{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:D2C5KKQJ2VMESNC3S7MWAO7UNK","short_pith_number":"pith:D2C5KKQJ","canonical_record":{"source":{"id":"2302.05676","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-02-11T12:19:47Z","cross_cats_sorted":[],"title_canon_sha256":"5eeaa80c3b12a7fd502314781573a4d1aa3c2f271ed1a06f988b79325bfefe35","abstract_canon_sha256":"6dbabd985512957e2ef62fe29de20971b848b1e4a402fe5cedbecbcb131b4b4f"},"schema_version":"1.0"},"canonical_sha256":"1e85d52a09d55849345b97d9603bf46ab948423bb747a2762010a80469ea1078","source":{"kind":"arxiv","id":"2302.05676","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.05676","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"arxiv_version","alias_value":"2302.05676v2","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.05676","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"pith_short_12","alias_value":"D2C5KKQJ2VME","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"pith_short_16","alias_value":"D2C5KKQJ2VMESNC3","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"pith_short_8","alias_value":"D2C5KKQJ","created_at":"2026-07-05T08:10:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:D2C5KKQJ2VMESNC3S7MWAO7UNK","target":"record","payload":{"canonical_record":{"source":{"id":"2302.05676","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-02-11T12:19:47Z","cross_cats_sorted":[],"title_canon_sha256":"5eeaa80c3b12a7fd502314781573a4d1aa3c2f271ed1a06f988b79325bfefe35","abstract_canon_sha256":"6dbabd985512957e2ef62fe29de20971b848b1e4a402fe5cedbecbcb131b4b4f"},"schema_version":"1.0"},"canonical_sha256":"1e85d52a09d55849345b97d9603bf46ab948423bb747a2762010a80469ea1078","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:10:54.412028Z","signature_b64":"2MHTMQqGWYzO2kWEuguhWZKpcJq8bDQyWDKRqvmrNZFCOvcm9WBIZSUzaUS8s2P/jjvibpwNYegCTkxwYyHiDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e85d52a09d55849345b97d9603bf46ab948423bb747a2762010a80469ea1078","last_reissued_at":"2026-07-05T08:10:54.411615Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:10:54.411615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2302.05676","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:10:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hP9X7zDUu0kIux/7gqCPDyNRDWzlx1l11HyNxd+h4AFIDc7ckZ6iWhi5OChBB0vZG56eLI4j5PWbPuZt8T4wBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T02:16:39.744126Z"},"content_sha256":"205d4c2aafb4eed9d17fb7245cdeb583e9252ac94ce6de4967aa81d748f6adf9","schema_version":"1.0","event_id":"sha256:205d4c2aafb4eed9d17fb7245cdeb583e9252ac94ce6de4967aa81d748f6adf9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:D2C5KKQJ2VMESNC3S7MWAO7UNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniform Banach-Saks properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"G. Grelier","submitted_at":"2023-02-11T12:19:47Z","abstract_excerpt":"The principal aim of this paper is to study the Banach-Saks property when the speed of convergence of a Cesaro mean sequence can be chosen independtly from the choice of the initial sequence. We establish links between the uniform Banach-Saks property, properties $(A_\\infty)$ of Partington and the $p$-Banach-Saks property. We also prove that the $p$-Banach-Saks property and the strong $p$-Banach-Saks property are equivalent. Many examples are given and we apply the results to the symmetric Kottman constant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.05676","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2302.05676/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:10:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BwU4mAi3X1q2nwpyexR65DORhLNB5nIpKwqvannFDyzAxiZafEk+LTFyaUfEez9Mlu+4Y0xkLbJzZM0GEgliCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T02:16:39.744629Z"},"content_sha256":"acb4acbe6c2a7a5c36b0b884cca9c502c00c5bd6f0910c7cde768e6ad0b70484","schema_version":"1.0","event_id":"sha256:acb4acbe6c2a7a5c36b0b884cca9c502c00c5bd6f0910c7cde768e6ad0b70484"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D2C5KKQJ2VMESNC3S7MWAO7UNK/bundle.json","state_url":"https://pith.science/pith/D2C5KKQJ2VMESNC3S7MWAO7UNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D2C5KKQJ2VMESNC3S7MWAO7UNK/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":"2026-08-24T02:16:39Z","links":{"resolver":"https://pith.science/pith/D2C5KKQJ2VMESNC3S7MWAO7UNK","bundle":"https://pith.science/pith/D2C5KKQJ2VMESNC3S7MWAO7UNK/bundle.json","state":"https://pith.science/pith/D2C5KKQJ2VMESNC3S7MWAO7UNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D2C5KKQJ2VMESNC3S7MWAO7UNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:D2C5KKQJ2VMESNC3S7MWAO7UNK","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":"6dbabd985512957e2ef62fe29de20971b848b1e4a402fe5cedbecbcb131b4b4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-02-11T12:19:47Z","title_canon_sha256":"5eeaa80c3b12a7fd502314781573a4d1aa3c2f271ed1a06f988b79325bfefe35"},"schema_version":"1.0","source":{"id":"2302.05676","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2302.05676","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"arxiv_version","alias_value":"2302.05676v2","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2302.05676","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"pith_short_12","alias_value":"D2C5KKQJ2VME","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"pith_short_16","alias_value":"D2C5KKQJ2VMESNC3","created_at":"2026-07-05T08:10:54Z"},{"alias_kind":"pith_short_8","alias_value":"D2C5KKQJ","created_at":"2026-07-05T08:10:54Z"}],"graph_snapshots":[{"event_id":"sha256:acb4acbe6c2a7a5c36b0b884cca9c502c00c5bd6f0910c7cde768e6ad0b70484","target":"graph","created_at":"2026-07-05T08:10:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2302.05676/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The principal aim of this paper is to study the Banach-Saks property when the speed of convergence of a Cesaro mean sequence can be chosen independtly from the choice of the initial sequence. We establish links between the uniform Banach-Saks property, properties $(A_\\infty)$ of Partington and the $p$-Banach-Saks property. We also prove that the $p$-Banach-Saks property and the strong $p$-Banach-Saks property are equivalent. Many examples are given and we apply the results to the symmetric Kottman constant.","authors_text":"G. Grelier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-02-11T12:19:47Z","title":"Uniform Banach-Saks properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2302.05676","kind":"arxiv","version":2},"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":"sha256:205d4c2aafb4eed9d17fb7245cdeb583e9252ac94ce6de4967aa81d748f6adf9","target":"record","created_at":"2026-07-05T08:10:54Z","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":"6dbabd985512957e2ef62fe29de20971b848b1e4a402fe5cedbecbcb131b4b4f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2023-02-11T12:19:47Z","title_canon_sha256":"5eeaa80c3b12a7fd502314781573a4d1aa3c2f271ed1a06f988b79325bfefe35"},"schema_version":"1.0","source":{"id":"2302.05676","kind":"arxiv","version":2}},"canonical_sha256":"1e85d52a09d55849345b97d9603bf46ab948423bb747a2762010a80469ea1078","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e85d52a09d55849345b97d9603bf46ab948423bb747a2762010a80469ea1078","first_computed_at":"2026-07-05T08:10:54.411615Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:10:54.411615Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2MHTMQqGWYzO2kWEuguhWZKpcJq8bDQyWDKRqvmrNZFCOvcm9WBIZSUzaUS8s2P/jjvibpwNYegCTkxwYyHiDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:10:54.412028Z","signed_message":"canonical_sha256_bytes"},"source_id":"2302.05676","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:205d4c2aafb4eed9d17fb7245cdeb583e9252ac94ce6de4967aa81d748f6adf9","sha256:acb4acbe6c2a7a5c36b0b884cca9c502c00c5bd6f0910c7cde768e6ad0b70484"],"state_sha256":"e8de66aa9048a6a47d1b1e559418ab4cb0ba49f4c634cd9207776814d2f2078a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nICjnYx8XNq6rm7oI4wWWaghyYT4KUW/9fR6JZRv1zWRvrV1BYcB7sgrB5saKm/XLmrYuzz0O7CZe8DDk/o8Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T02:16:39.749127Z","bundle_sha256":"4f0883543673813954deeb8692dd38423193043119fe43167716b87c41e890df"}}