{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MEON2ATHMUKALVDVVNA4W4CHG6","short_pith_number":"pith:MEON2ATH","canonical_record":{"source":{"id":"1806.09366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-25T10:24:57Z","cross_cats_sorted":[],"title_canon_sha256":"cd17f09f8b928dc3a84e4aff47f389652a1dbe4f1e1c145f531b47b95ce76b21","abstract_canon_sha256":"ae49e11b6e88f694206b0418f711cfdf778df16054035161d6b8ac9ce9fd1a31"},"schema_version":"1.0"},"canonical_sha256":"611cdd0267651405d475ab41cb704737b8c482284e663572b4c5b85f990e72e0","source":{"kind":"arxiv","id":"1806.09366","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09366","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09366v2","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09366","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"MEON2ATHMUKA","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MEON2ATHMUKALVDV","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MEON2ATH","created_at":"2026-05-18T12:32:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MEON2ATHMUKALVDVVNA4W4CHG6","target":"record","payload":{"canonical_record":{"source":{"id":"1806.09366","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-25T10:24:57Z","cross_cats_sorted":[],"title_canon_sha256":"cd17f09f8b928dc3a84e4aff47f389652a1dbe4f1e1c145f531b47b95ce76b21","abstract_canon_sha256":"ae49e11b6e88f694206b0418f711cfdf778df16054035161d6b8ac9ce9fd1a31"},"schema_version":"1.0"},"canonical_sha256":"611cdd0267651405d475ab41cb704737b8c482284e663572b4c5b85f990e72e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:47:59.863169Z","signature_b64":"Px+aLYW95PXDrkWgWFOE5F5UQ8O7vdKC4JrjLUw+PDJQ4uGvFzM1PmjDkI4QF4I48HxhmruZBr71Z9tQb/s5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"611cdd0267651405d475ab41cb704737b8c482284e663572b4c5b85f990e72e0","last_reissued_at":"2026-05-17T23:47:59.862775Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:47:59.862775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.09366","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":"2026-05-17T23:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FNYfk444KUpkUvlnbwrjyJR6+9e0/K/CkOJmiHm7nNM1wshUppnJZC2qSXBU78ShZnILuFc1vboa4ClXgPFPAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:57:42.759234Z"},"content_sha256":"669412eba91666afd89d42d13583e1ae09e4fc4f29fbbb779afb498ddbb4cc4c","schema_version":"1.0","event_id":"sha256:669412eba91666afd89d42d13583e1ae09e4fc4f29fbbb779afb498ddbb4cc4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MEON2ATHMUKALVDVVNA4W4CHG6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Bishop-Phelps-Bollob\\'as property and absolute sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Miguel Mart\\'in, Mingu Jung, Sheldon Dantas, Yun Sung Choi","submitted_at":"2018-06-25T10:24:57Z","abstract_excerpt":"In this paper we study conditions assuring that the Bishop-Phelps-Bollob\\'as property (BPBp, for short) is inherited by absolute summands of the range space or of the domain space. Concretely, given a pair (X, Y) of Banach spaces having the BPBp, (a) if Y1 is an absolute summand of Y, then (X, Y1) has the BPBp; (b) if X1 is an absolute summand of X of type 1 or \\infty, then (X1, Y) has the BPBp. Besides, analogous results for the BPBp for compact operators and for the density of norm attaining operators are also given. We also show that the Bishop-Phelps-Bollob\\'as property for numerical radiu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09366","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":"2026-05-17T23:47:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JhG7Yhnx0tNjaHh+GFaG4tudipGNaKI6bCFwQMhvcp8g3i6z8szUNkmm/V99lVCafPsSdM7qp2JB+QcsaEB4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T04:57:42.759945Z"},"content_sha256":"a36427d1a08c2da030cdb092c30b3b3cac59d7f94328450144091a2a1122b5f6","schema_version":"1.0","event_id":"sha256:a36427d1a08c2da030cdb092c30b3b3cac59d7f94328450144091a2a1122b5f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MEON2ATHMUKALVDVVNA4W4CHG6/bundle.json","state_url":"https://pith.science/pith/MEON2ATHMUKALVDVVNA4W4CHG6