{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:4GZPNFS5VZ6HXSEEGFK27TO2BO","short_pith_number":"pith:4GZPNFS5","canonical_record":{"source":{"id":"1810.08932","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-21T12:30:38Z","cross_cats_sorted":[],"title_canon_sha256":"9d83dd2e6cc2298598164f0118d3a01ec2028c138bb5e1c5f0534f2a7f0f12fc","abstract_canon_sha256":"a2e48c67ca04ea11d8b83011dcbff71c62726e8e80156d6e334b10566108c4f6"},"schema_version":"1.0"},"canonical_sha256":"e1b2f6965dae7c7bc8843155afcdda0b9463baf74faba5bb6123ee3a16d37df4","source":{"kind":"arxiv","id":"1810.08932","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08932","created_at":"2026-05-18T00:02:41Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08932v1","created_at":"2026-05-18T00:02:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08932","created_at":"2026-05-18T00:02:41Z"},{"alias_kind":"pith_short_12","alias_value":"4GZPNFS5VZ6H","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4GZPNFS5VZ6HXSEE","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4GZPNFS5","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:4GZPNFS5VZ6HXSEEGFK27TO2BO","target":"record","payload":{"canonical_record":{"source":{"id":"1810.08932","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-21T12:30:38Z","cross_cats_sorted":[],"title_canon_sha256":"9d83dd2e6cc2298598164f0118d3a01ec2028c138bb5e1c5f0534f2a7f0f12fc","abstract_canon_sha256":"a2e48c67ca04ea11d8b83011dcbff71c62726e8e80156d6e334b10566108c4f6"},"schema_version":"1.0"},"canonical_sha256":"e1b2f6965dae7c7bc8843155afcdda0b9463baf74faba5bb6123ee3a16d37df4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:41.419368Z","signature_b64":"csvP8T/Ghz/684cPpqqd3TRSCfYjc623ecQYzdA48dQcwCRX9lZdQEMEuqqv0iCF6SVO9PTnPY7I5aDcFgRbCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1b2f6965dae7c7bc8843155afcdda0b9463baf74faba5bb6123ee3a16d37df4","last_reissued_at":"2026-05-18T00:02:41.418937Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:41.418937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.08932","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":"2026-05-18T00:02:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JZWpDCzEVEB9f7KlUjwbKpBu+DFULBurPjT+jkvwEoj/pAkNXZhWOwfVGALGuGZWrIS7+VY+ShDKrE+NMqMTBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:34:48.485784Z"},"content_sha256":"dc3d460c257eed8f4496e6eed677e4639a906415ce3916f8eb0e86ba83a32880","schema_version":"1.0","event_id":"sha256:dc3d460c257eed8f4496e6eed677e4639a906415ce3916f8eb0e86ba83a32880"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:4GZPNFS5VZ6HXSEEGFK27TO2BO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Constructing $2\\times2\\times4$ and $4\\times4$ unextendible product bases and positive-partial-transpose entangled states","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Kai Wang, Lijun Zhao, Lin Chen, Yi Shen, Yize Sun","submitted_at":"2018-10-21T12:30:38Z","abstract_excerpt":"The 4-qubit unextendible product basis (UPB) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. From this result we show that there is only one UPB of size $6$ and six UPBs of size $9$ in $\\cH=\\bbC^2\\ox\\bbC^2\\ox\\bbC^4$, three UPBs of size $9$ in $\\cK=\\bbC^4\\ox\\bbC^4$, and no UPB of size $7$ in $\\cH$ and $\\cK$. Furthermore we construct a 4-qubit positive-partial-transpose (PPT) entangled state $\\r$ of rank seven, and show that it is also a PPT entangled state in $\\cH$ and $\\cK$, respectively. We analytically derive the geometric measure of entanglement of a