{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:J7JZUBKALU4CEHWYSKIGHCUUJJ","short_pith_number":"pith:J7JZUBKA","schema_version":"1.0","canonical_sha256":"4fd39a05405d38221ed89290638a944a4a00cc84121810066a3d270b78bfed75","source":{"kind":"arxiv","id":"1807.03636","version":2},"attestation_state":"computed","paper":{"title":"The positive partial transpose conjecture for n=3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lin Chen, Waishing Tang, Yu Yang","submitted_at":"2018-07-07T02:18:34Z","abstract_excerpt":"We present the PPT square conjecture introduced by M. Christandl. We prove the conjecture in the case $n=3$ as a consequence of the fact that two-qutrit PPT states have Schmidt at most two. Our result in Lemma 3 is independent from the proof found M\\\"uller-Hermes. M\\\"uller-Hermes announced that this conjecture is true for the states on $\\mathbb{C}_3\\otimes\\mathbb{C}_3$ \\cite{hermes} recently. The PPT square conjecture in the case $n\\ge4$ is still open."},"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":"1807.03636","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-07-07T02:18:34Z","cross_cats_sorted":[],"title_canon_sha256":"288226b9dd493733610c364f79436ce3499c1892d143642c59a8aa9a32aea3ce","abstract_canon_sha256":"28721bf4aa3366cc73fd93c26e098d1ac1d5b25a56b3fe8b24634cadfcc2501b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:14.116982Z","signature_b64":"zJLP1CudHeXo+Xqda+4esnkdj7vrZCD1bgUGniwha5By7o7G3fp5cW8xVytYB7lZWfy8PBf3yxO8Tk0pBZuxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fd39a05405d38221ed89290638a944a4a00cc84121810066a3d270b78bfed75","last_reissued_at":"2026-05-17T23:55:14.116374Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:14.116374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The positive partial transpose conjecture for n=3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Lin Chen, Waishing Tang, Yu Yang","submitted_at":"2018-07-07T02:18:34Z","abstract_excerpt":"We present the PPT square conjecture introduced by M. Christandl. We prove the conjecture in the case $n=3$ as a consequence of the fact that two-qutrit PPT states have Schmidt at most two. Our result in Lemma 3 is independent from the proof found M\\\"uller-Hermes. M\\\"uller-Hermes announced that this conjecture is true for the states on $\\mathbb{C}_3\\otimes\\mathbb{C}_3$ \\cite{hermes} recently. The PPT square conjecture in the case $n\\ge4$ is still open."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.03636","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1807.03636","created_at":"2026-05-17T23:55:14.116481+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.03636v2","created_at":"2026-05-17T23:55:14.116481+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.03636","created_at":"2026-05-17T23:55:14.116481+00:00"},{"alias_kind":"pith_short_12","alias_value":"J7JZUBKALU4C","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_16","alias_value":"J7JZUBKALU4CEHWY","created_at":"2026-05-18T12:32:31.084164+00:00"},{"alias_kind":"pith_short_8","alias_value":"J7JZUBKA","created_at":"2026-05-18T12:32:31.084164+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/J7JZUBKALU4CEHWYSKIGHCUUJJ","json":"https://pith.science/pith/J7JZUBKALU4CEHWYSKIGHCUUJJ.json","graph_json":"https://pith.science/api/pith-number/J7JZUBKALU4CEHWYSKIGHCUUJJ/graph.json","events_json":"https://pith.science/api/pith-number/J7JZUBKALU4CEHWYSKIGHCUUJJ/events.json","paper":"https://pith.science/paper/J7JZUBKA"},"agent_actions":{"view_html":"https://pith.science/pith/J7JZUBKALU4CEHWYSKIGHCUUJJ","download_json":"https://pith.science/pith/J7JZUBKALU4CEHWYSKIGHCUUJJ.json","view_paper":"https://pith.science/paper/J7JZUBKA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.03636&json=true","fetch_graph":"https://pith.science/api/pith-number/J7JZUBKALU4CEHWYSKIGHCUUJJ/graph.json","fetch_events":"https://pith.science/api/pith-number/J7JZUBKALU4CEHWYSKIGHCUUJJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J7JZUBKALU4CEHWYSKIGHCUUJJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J7JZUBKALU4CEHWYSKIGHCUUJJ/action/storage_attestation","attest_author":"https://pith.science/pith/J7JZUBKALU4CEHWYSKIGHCUUJJ/action/author_attestation","sign_citation":"https://pith.science/pith/J7JZUBKALU4CEHWYSKIGHCUUJJ/action/citation_signature","submit_replication":"https://pith.science/pith/J7JZUBKALU4CEHWYSKIGHCUUJJ/action/replication_record"}},"created_at":"2026-05-17T23:55:14.116481+00:00","updated_at":"2026-05-17T23:55:14.116481+00:00"}