{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:SIF76VRX7MZIDABNIQPL5W74IO","short_pith_number":"pith:SIF76VRX","canonical_record":{"source":{"id":"1105.2709","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-13T12:38:05Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"de90b467c991d60d13c9eb2d001c51f40042f2ca67640f6194d02f66cdf02e19","abstract_canon_sha256":"39e776f129916286d876652dd6f0e6447498968db40305bbf34ec75f834c930f"},"schema_version":"1.0"},"canonical_sha256":"920bff5637fb3281802d441ebedbfc438f57a7ae7badc722ad858ef3573fbd0c","source":{"kind":"arxiv","id":"1105.2709","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2709","created_at":"2026-05-18T01:14:45Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2709v1","created_at":"2026-05-18T01:14:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2709","created_at":"2026-05-18T01:14:45Z"},{"alias_kind":"pith_short_12","alias_value":"SIF76VRX7MZI","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SIF76VRX7MZIDABN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SIF76VRX","created_at":"2026-05-18T12:26:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:SIF76VRX7MZIDABNIQPL5W74IO","target":"record","payload":{"canonical_record":{"source":{"id":"1105.2709","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-13T12:38:05Z","cross_cats_sorted":["math.MP","quant-ph"],"title_canon_sha256":"de90b467c991d60d13c9eb2d001c51f40042f2ca67640f6194d02f66cdf02e19","abstract_canon_sha256":"39e776f129916286d876652dd6f0e6447498968db40305bbf34ec75f834c930f"},"schema_version":"1.0"},"canonical_sha256":"920bff5637fb3281802d441ebedbfc438f57a7ae7badc722ad858ef3573fbd0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:45.933389Z","signature_b64":"TcoADJ6bd3djeJqts4c0aGTpM0Nmvtf2XYwfkukHOFX6wVIRkFF8k5YJVJWIssUedo0fq879C6Bmy0xxhDlxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"920bff5637fb3281802d441ebedbfc438f57a7ae7badc722ad858ef3573fbd0c","last_reissued_at":"2026-05-18T01:14:45.932752Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:45.932752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.2709","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":"2026-05-18T01:14:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"evc+SlZXVTSa5Ag5+lvs8dW0SMemp6c29icq3fGg9PXTJn+XTdQs2/v0qlhKUnAVaAR51nhIlHreHClBc8amAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:10:18.035025Z"},"content_sha256":"143c35702f5734e2957ace4396e01e5ade5309e87ea1853860626f9eb7bdc009","schema_version":"1.0","event_id":"sha256:143c35702f5734e2957ace4396e01e5ade5309e87ea1853860626f9eb7bdc009"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:SIF76VRX7MZIDABNIQPL5W74IO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Three-by-three bound entanglement with general unextendible product bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"{\\L}ukasz Skowronek","submitted_at":"2011-05-13T12:38:05Z","abstract_excerpt":"We discuss the subject of Unextendible Product Bases with the orthogonality condition dropped and we prove that the lowest rank non-separable positive-partial-transpose states, i.e. states of rank 4 in 3 x 3 systems are always locally equivalent to a projection onto the orthogonal complement of a linear subspace spanned by an orthogonal Unextendible Product Basis. The product vectors in the kernels of the states belong to a non-zero measure subset of all general Unextendible Product Bases, nevertheless they can always be locally transformed to the orthogonal form. This fully confirms the