spec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08932","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":"2026-05-18T00:02:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EYH6z0hH3L+DTnvQV0qPBwnIM/lwCFASaITnyM7U1mOJ4WPuCU2SVU2ZESe09NITa82MNHnc+rRIFM84unNpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:34:48.486486Z"},"content_sha256":"daab0a9d199b8241ea2d9f3679d6bde264b30b41e0066ee481df2796dc93f825","schema_version":"1.0","event_id":"sha256:daab0a9d199b8241ea2d9f3679d6bde264b30b41e0066ee481df2796dc93f825"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO/bundle.json","state_url":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO/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":"2026-05-30T23:34:48Z","links":{"resolver":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO","bundle":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO/bundle.json","state":"https://pith.science/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4GZPNFS5VZ6HXSEEGFK27TO2BO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:4GZPNFS5VZ6HXSEEGFK27TO2BO","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":"a2e48c67ca04ea11d8b83011dcbff71c62726e8e80156d6e334b10566108c4f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-21T12:30:38Z","title_canon_sha256":"9d83dd2e6cc2298598164f0118d3a01ec2028c138bb5e1c5f0534f2a7f0f12fc"},"schema_version":"1.0","source":{"id":"1810.08932","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08932","created_at":"2026-05-18T00:02:41Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08932v1","created_at":"2026-05-18T00:02:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08932","created_at":"2026-05-18T00:02:41Z"},{"alias_kind":"pith_short_12","alias_value":"4GZPNFS5VZ6H","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"4GZPNFS5VZ6HXSEE","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"4GZPNFS5","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:daab0a9d199b8241ea2d9f3679d6bde264b30b41e0066ee481df2796dc93f825","target":"graph","created_at":"2026-05-18T00:02:41Z","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":"The 4-qubit unextendible product basis (UPB) has been recently studied by [Johnston, J. Phys. A: Math. Theor. 47 (2014) 424034]. From this result we show that there is only one UPB of size $6$ and six UPBs of size $9$ in $\\cH=\\bbC^2\\ox\\bbC^2\\ox\\bbC^4$, three UPBs of size $9$ in $\\cK=\\bbC^4\\ox\\bbC^4$, and no UPB of size $7$ in $\\cH$ and $\\cK$. Furthermore we construct a 4-qubit positive-partial-transpose (PPT) entangled state $\\r$ of rank seven, and show that it is also a PPT entangled state in $\\cH$ and $\\cK$, respectively. We analytically derive the geometric measure of entanglement of a spec","authors_text":"Kai Wang, Lijun Zhao, Lin Chen, Yi Shen, Yize Sun","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-21T12:30:38Z","title":"Constructing $2\\times2\\times4$ and $4\\times4$ unextendible product bases and positive-partial-transpose entangled states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08932","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:dc3d460c257eed8f4496e6eed677e4639a906415ce3916f8eb0e86ba83a32880","target":"record","created_at":"2026-05-18T00:02:41Z","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":"a2e48c67ca04ea11d8b83011dcbff71c62726e8e80156d6e334b10566108c4f6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-10-21T12:30:38Z","title_canon_sha256":"9d83dd2e6cc2298598164f0118d3a01ec2028c138bb5e1c5f0534f2a7f0f12fc"},"schema_version":"1.0","source":{"id":"1810.08932","kind":"arxiv","version":1}},"canonical_sha256":"e1b2f6965dae7c7bc8843155afcdda0b9463baf74faba5bb6123ee3a16d37df4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1b2f6965dae7c7bc8843155afcdda0b9463baf74faba5bb6123ee3a16d37df4","first_computed_at":"2026-05-18T00:02:41.418937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:41.418937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"csvP8T/Ghz/684cPpqqd3TRSCfYjc623ecQYzdA48dQcwCRX9lZdQEMEuqqv0iCF6SVO9PTnPY7I5aDcFgRbCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:41.419368Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08932","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc3d460c257eed8f4496e6eed677e4639a906415ce3916f8eb0e86ba83a32880","sha256:daab0a9d199b8241ea2d9f3679d6bde264b30b41e0066ee481df2796dc93f825"],"state_sha256":"4df114e0048f59cd19395ee5b2262f69ed68daface45456035dd458901af5d8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jtcKinrzsA3f0QKGBmyDuLsi31PvPnvSUh9wdt51FXyN2etMGkNxey4ZXDLDMWMriIPTuYB9mZjnXDUNbIGTAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:34:48.490408Z","bundle_sha256":"304c801ff0cdd2bcb12d097407d580836a75f5c0d3a962acd6e0f0e5cf328246"}}