{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:5VQUZEPHOD7W4OFIMLXNGLFLP5","short_pith_number":"pith:5VQUZEPH","schema_version":"1.0","canonical_sha256":"ed614c91e770ff6e38a862eed32cab7f4f7d86ea622b0814934b3311dc5d1606","source":{"kind":"arxiv","id":"2501.07084","version":3},"attestation_state":"computed","paper":{"title":"The exact convex roof for GHZ-W mixtures for three qubits and beyond","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Andreas Osterloh","submitted_at":"2025-01-13T06:40:36Z","abstract_excerpt":"I present an exact solution for the convex roof of the square root of the threetangle for rank two density matrices and for all states within the Bloch sphere. Aside the formerly known two tetrahedra it contains three additional optimal tetrahedra and connecting triangular optimal decompositions. The remaining optimal decompositions are one-dimensional. Optimal decompositions are proved to contain as many states from the zero-polytope as possible, a property that is called zero-state locking; it will be the working horse throughout this work. In addition, an inequality is derived which decides"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2501.07084","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2025-01-13T06:40:36Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"d7757948c5820a62ca71bf011c92304f7bc79b5894676ecaa500eb30684707fe","abstract_canon_sha256":"06051f620fc5a834823ada2f875d2e8600e416c25b646fb1ab421e6f927ab9c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-26T00:15:21.850265Z","signature_b64":"B0NUwZfdjycUC3J+0MbZs64Udql1Hpi/WEbJ9E+3Xx+H4J5yu1oij1hFX9cYF+hGXGD3AgYdI7yQrjLHygMzDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ed614c91e770ff6e38a862eed32cab7f4f7d86ea622b0814934b3311dc5d1606","last_reissued_at":"2026-06-26T00:15:21.849781Z","signature_status":"signed_v1","first_computed_at":"2026-06-26T00:15:21.849781Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The exact convex roof for GHZ-W mixtures for three qubits and beyond","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Andreas Osterloh","submitted_at":"2025-01-13T06:40:36Z","abstract_excerpt":"I present an exact solution for the convex roof of the square root of the threetangle for rank two density matrices and for all states within the Bloch sphere. Aside the formerly known two tetrahedra it contains three additional optimal tetrahedra and connecting triangular optimal decompositions. The remaining optimal decompositions are one-dimensional. Optimal decompositions are proved to contain as many states from the zero-polytope as possible, a property that is called zero-state locking; it will be the working horse throughout this work. In addition, an inequality is derived which decides"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.07084","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.07084/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2501.07084","created_at":"2026-06-26T00:15:21.849841+00:00"},{"alias_kind":"arxiv_version","alias_value":"2501.07084v3","created_at":"2026-06-26T00:15:21.849841+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.07084","created_at":"2026-06-26T00:15:21.849841+00:00"},{"alias_kind":"pith_short_12","alias_value":"5VQUZEPHOD7W","created_at":"2026-06-26T00:15:21.849841+00:00"},{"alias_kind":"pith_short_16","alias_value":"5VQUZEPHOD7W4OFI","created_at":"2026-06-26T00:15:21.849841+00:00"},{"alias_kind":"pith_short_8","alias_value":"5VQUZEPH","created_at":"2026-06-26T00:15:21.849841+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2608.07145","citing_title":"From triangles to prisms: towards a geometric extension of concurrence fill for three-qubit mixed states","ref_index":25,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5VQUZEPHOD7W4OFIMLXNGLFLP5","json":"https://pith.science/pith/5VQUZEPHOD7W4OFIMLXNGLFLP5.json","graph_json":"https://pith.science/api/pith-number/5VQUZEPHOD7W4OFIMLXNGLFLP5/graph.json","events_json":"https://pith.science/api/pith-number/5VQUZEPHOD7W4OFIMLXNGLFLP5/events.json","paper":"https://pith.science/paper/5VQUZEPH"},"agent_actions":{"view_html":"https://pith.science/pith/5VQUZEPHOD7W4OFIMLXNGLFLP5","download_json":"https://pith.science/pith/5VQUZEPHOD7W4OFIMLXNGLFLP5.json","view_paper":"https://pith.science/paper/5VQUZEPH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2501.07084&json=true","fetch_graph":"https://pith.science/api/pith-number/5VQUZEPHOD7W4OFIMLXNGLFLP5/graph.json","fetch_events":"https://pith.science/api/pith-number/5VQUZEPHOD7W4OFIMLXNGLFLP5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5VQUZEPHOD7W4OFIMLXNGLFLP5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5VQUZEPHOD7W4OFIMLXNGLFLP5/action/storage_attestation","attest_author":"https://pith.science/pith/5VQUZEPHOD7W4OFIMLXNGLFLP5/action/author_attestation","sign_citation":"https://pith.science/pith/5VQUZEPHOD7W4OFIMLXNGLFLP5/action/citation_signature","submit_replication":"https://pith.science/pith/5VQUZEPHOD7W4OFIMLXNGLFLP5/action/replication_record"}},"created_at":"2026-06-26T00:15:21.849841+00:00","updated_at":"2026-06-26T00:15:21.849841+00:00"}