{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GVQJG56RRX7PWXCASCVSWAMEBR","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":"359fc0fcb346ea23d226a9421e05f22c657accd7a3096b2c9ec1a5f0df4245a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-07-03T22:54:56Z","title_canon_sha256":"57047a1bb126048178cbdb5fe029f69c53b2031c73c3993342c40076928695ca"},"schema_version":"1.0","source":{"id":"1107.0505","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0505","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0505v3","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0505","created_at":"2026-05-18T04:05:57Z"},{"alias_kind":"pith_short_12","alias_value":"GVQJG56RRX7P","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GVQJG56RRX7PWXCA","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GVQJG56R","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:dee5596da9da4f8e756f1b53558844a915837cfd9f3ee265dee636442257c337","target":"graph","created_at":"2026-05-18T04:05:57Z","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":"One of the unsolved problems in the characterization of the optimal entanglement witnesses is the existence of optimal witnesses acting on bipartite Hilbert spaces H_{m,n}=C^m\\otimes C^n such that the product vectors obeying <e,f|W|e,f>=0 do not span H_{m,n}. So far, the only known examples of such witnesses were found among indecomposable witnesses, one of them being the witness corresponding to the Choi map. However, it remains an open question whether decomposable witnesses exist without the property of spanning. Here we answer this question affirmatively, providing systematic examples of s","authors_text":"Gniewomir Sarbicki, Maciej Lewenstein, Remigiusz Augusiak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-07-03T22:54:56Z","title":"Optimal decomposable witnesses without the spanning property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0505","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":"sha256:73ded45a0704a7373be138c2a15d1ae8cb808824cd62a17456f9c29d3c6c1338","target":"record","created_at":"2026-05-18T04:05:57Z","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":"359fc0fcb346ea23d226a9421e05f22c657accd7a3096b2c9ec1a5f0df4245a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-07-03T22:54:56Z","title_canon_sha256":"57047a1bb126048178cbdb5fe029f69c53b2031c73c3993342c40076928695ca"},"schema_version":"1.0","source":{"id":"1107.0505","kind":"arxiv","version":3}},"canonical_sha256":"35609377d18dfefb5c4090ab2b01840c65cd4fd045cb27b9c995650ba5066f09","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"35609377d18dfefb5c4090ab2b01840c65cd4fd045cb27b9c995650ba5066f09","first_computed_at":"2026-05-18T04:05:57.602307Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:57.602307Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UomIVoAheRVx2RUDI/5n2wTpNcgFCdLq2BxwN3AIcOpHSJstevbtypAPzlyK8hTQVn4zeAQlzhB/9oETMxoHCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:57.602843Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0505","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:73ded45a0704a7373be138c2a15d1ae8cb808824cd62a17456f9c29d3c6c1338","sha256:dee5596da9da4f8e756f1b53558844a915837cfd9f3ee265dee636442257c337"],"state_sha256":"7a9c1cb380e7459de7d04352f3d3569363f61eb6061ba0f35879b4ac64f6e777"}