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MEON2ATHMUKALVDVVNA4W4CHG6/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":"2026-05-31T04:57:42Z","links":{"resolver":"https://pith.science/pith/MEON2ATHMUKALVDVVNA4W4CHG6","bundle":"https://pith.science/pith/MEON2ATHMUKALVDVVNA4W4CHG6/bundle.json","state":"https://pith.science/pith/MEON2ATHMUKALVDVVNA4W4CHG6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MEON2ATHMUKALVDVVNA4W4CHG6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MEON2ATHMUKALVDVVNA4W4CHG6","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":"ae49e11b6e88f694206b0418f711cfdf778df16054035161d6b8ac9ce9fd1a31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-25T10:24:57Z","title_canon_sha256":"cd17f09f8b928dc3a84e4aff47f389652a1dbe4f1e1c145f531b47b95ce76b21"},"schema_version":"1.0","source":{"id":"1806.09366","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.09366","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"arxiv_version","alias_value":"1806.09366v2","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.09366","created_at":"2026-05-17T23:47:59Z"},{"alias_kind":"pith_short_12","alias_value":"MEON2ATHMUKA","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_16","alias_value":"MEON2ATHMUKALVDV","created_at":"2026-05-18T12:32:37Z"},{"alias_kind":"pith_short_8","alias_value":"MEON2ATH","created_at":"2026-05-18T12:32:37Z"}],"graph_snapshots":[{"event_id":"sha256:a36427d1a08c2da030cdb092c30b3b3cac59d7f94328450144091a2a1122b5f6","target":"graph","created_at":"2026-05-17T23:47:59Z","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 study conditions assuring that the Bishop-Phelps-Bollob\\'as property (BPBp, for short) is inherited by absolute summands of the range space or of the domain space. Concretely, given a pair (X, Y) of Banach spaces having the BPBp, (a) if Y1 is an absolute summand of Y, then (X, Y1) has the BPBp; (b) if X1 is an absolute summand of X of type 1 or \\infty, then (X1, Y) has the BPBp. Besides, analogous results for the BPBp for compact operators and for the density of norm attaining operators are also given. We also show that the Bishop-Phelps-Bollob\\'as property for numerical radiu","authors_text":"Miguel Mart\\'in, Mingu Jung, Sheldon Dantas, Yun Sung Choi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-25T10:24:57Z","title":"The Bishop-Phelps-Bollob\\'as property and absolute sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.09366","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":"sha256:669412eba91666afd89d42d13583e1ae09e4fc4f29fbbb779afb498ddbb4cc4c","target":"record","created_at":"2026-05-17T23:47:59Z","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":"ae49e11b6e88f694206b0418f711cfdf778df16054035161d6b8ac9ce9fd1a31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-06-25T10:24:57Z","title_canon_sha256":"cd17f09f8b928dc3a84e4aff47f389652a1dbe4f1e1c145f531b47b95ce76b21"},"schema_version":"1.0","source":{"id":"1806.09366","kind":"arxiv","version":2}},"canonical_sha256":"611cdd0267651405d475ab41cb704737b8c482284e663572b4c5b85f990e72e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"611cdd0267651405d475ab41cb704737b8c482284e663572b4c5b85f990e72e0","first_computed_at":"2026-05-17T23:47:59.862775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:59.862775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Px+aLYW95PXDrkWgWFOE5F5UQ8O7vdKC4JrjLUw+PDJQ4uGvFzM1PmjDkI4QF4I48HxhmruZBr71Z9tQb/s5AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:59.863169Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.09366","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:669412eba91666afd89d42d13583e1ae09e4fc4f29fbbb779afb498ddbb4cc4c","sha256:a36427d1a08c2da030cdb092c30b3b3cac59d7f94328450144091a2a1122b5f6"],"state_sha256":"c747202b8b2312e6faa2b8fb7c4bfb47818e47d5493c22ea9d9f350779206aa4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XfycY44RjoFIlgAuAODBH4dgPVZnxg6CFP7fDQfJk6JZNla//NA2GlT2uxsZj9Z+xTHZ9TUd/zg4VJKycgLqBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T04:57:42.763599Z","bundle_sha256":"b210811dfa02c858d540cdb3239016f7f7acea22e5cd5c99ae4dbc40b2b28c53"}}