{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:OFUJVFMOYGWDQ27C4TBGZSDDIU","short_pith_number":"pith:OFUJVFMO","canonical_record":{"source":{"id":"1504.08223","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-30T13:47:00Z","cross_cats_sorted":[],"title_canon_sha256":"fb08c9d14c5712101dc8133a3fe3dd64438f5f2d844d4b6c03b139aa21b3a2ae","abstract_canon_sha256":"5be0b78d2afe33d844b979a8daeb657c6fc6416d0327ba9e94b395ac916599f7"},"schema_version":"1.0"},"canonical_sha256":"71689a958ec1ac386be2e4c26cc863452c70b4f997a44e032e5bf514f737203c","source":{"kind":"arxiv","id":"1504.08223","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.08223","created_at":"2026-05-18T01:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"1504.08223v1","created_at":"2026-05-18T01:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08223","created_at":"2026-05-18T01:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"OFUJVFMOYGWD","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OFUJVFMOYGWDQ27C","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OFUJVFMO","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:OFUJVFMOYGWDQ27C4TBGZSDDIU","target":"record","payload":{"canonical_record":{"source":{"id":"1504.08223","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-30T13:47:00Z","cross_cats_sorted":[],"title_canon_sha256":"fb08c9d14c5712101dc8133a3fe3dd64438f5f2d844d4b6c03b139aa21b3a2ae","abstract_canon_sha256":"5be0b78d2afe33d844b979a8daeb657c6fc6416d0327ba9e94b395ac916599f7"},"schema_version":"1.0"},"canonical_sha256":"71689a958ec1ac386be2e4c26cc863452c70b4f997a44e032e5bf514f737203c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:03.687854Z","signature_b64":"5fAXVQlQqZJ9LG0Qm/AxsFRtXoJLoPpMFMMY6/o/s8pCg7KZqdk6Rojo3qoGPs60Cyb05TFY5SsxK8mja8dxAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"71689a958ec1ac386be2e4c26cc863452c70b4f997a44e032e5bf514f737203c","last_reissued_at":"2026-05-18T01:19:03.687346Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:03.687346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.08223","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":"2026-05-18T01:19:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jeGazY8fJRRYaS2uJMV6BZZz14QCoH9fRxXWRUVtuyYHW8TmWxWpAvSBDuoOE+jOf5gDPDoawC0gpLu/+PgTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:57:57.537632Z"},"content_sha256":"0cb4cd3c32b10303e8db618fb9c506b01131d42a882cd7afb5949ec288b3d751","schema_version":"1.0","event_id":"sha256:0cb4cd3c32b10303e8db618fb9c506b01131d42a882cd7afb5949ec288b3d751"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:OFUJVFMOYGWDQ27C4TBGZSDDIU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the structure of separable $\\mathcal{L}_\\infty$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ioannis Gasparis, Pavlos Motakis, Spiros A. Argyros","submitted_at":"2015-04-30T13:47:00Z","abstract_excerpt":"Based on a construction method introduced by J. Bourgain and F. Delbaen, we give a general definition of a Bourgain-Delbaen space and prove that every infinite dimensional separable $\\mathcal{L}_\\infty$-space is isomorphic to such a space. Furthermore, we provide an example of a $\\mathcal{L}_\\infty$ and asymptotic $c_0$ space not containing $c_0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08223","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":"2026-05-18T01:19:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z7xOPaV8RUMOLC1S80DxQ0mYu0AAdFTOxxeXAxmcu5PS6R4JJQl2+wCT32qbJ7auooVBv/1zszJDwBaifSpNCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:57:57.538281Z"},"content_sha256":"72c3414be286b6d2b0d989e1e66f79273266763a83267df2c332b140a1ccf6dc","schema_version":"1.0","event_id":"sha256:72c3414be286b6d2b0d989e1e66f79273266763a83267df2c332b140a1ccf6dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OFUJVFMOYGWDQ27C4TBGZSDDIU/bundle.json","state_url":"https://pith.science/pith/OFUJVFMOYGWDQ27C4TBGZSDDIU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OFUJVFMOYGWDQ27C4TBGZSDDIU/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":"2026-05-26T12:57:57Z","links":{"resolver":"https://pith.science/pith/OFUJVFMOYGWDQ27C4TBGZSDDIU","bundle":"https://pith.science/pith/OFUJVFMOYGWDQ27C4TBGZSDDIU/bundle.json","state":"https://pith.science/pith/OFUJVFMOYGWDQ27C4TBGZSDDIU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OFUJVFMOYGWDQ27C4TBGZSDDIU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:OFUJVFMOYGWDQ27C4TBGZSDDIU","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":"5be0b78d2afe33d844b979a8daeb657c6fc6416d0327ba9e94b395ac916599f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-30T13:47:00Z","title_canon_sha256":"fb08c9d14c5712101dc8133a3fe3dd64438f5f2d844d4b6c03b139aa21b3a2ae"},"schema_version":"1.0","source":{"id":"1504.08223","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.08223","created_at":"2026-05-18T01:19:03Z"},{"alias_kind":"arxiv_version","alias_value":"1504.08223v1","created_at":"2026-05-18T01:19:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.08223","created_at":"2026-05-18T01:19:03Z"},{"alias_kind":"pith_short_12","alias_value":"OFUJVFMOYGWD","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"OFUJVFMOYGWDQ27C","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"OFUJVFMO","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:72c3414be286b6d2b0d989e1e66f79273266763a83267df2c332b140a1ccf6dc","target":"graph","created_at":"2026-05-18T01:19:03Z","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":"Based on a construction method introduced by J. Bourgain and F. Delbaen, we give a general definition of a Bourgain-Delbaen space and prove that every infinite dimensional separable $\\mathcal{L}_\\infty$-space is isomorphic to such a space. Furthermore, we provide an example of a $\\mathcal{L}_\\infty$ and asymptotic $c_0$ space not containing $c_0$.","authors_text":"Ioannis Gasparis, Pavlos Motakis, Spiros A. Argyros","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-30T13:47:00Z","title":"On the structure of separable $\\mathcal{L}_\\infty$-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08223","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":"sha256:0cb4cd3c32b10303e8db618fb9c506b01131d42a882cd7afb5949ec288b3d751","target":"record","created_at":"2026-05-18T01:19:03Z","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":"5be0b78d2afe33d844b979a8daeb657c6fc6416d0327ba9e94b395ac916599f7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-04-30T13:47:00Z","title_canon_sha256":"fb08c9d14c5712101dc8133a3fe3dd64438f5f2d844d4b6c03b139aa21b3a2ae"},"schema_version":"1.0","source":{"id":"1504.08223","kind":"arxiv","version":1}},"canonical_sha256":"71689a958ec1ac386be2e4c26cc863452c70b4f997a44e032e5bf514f737203c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"71689a958ec1ac386be2e4c26cc863452c70b4f997a44e032e5bf514f737203c","first_computed_at":"2026-05-18T01:19:03.687346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:19:03.687346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5fAXVQlQqZJ9LG0Qm/AxsFRtXoJLoPpMFMMY6/o/s8pCg7KZqdk6Rojo3qoGPs60Cyb05TFY5SsxK8mja8dxAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:19:03.687854Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.08223","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cb4cd3c32b10303e8db618fb9c506b01131d42a882cd7afb5949ec288b3d751","sha256:72c3414be286b6d2b0d989e1e66f79273266763a83267df2c332b140a1ccf6dc"],"state_sha256":"9d6eb5fa83adab2e55c52db422f23acc20ccda2a0244cc86d1158fc8b44dec53"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LUzM1XxMqIb1NtYXhjx1vqX63xc0MKXoDyopWei9eIvEdAySf8B/4rhuSti/Et8Ie9tEisXToQDsJ6he9mHjAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:57:57.541704Z","bundle_sha256":"555718e02f4ff35bd288ab1106ebf475f37269b81c8ecaf4ad76d0d89622016e"}}