{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:LY6THKVH2RAEG2BH6BJWDPUAQU","short_pith_number":"pith:LY6THKVH","canonical_record":{"source":{"id":"1103.2975","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-03-15T17:52:41Z","cross_cats_sorted":[],"title_canon_sha256":"e49f05d40d0fa713da19004578e743a8bfe943026ffc6ae42390fdc20b5bb60c","abstract_canon_sha256":"aa4af9ca87dd908038f49ba6060e0bab6c21de128eb3693426ab0917b21e3baf"},"schema_version":"1.0"},"canonical_sha256":"5e3d33aaa7d440436827f05361be80852bd9549a81e667114084843f416d7209","source":{"kind":"arxiv","id":"1103.2975","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2975","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2975v2","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2975","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"LY6THKVH2RAE","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LY6THKVH2RAEG2BH","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LY6THKVH","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:LY6THKVH2RAEG2BH6BJWDPUAQU","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2975","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-03-15T17:52:41Z","cross_cats_sorted":[],"title_canon_sha256":"e49f05d40d0fa713da19004578e743a8bfe943026ffc6ae42390fdc20b5bb60c","abstract_canon_sha256":"aa4af9ca87dd908038f49ba6060e0bab6c21de128eb3693426ab0917b21e3baf"},"schema_version":"1.0"},"canonical_sha256":"5e3d33aaa7d440436827f05361be80852bd9549a81e667114084843f416d7209","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:25.635272Z","signature_b64":"87jNZjYHeIoDSCV3+7gB6b49wArFZl/uploLGKiQy0hsrCVp48mveQGgiJnDoIl6m4eW9WlP49akz9gNAowaCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e3d33aaa7d440436827f05361be80852bd9549a81e667114084843f416d7209","last_reissued_at":"2026-05-18T01:09:25.634743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:25.634743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2975","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":"2026-05-18T01:09:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nAqScIfrbMdH2Tva8wBvo2l7TSXkat61D2zWjnNJouZf3AN2SOoMAVfQrYCi28KpyAKEkPt/Q3WqSgFRimiyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:28:25.963270Z"},"content_sha256":"99eac9d87a901a430d145ce502d2e8d14d823e77c2cfb5cb42ed6320e96403af","schema_version":"1.0","event_id":"sha256:99eac9d87a901a430d145ce502d2e8d14d823e77c2cfb5cb42ed6320e96403af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:LY6THKVH2RAEG2BH6BJWDPUAQU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a difference between quantitative weak sequential completeness and the quantitative Schur property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ji\\v{r}\\'i Spurn\\'y, Ond\\v{r}ej F.K. Kalenda","submitted_at":"2011-03-15T17:52:41Z","abstract_excerpt":"We study quantitative versions of the Schur property and weak sequential completeness, proceeding thus with investigations started by G. Godefroy, N. Kalton and D. Li and continued by H. Pfitzner and the authors. We show that the Schur property of $\\ell_1$ holds quantitatively in the strongest possible way and construct an example of a Banach space which is quantitatively weakly sequentially complete, has the Schur property but fails the quantitative form of the Schur property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2975","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":""},"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":"2026-05-18T01:09:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zo72tbh8TlbM4noA5bLHGkczR3wkEweHtFZeJM7yCNAidVMJJQSyKpc30OOP+KxgqCE3JOtUn2TQqJzZt9SeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T03:28:25.963652Z"},"content_sha256":"55d882bbaa6e05f6060246a99b20607c0b65ac338c292236c30c0cd0f34e8bef","schema_version":"1.0","event_id":"sha256:55d882bbaa6e05f6060246a99b20607c0b65ac338c292236c30c0cd0f34e8bef"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LY6THKVH2RAEG2BH6BJWDPUAQU/bundle.json","state_url":"https://pith.science/pith/LY6THKVH2RAEG2BH6BJWDPUAQU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LY6THKVH2RAEG2BH6BJWDPUAQU/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":"2026-06-01T03:28:25Z","links":{"resolver":"https://pith.science/pith/LY6THKVH2RAEG2BH6BJWDPUAQU","bundle":"https://pith.science/pith/LY6THKVH2RAEG2BH6BJWDPUAQU/bundle.json","state":"https://pith.science/pith/LY6THKVH2RAEG2BH6BJWDPUAQU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LY6THKVH2RAEG2BH6BJWDPUAQU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:LY6THKVH2RAEG2BH6BJWDPUAQU","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":"aa4af9ca87dd908038f49ba6060e0bab6c21de128eb3693426ab0917b21e3baf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-03-15T17:52:41Z","title_canon_sha256":"e49f05d40d0fa713da19004578e743a8bfe943026ffc6ae42390fdc20b5bb60c"},"schema_version":"1.0","source":{"id":"1103.2975","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2975","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2975v2","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2975","created_at":"2026-05-18T01:09:25Z"},{"alias_kind":"pith_short_12","alias_value":"LY6THKVH2RAE","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"LY6THKVH2RAEG2BH","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"LY6THKVH","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:55d882bbaa6e05f6060246a99b20607c0b65ac338c292236c30c0cd0f34e8bef","target":"graph","created_at":"2026-05-18T01:09:25Z","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 study quantitative versions of the Schur property and weak sequential completeness, proceeding thus with investigations started by G. Godefroy, N. Kalton and D. Li and continued by H. Pfitzner and the authors. We show that the Schur property of $\\ell_1$ holds quantitatively in the strongest possible way and construct an example of a Banach space which is quantitatively weakly sequentially complete, has the Schur property but fails the quantitative form of the Schur property.","authors_text":"Ji\\v{r}\\'i Spurn\\'y, Ond\\v{r}ej F.K. Kalenda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-03-15T17:52:41Z","title":"On a difference between quantitative weak sequential completeness and the quantitative Schur property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2975","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":"sha256:99eac9d87a901a430d145ce502d2e8d14d823e77c2cfb5cb42ed6320e96403af","target":"record","created_at":"2026-05-18T01:09:25Z","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":"aa4af9ca87dd908038f49ba6060e0bab6c21de128eb3693426ab0917b21e3baf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-03-15T17:52:41Z","title_canon_sha256":"e49f05d40d0fa713da19004578e743a8bfe943026ffc6ae42390fdc20b5bb60c"},"schema_version":"1.0","source":{"id":"1103.2975","kind":"arxiv","version":2}},"canonical_sha256":"5e3d33aaa7d440436827f05361be80852bd9549a81e667114084843f416d7209","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e3d33aaa7d440436827f05361be80852bd9549a81e667114084843f416d7209","first_computed_at":"2026-05-18T01:09:25.634743Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:25.634743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"87jNZjYHeIoDSCV3+7gB6b49wArFZl/uploLGKiQy0hsrCVp48mveQGgiJnDoIl6m4eW9WlP49akz9gNAowaCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:25.635272Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2975","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:99eac9d87a901a430d145ce502d2e8d14d823e77c2cfb5cb42ed6320e96403af","sha256:55d882bbaa6e05f6060246a99b20607c0b65ac338c292236c30c0cd0f34e8bef"],"state_sha256":"215fc24b968d5835b413b35f1ac15991e19be017ad4a7aa2a35cb5dda49af9c1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ClAyRpyUPZZJLmS7JqXPBezfgLf9LNYCoiVqnFBUBzjarRkCjoPFzh90nwnor2YrFliMUCebh3pGtUvxD5hVDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T03:28:25.965671Z","bundle_sha256":"d855f80b2c7ef34ad00cf393c4f53a2366257e8b1804019da960252eb3efabf2"}}