{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Q4JGH23YJA3NLTBARGGNVOKJKF","short_pith_number":"pith:Q4JGH23Y","canonical_record":{"source":{"id":"1507.05709","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-21T05:03:50Z","cross_cats_sorted":[],"title_canon_sha256":"45e864e92d90e4ef5e0dc3e8fe11e1c34d1e98611aa5a3a9024ea5aeea0e7988","abstract_canon_sha256":"f4c3f59e637c3fae9ae74c3b746f3733fda1fad3afe39d7d0483aa7b0a6100dc"},"schema_version":"1.0"},"canonical_sha256":"871263eb784836d5cc20898cdab9495178201a413813de308704c3a5a962d27c","source":{"kind":"arxiv","id":"1507.05709","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05709","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05709v3","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05709","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"Q4JGH23YJA3N","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q4JGH23YJA3NLTBA","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q4JGH23Y","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Q4JGH23YJA3NLTBARGGNVOKJKF","target":"record","payload":{"canonical_record":{"source":{"id":"1507.05709","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-21T05:03:50Z","cross_cats_sorted":[],"title_canon_sha256":"45e864e92d90e4ef5e0dc3e8fe11e1c34d1e98611aa5a3a9024ea5aeea0e7988","abstract_canon_sha256":"f4c3f59e637c3fae9ae74c3b746f3733fda1fad3afe39d7d0483aa7b0a6100dc"},"schema_version":"1.0"},"canonical_sha256":"871263eb784836d5cc20898cdab9495178201a413813de308704c3a5a962d27c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:09:12.693471Z","signature_b64":"zjbpJSjX7Nd4YHOXwFhN/io0guGTAj9iu+j8NkQEBPAb8prprV8MfGmF6oYKBOom0GGAw1cKTk5bMBQnR1XNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"871263eb784836d5cc20898cdab9495178201a413813de308704c3a5a962d27c","last_reissued_at":"2026-05-18T01:09:12.692790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:09:12.692790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.05709","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:09:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VX5GkcvMrWQ9z44twSPosuedCAVdPmuf4jWyrCPYJFdXi3eBK+PLfL9ZUEqZkvXzV8m8Yt+CBba7fOIk4ir/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T17:24:30.607786Z"},"content_sha256":"58fa678f13056477e4dc246a936856bb93d760b110f693bd7eced78e6c8a997c","schema_version":"1.0","event_id":"sha256:58fa678f13056477e4dc246a936856bb93d760b110f693bd7eced78e6c8a997c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Q4JGH23YJA3NLTBARGGNVOKJKF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Separable determination of (generalized-)lushness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marek Cuth","submitted_at":"2015-07-21T05:03:50Z","abstract_excerpt":"We prove that every Asplund lush space is generalized-lush using the method of separable reduction. This gives a partial positive answer to a question by Jan-David Hardtke."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05709","kind":"arxiv","version":3},"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":"2026-05-18T01:09:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R1tcQX0NNdc9MRhy5ieVQxNopc4ZEWBaEnyRBP/s5+EgRnXgrhdP/2hEwhbF/avlE/18MPe/1HC+p93kNRTgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T17:24:30.608130Z"},"content_sha256":"06422cb8535473192ff6e75dde3f15f1704e9dd6b8a9d4d66cdfe043e3f7769c","schema_version":"1.0","event_id":"sha256:06422cb8535473192ff6e75dde3f15f1704e9dd6b8a9d4d66cdfe043e3f7769c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4JGH23YJA3NLTBARGGNVOKJKF/bundle.json","state_url":"https://pith.science/pith/Q4JGH23YJA3NLTBARGGNVOKJKF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4JGH23YJA3NLTBARGGNVOKJKF/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":"2026-06-20T17:24:30Z","links":{"resolver":"https://pith.science/pith/Q4JGH23YJA3NLTBARGGNVOKJKF","bundle":"https://pith.science/pith/Q4JGH23YJA3NLTBARGGNVOKJKF/bundle.json","state":"https://pith.science/pith/Q4JGH23YJA3NLTBARGGNVOKJKF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4JGH23YJA3NLTBARGGNVOKJKF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Q4JGH23YJA3NLTBARGGNVOKJKF","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":"f4c3f59e637c3fae9ae74c3b746f3733fda1fad3afe39d7d0483aa7b0a6100dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-21T05:03:50Z","title_canon_sha256":"45e864e92d90e4ef5e0dc3e8fe11e1c34d1e98611aa5a3a9024ea5aeea0e7988"},"schema_version":"1.0","source":{"id":"1507.05709","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.05709","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"arxiv_version","alias_value":"1507.05709v3","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.05709","created_at":"2026-05-18T01:09:12Z"},{"alias_kind":"pith_short_12","alias_value":"Q4JGH23YJA3N","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"Q4JGH23YJA3NLTBA","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"Q4JGH23Y","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:06422cb8535473192ff6e75dde3f15f1704e9dd6b8a9d4d66cdfe043e3f7769c","target":"graph","created_at":"2026-05-18T01:09:12Z","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 prove that every Asplund lush space is generalized-lush using the method of separable reduction. This gives a partial positive answer to a question by Jan-David Hardtke.","authors_text":"Marek Cuth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-21T05:03:50Z","title":"Separable determination of (generalized-)lushness"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05709","kind":"arxiv","version":3},"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":"sha256:58fa678f13056477e4dc246a936856bb93d760b110f693bd7eced78e6c8a997c","target":"record","created_at":"2026-05-18T01:09:12Z","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":"f4c3f59e637c3fae9ae74c3b746f3733fda1fad3afe39d7d0483aa7b0a6100dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-07-21T05:03:50Z","title_canon_sha256":"45e864e92d90e4ef5e0dc3e8fe11e1c34d1e98611aa5a3a9024ea5aeea0e7988"},"schema_version":"1.0","source":{"id":"1507.05709","kind":"arxiv","version":3}},"canonical_sha256":"871263eb784836d5cc20898cdab9495178201a413813de308704c3a5a962d27c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"871263eb784836d5cc20898cdab9495178201a413813de308704c3a5a962d27c","first_computed_at":"2026-05-18T01:09:12.692790Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:12.692790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zjbpJSjX7Nd4YHOXwFhN/io0guGTAj9iu+j8NkQEBPAb8prprV8MfGmF6oYKBOom0GGAw1cKTk5bMBQnR1XNAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:12.693471Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.05709","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58fa678f13056477e4dc246a936856bb93d760b110f693bd7eced78e6c8a997c","sha256:06422cb8535473192ff6e75dde3f15f1704e9dd6b8a9d4d66cdfe043e3f7769c"],"state_sha256":"2d1fe30bf9d4ad4c788d4ebbddae8b5aa6ca608a5cd29da0bf072036f2187e1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5Z4JaDbQCNB1FoIZtxWhastLZVyJ5zhtw15ivYnIy/ZC1cOT338Xt4JYN8QsLYUAUU8NUXPq9c9DyRVAnLrvCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T17:24:30.610043Z","bundle_sha256":"b801b1f85401737954ab7af051cb240c8ab0bc1f595e49be4c90d6ed1ce4607a"}}