{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:ONVZXRAN4NEML3NEKNHN3ZLDNG","short_pith_number":"pith:ONVZXRAN","canonical_record":{"source":{"id":"1401.4231","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-17T03:13:56Z","cross_cats_sorted":[],"title_canon_sha256":"e61b28214728c2b2a8d633eafac6a4c5e4d43acd5576af5913bdb5bd30061806","abstract_canon_sha256":"51ab670d32ff79434d9ed67a890880d3e7611c0f83766cb5495d6b4b8d1e98b4"},"schema_version":"1.0"},"canonical_sha256":"736b9bc40de348c5eda4534edde56369bdd3ce2b1c2bdbe30169c47547e5d67c","source":{"kind":"arxiv","id":"1401.4231","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4231","created_at":"2026-05-18T03:01:55Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4231v1","created_at":"2026-05-18T03:01:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4231","created_at":"2026-05-18T03:01:55Z"},{"alias_kind":"pith_short_12","alias_value":"ONVZXRAN4NEM","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"ONVZXRAN4NEML3NE","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"ONVZXRAN","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:ONVZXRAN4NEML3NEKNHN3ZLDNG","target":"record","payload":{"canonical_record":{"source":{"id":"1401.4231","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-17T03:13:56Z","cross_cats_sorted":[],"title_canon_sha256":"e61b28214728c2b2a8d633eafac6a4c5e4d43acd5576af5913bdb5bd30061806","abstract_canon_sha256":"51ab670d32ff79434d9ed67a890880d3e7611c0f83766cb5495d6b4b8d1e98b4"},"schema_version":"1.0"},"canonical_sha256":"736b9bc40de348c5eda4534edde56369bdd3ce2b1c2bdbe30169c47547e5d67c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:55.661470Z","signature_b64":"Ux+LSmxNC/Mh+JL/aQne1GOwZK0dD9mIqX+ijh70W/O0vzmRVXncXhnlini3oFLvei76gcHkXYxwDpFliWIPAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"736b9bc40de348c5eda4534edde56369bdd3ce2b1c2bdbe30169c47547e5d67c","last_reissued_at":"2026-05-18T03:01:55.660722Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:55.660722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.4231","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":"2026-05-18T03:01:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QmQMpHw/9/jIMbT8Tez7XRBoSOZI1ES9OoFL/IFENnMEpgNwT/JXMKFiyHYwt3mXnjY7pj3jzObH7yllJMRVBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T15:55:59.857898Z"},"content_sha256":"69a6720acbc67e52e2ef550972b3553cf71db0a70e9005f1b2255f2e5402c1d2","schema_version":"1.0","event_id":"sha256:69a6720acbc67e52e2ef550972b3553cf71db0a70e9005f1b2255f2e5402c1d2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:ONVZXRAN4NEML3NEKNHN3ZLDNG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Subprojective Banach spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Eugeniu Spinu, Timur Oikhberg","submitted_at":"2014-01-17T03:13:56Z","abstract_excerpt":"A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the stability of subprojectivity of Banach spaces under various operations, such us direct or twisted sums, tensor products, and forming spaces of operators. Along the way, we obtain new classes of subprojective spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4231","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":"2026-05-18T03:01:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EJFlELyZcYmCaxOfCUcW7PaM8t7UygbdRpydO1TABLvyip6ZHUFOwQvbsLh7ZbYut4VqAZkDAGfuKgZtvYpMDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T15:55:59.858240Z"},"content_sha256":"16d9c7f8d0423874e8f86ab748884f970054d093a603a7ea7dd3eb801fa3d961","schema_version":"1.0","event_id":"sha256:16d9c7f8d0423874e8f86ab748884f970054d093a603a7ea7dd3eb801fa3d961"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ONVZXRAN4NEML3NEKNHN3ZLDNG/bundle.json","state_url":"https://pith.science/pith/ONVZXRAN4NEML3NEKNHN3ZLDNG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ONVZXRAN4NEML3NEKNHN3ZLDNG/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":"2026-07-04T15:55:59Z","links":{"resolver":"https://pith.science/pith/ONVZXRAN4NEML3NEKNHN3ZLDNG","bundle":"https://pith.science/pith/ONVZXRAN4NEML3NEKNHN3ZLDNG/bundle.json","state":"https://pith.science/pith/ONVZXRAN4NEML3NEKNHN3ZLDNG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ONVZXRAN4NEML3NEKNHN3ZLDNG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:ONVZXRAN4NEML3NEKNHN3ZLDNG","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":"51ab670d32ff79434d9ed67a890880d3e7611c0f83766cb5495d6b4b8d1e98b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-17T03:13:56Z","title_canon_sha256":"e61b28214728c2b2a8d633eafac6a4c5e4d43acd5576af5913bdb5bd30061806"},"schema_version":"1.0","source":{"id":"1401.4231","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.4231","created_at":"2026-05-18T03:01:55Z"},{"alias_kind":"arxiv_version","alias_value":"1401.4231v1","created_at":"2026-05-18T03:01:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.4231","created_at":"2026-05-18T03:01:55Z"},{"alias_kind":"pith_short_12","alias_value":"ONVZXRAN4NEM","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"ONVZXRAN4NEML3NE","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"ONVZXRAN","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:16d9c7f8d0423874e8f86ab748884f970054d093a603a7ea7dd3eb801fa3d961","target":"graph","created_at":"2026-05-18T03:01:55Z","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":"A Banach space $X$ is called subprojective if any of its infinite dimensional subspaces $Y$ contains a further infinite dimensional subspace complemented in $X$. This paper is devoted to systematic study of subprojectivity. We examine the stability of subprojectivity of Banach spaces under various operations, such us direct or twisted sums, tensor products, and forming spaces of operators. Along the way, we obtain new classes of subprojective spaces.","authors_text":"Eugeniu Spinu, Timur Oikhberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-17T03:13:56Z","title":"Subprojective Banach spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4231","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":"sha256:69a6720acbc67e52e2ef550972b3553cf71db0a70e9005f1b2255f2e5402c1d2","target":"record","created_at":"2026-05-18T03:01:55Z","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":"51ab670d32ff79434d9ed67a890880d3e7611c0f83766cb5495d6b4b8d1e98b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-01-17T03:13:56Z","title_canon_sha256":"e61b28214728c2b2a8d633eafac6a4c5e4d43acd5576af5913bdb5bd30061806"},"schema_version":"1.0","source":{"id":"1401.4231","kind":"arxiv","version":1}},"canonical_sha256":"736b9bc40de348c5eda4534edde56369bdd3ce2b1c2bdbe30169c47547e5d67c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"736b9bc40de348c5eda4534edde56369bdd3ce2b1c2bdbe30169c47547e5d67c","first_computed_at":"2026-05-18T03:01:55.660722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:55.660722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ux+LSmxNC/Mh+JL/aQne1GOwZK0dD9mIqX+ijh70W/O0vzmRVXncXhnlini3oFLvei76gcHkXYxwDpFliWIPAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:55.661470Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.4231","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69a6720acbc67e52e2ef550972b3553cf71db0a70e9005f1b2255f2e5402c1d2","sha256:16d9c7f8d0423874e8f86ab748884f970054d093a603a7ea7dd3eb801fa3d961"],"state_sha256":"b695a81effd6d75bba1310108aca8c7e0a55a97c8a53754b2ac1f435e423645c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pG1/OnRWx4r/FCJDn2Mi4sFJR58C3F6X3JLw+s8VClr3S8FreFlrIjQrnCdUKnxeE0Qsi/m7CcS+MQojSyF9Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T15:55:59.860181Z","bundle_sha256":"7587cc7f3e6b99386561049b8861a56dc4a070e9a3a74badd8a6217f1c9b3b52"}}