{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VRBVI4444GQPFZ4WU7F5XB44NE","short_pith_number":"pith:VRBVI444","canonical_record":{"source":{"id":"1408.4033","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-18T15:06:44Z","cross_cats_sorted":[],"title_canon_sha256":"b7c4e4cd0efec16fd04121b35e7bd66daa757d57753f3b948a59f23f9fbd2f67","abstract_canon_sha256":"41b1dbb90d2d9046d62c726dd19d052d172f89aca5824159dd699f75acd712c3"},"schema_version":"1.0"},"canonical_sha256":"ac4354739ce1a0f2e796a7cbdb879c691bb25c1fb59426889d218e5b77fa2ef3","source":{"kind":"arxiv","id":"1408.4033","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4033","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4033v2","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4033","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"VRBVI4444GQP","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VRBVI4444GQPFZ4W","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VRBVI444","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VRBVI4444GQPFZ4WU7F5XB44NE","target":"record","payload":{"canonical_record":{"source":{"id":"1408.4033","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-18T15:06:44Z","cross_cats_sorted":[],"title_canon_sha256":"b7c4e4cd0efec16fd04121b35e7bd66daa757d57753f3b948a59f23f9fbd2f67","abstract_canon_sha256":"41b1dbb90d2d9046d62c726dd19d052d172f89aca5824159dd699f75acd712c3"},"schema_version":"1.0"},"canonical_sha256":"ac4354739ce1a0f2e796a7cbdb879c691bb25c1fb59426889d218e5b77fa2ef3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:46.507728Z","signature_b64":"GQvDEQb/9ycCBsa+3gOyFeTGf43vf+PeBfdhx5LkXR4ro3iTL/AyKLAsmwDGMkk5RVU3H82aZcxoE1gZM56ZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac4354739ce1a0f2e796a7cbdb879c691bb25c1fb59426889d218e5b77fa2ef3","last_reissued_at":"2026-05-18T01:05:46.507095Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:46.507095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.4033","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":"2026-05-18T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DE611SHEXC1oaf4LYdzccgNMuk/NhxEeBEkCkOqTR+on9RUQDHlTpH3/F/PPak8/sIwbgGcKqaImq7W+4doYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:47:28.719158Z"},"content_sha256":"8d10a6a86faef538c603f225c1cc9930fe22dbfbfc4d256372c11fb7e779dc79","schema_version":"1.0","event_id":"sha256:8d10a6a86faef538c603f225c1cc9930fe22dbfbfc4d256372c11fb7e779dc79"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VRBVI4444GQPFZ4WU7F5XB44NE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on non-unital absorbing extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"James Gabe","submitted_at":"2014-08-18T15:06:44Z","abstract_excerpt":"Elliott and Kucerovsky stated that a non-unital extension of separable $C^\\ast$-algebras with a stable ideal, is nuclearly absorbing if and only if the extension is purely large. However, their proof was flawed. We give a counter example to their theorem as stated, but establish an equivalent formulation of nuclear absorption under a very mild additional assumption to being purely large. In particular, if the quotient algebra is non-unital, then we show that the original theorem applies. We also examine how this effects results in classification theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4033","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":"2026-05-18T01:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HPO6ZULuLXqC829fhEbc9QrqBklZGpnrusYzRQy8rcLRA1Pkpqnk/Bu9ZRV0Mxl2qltpECwQnKcfR+c3WQCABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:47:28.719521Z"},"content_sha256":"c18c2bbdd05c1d170b5ac878a23754e482893bafe37268f90f4e159675ce8be9","schema_version":"1.0","event_id":"sha256:c18c2bbdd05c1d170b5ac878a23754e482893bafe37268f90f4e159675ce8be9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VRBVI4444GQPFZ4WU7F5XB44NE/bundle.json","state_url":"https://pith.science/pith/VRBVI4444GQPFZ4WU7F5XB44NE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VRBVI4444GQPFZ4WU7F5XB44NE/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":"2026-06-24T19:47:28Z","links":{"resolver":"https://pith.science/pith/VRBVI4444GQPFZ4WU7F5XB44NE","bundle":"https://pith.science/pith/VRBVI4444GQPFZ4WU7F5XB44NE/bundle.json","state":"https://pith.science/pith/VRBVI4444GQPFZ4WU7F5XB44NE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VRBVI4444GQPFZ4WU7F5XB44NE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VRBVI4444GQPFZ4WU7F5XB44NE","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":"41b1dbb90d2d9046d62c726dd19d052d172f89aca5824159dd699f75acd712c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-18T15:06:44Z","title_canon_sha256":"b7c4e4cd0efec16fd04121b35e7bd66daa757d57753f3b948a59f23f9fbd2f67"},"schema_version":"1.0","source":{"id":"1408.4033","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4033","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4033v2","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4033","created_at":"2026-05-18T01:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"VRBVI4444GQP","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VRBVI4444GQPFZ4W","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VRBVI444","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:c18c2bbdd05c1d170b5ac878a23754e482893bafe37268f90f4e159675ce8be9","target":"graph","created_at":"2026-05-18T01:05:46Z","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":"Elliott and Kucerovsky stated that a non-unital extension of separable $C^\\ast$-algebras with a stable ideal, is nuclearly absorbing if and only if the extension is purely large. However, their proof was flawed. We give a counter example to their theorem as stated, but establish an equivalent formulation of nuclear absorption under a very mild additional assumption to being purely large. In particular, if the quotient algebra is non-unital, then we show that the original theorem applies. We also examine how this effects results in classification theory.","authors_text":"James Gabe","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-18T15:06:44Z","title":"A note on non-unital absorbing extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4033","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":"sha256:8d10a6a86faef538c603f225c1cc9930fe22dbfbfc4d256372c11fb7e779dc79","target":"record","created_at":"2026-05-18T01:05:46Z","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":"41b1dbb90d2d9046d62c726dd19d052d172f89aca5824159dd699f75acd712c3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-08-18T15:06:44Z","title_canon_sha256":"b7c4e4cd0efec16fd04121b35e7bd66daa757d57753f3b948a59f23f9fbd2f67"},"schema_version":"1.0","source":{"id":"1408.4033","kind":"arxiv","version":2}},"canonical_sha256":"ac4354739ce1a0f2e796a7cbdb879c691bb25c1fb59426889d218e5b77fa2ef3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac4354739ce1a0f2e796a7cbdb879c691bb25c1fb59426889d218e5b77fa2ef3","first_computed_at":"2026-05-18T01:05:46.507095Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:46.507095Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GQvDEQb/9ycCBsa+3gOyFeTGf43vf+PeBfdhx5LkXR4ro3iTL/AyKLAsmwDGMkk5RVU3H82aZcxoE1gZM56ZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:46.507728Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4033","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d10a6a86faef538c603f225c1cc9930fe22dbfbfc4d256372c11fb7e779dc79","sha256:c18c2bbdd05c1d170b5ac878a23754e482893bafe37268f90f4e159675ce8be9"],"state_sha256":"bbc9e40d6f894dd7ea165575af66080416ae33e084ae3d4516660665f8299f54"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yl39C5CH1qV6mqfj6P6WXGkz7KEVdHB6WvvZXbh4PySIzlie/kDIKZtGrqbwomZq4ktAWhqrDVYXa2kEzvOTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:47:28.721498Z","bundle_sha256":"d33f0a4ab3d4e1295d4382a443516e8aa5aa03b84e8114f9c74a962819dd34dc"}}