{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4OKWE5PE6FX4X2DIF4RFFYMKSM","short_pith_number":"pith:4OKWE5PE","canonical_record":{"source":{"id":"1808.03254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-09T17:38:07Z","cross_cats_sorted":[],"title_canon_sha256":"44a2f1cefc8c15dd4720316ad209f3ca6a4a8a0063bcb5a0671b34546eb57a08","abstract_canon_sha256":"7646f1ae6e4a96d60c26503726d53ddcabed4d89105e78bcc8906edf27a7683e"},"schema_version":"1.0"},"canonical_sha256":"e3956275e4f16fcbe8682f2252e18a933fd522495083b057bf8d6858af7b33c2","source":{"kind":"arxiv","id":"1808.03254","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03254","created_at":"2026-05-18T00:08:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03254v1","created_at":"2026-05-18T00:08:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03254","created_at":"2026-05-18T00:08:29Z"},{"alias_kind":"pith_short_12","alias_value":"4OKWE5PE6FX4","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4OKWE5PE6FX4X2DI","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4OKWE5PE","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4OKWE5PE6FX4X2DIF4RFFYMKSM","target":"record","payload":{"canonical_record":{"source":{"id":"1808.03254","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-09T17:38:07Z","cross_cats_sorted":[],"title_canon_sha256":"44a2f1cefc8c15dd4720316ad209f3ca6a4a8a0063bcb5a0671b34546eb57a08","abstract_canon_sha256":"7646f1ae6e4a96d60c26503726d53ddcabed4d89105e78bcc8906edf27a7683e"},"schema_version":"1.0"},"canonical_sha256":"e3956275e4f16fcbe8682f2252e18a933fd522495083b057bf8d6858af7b33c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:29.798425Z","signature_b64":"7IdDjzmyrjzZxWAf30ajC+km2L/WukJL0bOuXsLSwWG/vnLbHFn5+B4lW+wtxEQ0uRI+nPR5ef/xs7DpsUv9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e3956275e4f16fcbe8682f2252e18a933fd522495083b057bf8d6858af7b33c2","last_reissued_at":"2026-05-18T00:08:29.797954Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:29.797954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.03254","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":"2026-05-18T00:08:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZZuGsGh/9Inybex0At63wC/ZzjxrFOD22CVV66/6YKK0c+WXiiDJgrMQany7rIqpi+un7M6Viq6B4iV6ULsaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:52:53.796076Z"},"content_sha256":"75f8929b477bc29ef79cc819f17ce048c82bafc9a99dc12f9f8833009ef02611","schema_version":"1.0","event_id":"sha256:75f8929b477bc29ef79cc819f17ce048c82bafc9a99dc12f9f8833009ef02611"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4OKWE5PE6FX4X2DIF4RFFYMKSM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On asymptotically uniformly smoothness and nonlinear geometry of Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Bruno de Mendon\\c{c}a Braga","submitted_at":"2018-08-09T17:38:07Z","abstract_excerpt":"These notes concern the nonlinear geometry of Banach spaces, asymptotic uniform smoothness and several Banach-Saks-like properties. We study the existence of certain concentration inequalities in asymptotically uniformly smooth Banach spaces as well as weakly sequentially continuous coarse (Lipschitz) embeddings into those spaces. Some results concerning the descriptive set theoretical complexity of those properties are also obtained. We finish the paper with a list of open problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03254","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":"2026-05-18T00:08:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EZ8GRTKgyN8EuDuxdA+JcmOtL1vmFeUeUA76vy+oFNUv8qlcKMN3rpIBi516cXvEAXyC15OGx56eQeEqWra7DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:52:53.796421Z"},"content_sha256":"d694180aaa0de19bfa7049b22aefd77679e3ced6a332847563cbcbe8ae79c3c9","schema_version":"1.0","event_id":"sha256:d694180aaa0de19bfa7049b22aefd77679e3ced6a332847563cbcbe8ae79c3c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4OKWE5PE6FX4X2DIF4RFFYMKSM/bundle.json","state_url":"https://pith.science/pith/4OKWE5PE6FX4X2DIF4RFFYMKSM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4OKWE5PE6FX4X2DIF4RFFYMKSM/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":"2026-06-02T07:52:53Z","links":{"resolver":"https://pith.science/pith/4OKWE5PE6FX4X2DIF4RFFYMKSM","bundle":"https://pith.science/pith/4OKWE5PE6FX4X2DIF4RFFYMKSM/bundle.json","state":"https://pith.science/pith/4OKWE5PE6FX4X2DIF4RFFYMKSM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4OKWE5PE6FX4X2DIF4RFFYMKSM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4OKWE5PE6FX4X2DIF4RFFYMKSM","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":"7646f1ae6e4a96d60c26503726d53ddcabed4d89105e78bcc8906edf27a7683e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-09T17:38:07Z","title_canon_sha256":"44a2f1cefc8c15dd4720316ad209f3ca6a4a8a0063bcb5a0671b34546eb57a08"},"schema_version":"1.0","source":{"id":"1808.03254","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.03254","created_at":"2026-05-18T00:08:29Z"},{"alias_kind":"arxiv_version","alias_value":"1808.03254v1","created_at":"2026-05-18T00:08:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.03254","created_at":"2026-05-18T00:08:29Z"},{"alias_kind":"pith_short_12","alias_value":"4OKWE5PE6FX4","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4OKWE5PE6FX4X2DI","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4OKWE5PE","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:d694180aaa0de19bfa7049b22aefd77679e3ced6a332847563cbcbe8ae79c3c9","target":"graph","created_at":"2026-05-18T00:08:29Z","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":"These notes concern the nonlinear geometry of Banach spaces, asymptotic uniform smoothness and several Banach-Saks-like properties. We study the existence of certain concentration inequalities in asymptotically uniformly smooth Banach spaces as well as weakly sequentially continuous coarse (Lipschitz) embeddings into those spaces. Some results concerning the descriptive set theoretical complexity of those properties are also obtained. We finish the paper with a list of open problem.","authors_text":"Bruno de Mendon\\c{c}a Braga","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-09T17:38:07Z","title":"On asymptotically uniformly smoothness and nonlinear geometry of Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.03254","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":"sha256:75f8929b477bc29ef79cc819f17ce048c82bafc9a99dc12f9f8833009ef02611","target":"record","created_at":"2026-05-18T00:08:29Z","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":"7646f1ae6e4a96d60c26503726d53ddcabed4d89105e78bcc8906edf27a7683e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-08-09T17:38:07Z","title_canon_sha256":"44a2f1cefc8c15dd4720316ad209f3ca6a4a8a0063bcb5a0671b34546eb57a08"},"schema_version":"1.0","source":{"id":"1808.03254","kind":"arxiv","version":1}},"canonical_sha256":"e3956275e4f16fcbe8682f2252e18a933fd522495083b057bf8d6858af7b33c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3956275e4f16fcbe8682f2252e18a933fd522495083b057bf8d6858af7b33c2","first_computed_at":"2026-05-18T00:08:29.797954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:29.797954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7IdDjzmyrjzZxWAf30ajC+km2L/WukJL0bOuXsLSwWG/vnLbHFn5+B4lW+wtxEQ0uRI+nPR5ef/xs7DpsUv9Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:29.798425Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.03254","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75f8929b477bc29ef79cc819f17ce048c82bafc9a99dc12f9f8833009ef02611","sha256:d694180aaa0de19bfa7049b22aefd77679e3ced6a332847563cbcbe8ae79c3c9"],"state_sha256":"d2c42549ac6580d74ee832d3bbc5c37e4af160c7e1539c6a230ed2b70bfb3ee4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VkmzLXoUVBmxS0/DAupd76WMDOWZq1fa7lUB2NF7nmJ3380qY2PmZo7ukFAawwWlWgIYwGrB5LiCVv3sDCfVCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:52:53.798174Z","bundle_sha256":"a0f0a42fb1a298242d788c770695a0ef2f4e9e815c76d7b5cdcb5aad699fad43"}}