{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:IP43TCEIGIISHY2JRE4TKZJNG5","short_pith_number":"pith:IP43TCEI","canonical_record":{"source":{"id":"1210.3424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-12T03:11:36Z","cross_cats_sorted":[],"title_canon_sha256":"8e6d3424477de082ead311bbcdbea8241d9cea3fddc4937979f63da024885506","abstract_canon_sha256":"fea0326ea1f1fc85f102161454ddd8d5248ede611d970999dbf150b1fbd6e509"},"schema_version":"1.0"},"canonical_sha256":"43f9b98888321123e349893935652d375ffe6ae9409c0acb637723debd68f34d","source":{"kind":"arxiv","id":"1210.3424","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3424","created_at":"2026-05-18T03:43:19Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3424v1","created_at":"2026-05-18T03:43:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3424","created_at":"2026-05-18T03:43:19Z"},{"alias_kind":"pith_short_12","alias_value":"IP43TCEIGIIS","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IP43TCEIGIISHY2J","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IP43TCEI","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:IP43TCEIGIISHY2JRE4TKZJNG5","target":"record","payload":{"canonical_record":{"source":{"id":"1210.3424","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-12T03:11:36Z","cross_cats_sorted":[],"title_canon_sha256":"8e6d3424477de082ead311bbcdbea8241d9cea3fddc4937979f63da024885506","abstract_canon_sha256":"fea0326ea1f1fc85f102161454ddd8d5248ede611d970999dbf150b1fbd6e509"},"schema_version":"1.0"},"canonical_sha256":"43f9b98888321123e349893935652d375ffe6ae9409c0acb637723debd68f34d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:19.922226Z","signature_b64":"pqykPqPdq28kr81HReVDBxw5a2XTJ7dEc/rFoX/5BG0qZoeUW36Xh2UZuMOAlgK+CCc9cVNULDxp8T5s2XIGDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"43f9b98888321123e349893935652d375ffe6ae9409c0acb637723debd68f34d","last_reissued_at":"2026-05-18T03:43:19.921632Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:19.921632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.3424","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":"2026-05-18T03:43:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pt+CmVUkhH3SHfFlAERkFxgDii9c4no5A0YasIWExrmpH8mkqGVrNlq0qdWGeNAYNNx+rzsK4fZImeGt4ZdcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T02:47:15.172257Z"},"content_sha256":"19162e67de570ba4f074ee6c8dd3083a7858f7d714f76270609fa1c3c5ab779f","schema_version":"1.0","event_id":"sha256:19162e67de570ba4f074ee6c8dd3083a7858f7d714f76270609fa1c3c5ab779f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:IP43TCEIGIISHY2JRE4TKZJNG5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A sufficient condition of violating the SPA conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Bang-Hai Wang, Dong-Yang Long","submitted_at":"2012-10-12T03:11:36Z","abstract_excerpt":"Based on the general form of entanglement witnesses constructed from separable states, we first show a sufficient condition of violating the structural physical approximation (SPA) conjecture [Phys. Rev. A 78, 062105 (2008)]. Then we discuss the SPA conjecture for decomposable entanglement witnesses. Moreover, we make geometric illustrations of the connection between entanglement witnesses and the sets of quantum states, separable states, and entangled states comparing with planes and vectors in Euclidean space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3424","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":"2026-05-18T03:43:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cxwQGheT7WzNjkm0ZMwmUD91/G+qNl9+PbkDcA6/FhElY0ZCFVcZz/buNT0270/CpFb916dfYHAEnGwI5BPwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T02:47:15.173166Z"},"content_sha256":"91be147f835e4cb0dc28434c3073a28bdeb25892952408ecb84a078afc957e5c","schema_version":"1.0","event_id":"sha256:91be147f835e4cb0dc28434c3073a28bdeb25892952408ecb84a078afc957e5c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IP43TCEIGIISHY2JRE4TKZJNG5/bundle.json","state_url":"https://pith.science/