{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:3TR3OROGZFVXKAXQSIMVKEXH7B","short_pith_number":"pith:3TR3OROG","canonical_record":{"source":{"id":"1508.02065","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-09T18:26:35Z","cross_cats_sorted":[],"title_canon_sha256":"40a680e5875f2d20dc9f72950c73af2acb85e0df980f14069b8630cd9039bd7b","abstract_canon_sha256":"00f458169f5b478b9c1145e12bb28fde47501bbdd1d297697697da5e95179e2e"},"schema_version":"1.0"},"canonical_sha256":"dce3b745c6c96b7502f092195512e7f858fb5e536caf8fc75248b1b0d1221c48","source":{"kind":"arxiv","id":"1508.02065","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02065","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02065v3","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02065","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"3TR3OROGZFVX","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3TR3OROGZFVXKAXQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3TR3OROG","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:3TR3OROGZFVXKAXQSIMVKEXH7B","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02065","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-09T18:26:35Z","cross_cats_sorted":[],"title_canon_sha256":"40a680e5875f2d20dc9f72950c73af2acb85e0df980f14069b8630cd9039bd7b","abstract_canon_sha256":"00f458169f5b478b9c1145e12bb28fde47501bbdd1d297697697da5e95179e2e"},"schema_version":"1.0"},"canonical_sha256":"dce3b745c6c96b7502f092195512e7f858fb5e536caf8fc75248b1b0d1221c48","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:54.243404Z","signature_b64":"tmfceC3iSf/dQLuQG41VMMX7JWGFl9bNKamCwqSCpWBUtsjE81/JqOCrfzE8rdIxMrzwDZwAB06sExhT5GmdCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dce3b745c6c96b7502f092195512e7f858fb5e536caf8fc75248b1b0d1221c48","last_reissued_at":"2026-05-18T01:34:54.242697Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:54.242697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02065","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":"2026-05-18T01:34:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"16dkWg9GTzVaBzROMNehY7QEin4Jyf7mPje5DUjBSr7wfqt6Nw0El1ah7CL1eMv9TTJiCo9/cLtviN/yVfpXDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T02:27:50.881239Z"},"content_sha256":"aacbfe9bc4ed9f6b77d2865f88cf04caaaebe820f2a99af36ed9dc6cfbd1fcdb","schema_version":"1.0","event_id":"sha256:aacbfe9bc4ed9f6b77d2865f88cf04caaaebe820f2a99af36ed9dc6cfbd1fcdb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:3TR3OROGZFVXKAXQSIMVKEXH7B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An ordinal index characterizing weak compactness of operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Ryan M. Causey","submitted_at":"2015-08-09T18:26:35Z","abstract_excerpt":"We introduce an ordinal index which characterizes weak compactness of operators between Banach spaces. We study when classes consisting of operators having bounded index form a closed ideal, the distinctness of the classes, and the descriptive set theoretic properties of this index."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02065","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":"2026-05-18T01:34:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tKv5p900pNTziviS50vAaiTO+D/MDddBgWTYaTQrUOyFMpEfwiyXCapIt/HlCajxyn/nJBM3sExYR0VRTKCZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-23T02:27:50.881950Z"},"content_sha256":"4b5eb0d315f5f7c5aa49621b26af1bace82d4d29a96627fca0a2c7bd99365629","schema_version":"1.0","event_id":"sha256:4b5eb0d315f5f7c5aa49621b26af1bace82d4d29a96627fca0a2c7bd99365629"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3TR3OROGZFVXKAXQSIMVKEXH7B/bundle.json","state_url":"https://pith.science/pith/3TR3OROGZFVXKAXQSIMVKEXH7B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3TR3OROGZFVXKAXQSIMVKEXH7B/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":"2026-05-23T02:27:50Z","links":{"resolver":"https://pith.science/pith/3TR3OROGZFVXKAXQSIMVKEXH7B","bundle":"https://pith.science/pith/3TR3OROGZFVXKAXQSIMVKEXH7B/bundle.json","state":"https://pith.science/pith/3TR3OROGZFVXKAXQSIMVKEXH7B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3TR3OROGZFVXKAXQSIMVKEXH7B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3TR3OROGZFVXKAXQSIMVKEXH7B","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":"00f458169f5b478b9c1145e12bb28fde47501bbdd1d297697697da5e95179e2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-09T18:26:35Z","title_canon_sha256":"40a680e5875f2d20dc9f72950c73af2acb85e0df980f14069b8630cd9039bd7b"},"schema_version":"1.0","source":{"id":"1508.02065","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02065","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02065v3","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02065","created_at":"2026-05-18T01:34:54Z"},{"alias_kind":"pith_short_12","alias_value":"3TR3OROGZFVX","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3TR3OROGZFVXKAXQ","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3TR3OROG","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:4b5eb0d315f5f7c5aa49621b26af1bace82d4d29a96627fca0a2c7bd99365629","target":"graph","created_at":"2026-05-18T01:34:54Z","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 introduce an ordinal index which characterizes weak compactness of operators between Banach spaces. We study when classes consisting of operators having bounded index form a closed ideal, the distinctness of the classes, and the descriptive set theoretic properties of this index.","authors_text":"Ryan M. Causey","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-09T18:26:35Z","title":"An ordinal index characterizing weak compactness of operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02065","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:aacbfe9bc4ed9f6b77d2865f88cf04caaaebe820f2a99af36ed9dc6cfbd1fcdb","target":"record","created_at":"2026-05-18T01:34:54Z","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":"00f458169f5b478b9c1145e12bb28fde47501bbdd1d297697697da5e95179e2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-09T18:26:35Z","title_canon_sha256":"40a680e5875f2d20dc9f72950c73af2acb85e0df980f14069b8630cd9039bd7b"},"schema_version":"1.0","source":{"id":"1508.02065","kind":"arxiv","version":3}},"canonical_sha256":"dce3b745c6c96b7502f092195512e7f858fb5e536caf8fc75248b1b0d1221c48","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dce3b745c6c96b7502f092195512e7f858fb5e536caf8fc75248b1b0d1221c48","first_computed_at":"2026-05-18T01:34:54.242697Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:54.242697Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tmfceC3iSf/dQLuQG41VMMX7JWGFl9bNKamCwqSCpWBUtsjE81/JqOCrfzE8rdIxMrzwDZwAB06sExhT5GmdCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:54.243404Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02065","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aacbfe9bc4ed9f6b77d2865f88cf04caaaebe820f2a99af36ed9dc6cfbd1fcdb","sha256:4b5eb0d315f5f7c5aa49621b26af1bace82d4d29a96627fca0a2c7bd99365629"],"state_sha256":"da9aa0c63079a5e9e9f17d70942e3bf55737b725c489f794348fa05da9a9551a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SCIHTBfFm8HT8Jq68CdCOJHU3JfwtteZfel08qYu2NhiuytIJQ81mKlHNrqtBq3kZ1DNdiZnq7qxZ+OIaP1fBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T02:27:50.885534Z","bundle_sha256":"0f2b5ecf4f406f244771f22e2e2dd05c95af92e4ae9bccfd9fd3f0fd9cebc36c"}}