","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3FUSAVRQUAU7JNO2","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3FUSAVRQ","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:7d062ef4b60445a1558437d202562e06a656d063d198bc6ec5d7b1797505bff4","target":"graph","created_at":"2026-05-18T01:28:26Z","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":"In this paper we focus on the relation between Riemann integrability and weak continuity. A Banach space $X$ is said to have the weak Lebesgue property if every Riemann integrable function from $[0,1]$ into $X$ is weakly continuous almost everywhere. We prove that the weak Lebesgue property is stable under $\\ell_1$-sums and obtain new examples of Banach spaces with and without this property. Furthermore, we characterize Dunford-Pettis operators in terms of Riemann integrability and provide a quantitative result about the size of the set of $\\tau$-continuous non Riemann integrable functions, wi","authors_text":"Gonzalo Mart\\'inez-Cervantes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-29T17:57:31Z","title":"Riemann integrability versus weak continuity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.08801","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:c52e2ee78ff5cb62f42782eaffe6dbdab494fdb64df2035e7dd1ebbe9303fa2c","target":"record","created_at":"2026-05-18T01:28:26Z","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":"3cb04cc49a526a5f9c32a3df54ebedb5554ffdd03e605d4a244030d129e3cc63","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-10-29T17:57:31Z","title_canon_sha256":"d5586c39a1f761c82c4123bc71f463752c02abb0b4b2fb3e969a86391bf45a95"},"schema_version":"1.0","source":{"id":"1510.08801","kind":"arxiv","version":1}},"canonical_sha256":"d969205630a029f4b5da5bddcfcb02d76393ae9741270850f0838b75a9b32b4b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d969205630a029f4b5da5bddcfcb02d76393ae9741270850f0838b75a9b32b4b","first_computed_at":"2026-05-18T01:28:26.685803Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:26.685803Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9v8NQzKuNZOrcSMAyczY3wpCmCk6f5VLJUBZF5rb5phXjnCqu0/bXs39f9i2e84QzH7FcbpkzFXyNOmSVPooCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:26.686391Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.08801","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c52e2ee78ff5cb62f42782eaffe6dbdab494fdb64df2035e7dd1ebbe9303fa2c","sha256:7d062ef4b60445a1558437d202562e06a656d063d198bc6ec5d7b1797505bff4"],"state_sha256":"612ff4b52d62372ebc558ce495c2e4f53484a7b322caa9cd76aa1386c22b3077"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"axRYc2SAVHqLBFCm/BvQjTLJG5K/uWEVuUbxaYd9ubrXGNDe8/HCoPrWnv4YTkHErBSanU5XDpCNOlrz9lxnCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T16:46:05.596228Z","bundle_sha256":"2cbd8b3d8a41b9600bd0223f63d80ea8005977f228cae004eb6925d9bce7205a"}}