pith/IP43TCEIGIISHY2JRE4TKZJNG5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IP43TCEIGIISHY2JRE4TKZJNG5/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":"2026-06-06T02:47:15Z","links":{"resolver":"https://pith.science/pith/IP43TCEIGIISHY2JRE4TKZJNG5","bundle":"https://pith.science/pith/IP43TCEIGIISHY2JRE4TKZJNG5/bundle.json","state":"https://pith.science/pith/IP43TCEIGIISHY2JRE4TKZJNG5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IP43TCEIGIISHY2JRE4TKZJNG5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:IP43TCEIGIISHY2JRE4TKZJNG5","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":"fea0326ea1f1fc85f102161454ddd8d5248ede611d970999dbf150b1fbd6e509","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-12T03:11:36Z","title_canon_sha256":"8e6d3424477de082ead311bbcdbea8241d9cea3fddc4937979f63da024885506"},"schema_version":"1.0","source":{"id":"1210.3424","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3424","created_at":"2026-05-18T03:43:19Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3424v1","created_at":"2026-05-18T03:43:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3424","created_at":"2026-05-18T03:43:19Z"},{"alias_kind":"pith_short_12","alias_value":"IP43TCEIGIIS","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"IP43TCEIGIISHY2J","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"IP43TCEI","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:91be147f835e4cb0dc28434c3073a28bdeb25892952408ecb84a078afc957e5c","target":"graph","created_at":"2026-05-18T03:43:19Z","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 the general form of entanglement witnesses constructed from separable states, we first show a sufficient condition of violating the structural physical approximation (SPA) conjecture [Phys. Rev. A 78, 062105 (2008)]. Then we discuss the SPA conjecture for decomposable entanglement witnesses. Moreover, we make geometric illustrations of the connection between entanglement witnesses and the sets of quantum states, separable states, and entangled states comparing with planes and vectors in Euclidean space.","authors_text":"Bang-Hai Wang, Dong-Yang Long","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-12T03:11:36Z","title":"A sufficient condition of violating the SPA conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3424","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":"sha256:19162e67de570ba4f074ee6c8dd3083a7858f7d714f76270609fa1c3c5ab779f","target":"record","created_at":"2026-05-18T03:43:19Z","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":"fea0326ea1f1fc85f102161454ddd8d5248ede611d970999dbf150b1fbd6e509","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-10-12T03:11:36Z","title_canon_sha256":"8e6d3424477de082ead311bbcdbea8241d9cea3fddc4937979f63da024885506"},"schema_version":"1.0","source":{"id":"1210.3424","kind":"arxiv","version":1}},"canonical_sha256":"43f9b98888321123e349893935652d375ffe6ae9409c0acb637723debd68f34d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"43f9b98888321123e349893935652d375ffe6ae9409c0acb637723debd68f34d","first_computed_at":"2026-05-18T03:43:19.921632Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:19.921632Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pqykPqPdq28kr81HReVDBxw5a2XTJ7dEc/rFoX/5BG0qZoeUW36Xh2UZuMOAlgK+CCc9cVNULDxp8T5s2XIGDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:19.922226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3424","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:19162e67de570ba4f074ee6c8dd3083a7858f7d714f76270609fa1c3c5ab779f","sha256:91be147f835e4cb0dc28434c3073a28bdeb25892952408ecb84a078afc957e5c"],"state_sha256":"cb27d8de456cf8ea2e5229b62f81a6545b61bd873c80741e127d6ce12d032a5f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQfchGv3FWTNjtLUVi9g3LlvkkrTGBOrz6vLXcV7EbKfiAzhElr2C+YfpFp+TpX8GX6pSVh86AkGnmB4/XAdBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T02:47:15.176934Z","bundle_sha256":"8def691992caa91ec3cba28554f6b50d99e2b63d05b9da36a32a604f895d025a"}}