surpr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2709","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":"2026-05-18T01:14:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uzO1LuacARcUrAQok6mHCdK90AZkuzFD6xSRdp9/0TFV3pkrej7ogAnVq65gCiljusTkBWzX+vKg2E1aPoRnBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T17:10:18.035489Z"},"content_sha256":"1dcf165be3da4c0741181dd1f842f329941c89ac63afa636889fbfe46265e138","schema_version":"1.0","event_id":"sha256:1dcf165be3da4c0741181dd1f842f329941c89ac63afa636889fbfe46265e138"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SIF76VRX7MZIDABNIQPL5W74IO/bundle.json","state_url":"https://pith.science/pith/SIF76VRX7MZIDABNIQPL5W74IO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SIF76VRX7MZIDABNIQPL5W74IO/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":"2026-06-06T17:10:18Z","links":{"resolver":"https://pith.science/pith/SIF76VRX7MZIDABNIQPL5W74IO","bundle":"https://pith.science/pith/SIF76VRX7MZIDABNIQPL5W74IO/bundle.json","state":"https://pith.science/pith/SIF76VRX7MZIDABNIQPL5W74IO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SIF76VRX7MZIDABNIQPL5W74IO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:SIF76VRX7MZIDABNIQPL5W74IO","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":"39e776f129916286d876652dd6f0e6447498968db40305bbf34ec75f834c930f","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-13T12:38:05Z","title_canon_sha256":"de90b467c991d60d13c9eb2d001c51f40042f2ca67640f6194d02f66cdf02e19"},"schema_version":"1.0","source":{"id":"1105.2709","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.2709","created_at":"2026-05-18T01:14:45Z"},{"alias_kind":"arxiv_version","alias_value":"1105.2709v1","created_at":"2026-05-18T01:14:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.2709","created_at":"2026-05-18T01:14:45Z"},{"alias_kind":"pith_short_12","alias_value":"SIF76VRX7MZI","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_16","alias_value":"SIF76VRX7MZIDABN","created_at":"2026-05-18T12:26:41Z"},{"alias_kind":"pith_short_8","alias_value":"SIF76VRX","created_at":"2026-05-18T12:26:41Z"}],"graph_snapshots":[{"event_id":"sha256:1dcf165be3da4c0741181dd1f842f329941c89ac63afa636889fbfe46265e138","target":"graph","created_at":"2026-05-18T01:14:45Z","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":"We discuss the subject of Unextendible Product Bases with the orthogonality condition dropped and we prove that the lowest rank non-separable positive-partial-transpose states, i.e. states of rank 4 in 3 x 3 systems are always locally equivalent to a projection onto the orthogonal complement of a linear subspace spanned by an orthogonal Unextendible Product Basis. The product vectors in the kernels of the states belong to a non-zero measure subset of all general Unextendible Product Bases, nevertheless they can always be locally transformed to the orthogonal form. This fully confirms the surpr","authors_text":"{\\L}ukasz Skowronek","cross_cats":["math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-13T12:38:05Z","title":"Three-by-three bound entanglement with general unextendible product bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.2709","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":"sha256:143c35702f5734e2957ace4396e01e5ade5309e87ea1853860626f9eb7bdc009","target":"record","created_at":"2026-05-18T01:14:45Z","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":"39e776f129916286d876652dd6f0e6447498968db40305bbf34ec75f834c930f","cross_cats_sorted":["math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-05-13T12:38:05Z","title_canon_sha256":"de90b467c991d60d13c9eb2d001c51f40042f2ca67640f6194d02f66cdf02e19"},"schema_version":"1.0","source":{"id":"1105.2709","kind":"arxiv","version":1}},"canonical_sha256":"920bff5637fb3281802d441ebedbfc438f57a7ae7badc722ad858ef3573fbd0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"920bff5637fb3281802d441ebedbfc438f57a7ae7badc722ad858ef3573fbd0c","first_computed_at":"2026-05-18T01:14:45.932752Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:45.932752Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TcoADJ6bd3djeJqts4c0aGTpM0Nmvtf2XYwfkukHOFX6wVIRkFF8k5YJVJWIssUedo0fq879C6Bmy0xxhDlxBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:45.933389Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.2709","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:143c35702f5734e2957ace4396e01e5ade5309e87ea1853860626f9eb7bdc009","sha256:1dcf165be3da4c0741181dd1f842f329941c89ac63afa636889fbfe46265e138"],"state_sha256":"d3f2449a70c3a5672fd0ff46bc3f80014a0738110bacc4c894445d2b07a65bc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ntSez7/mTRkNBN/ZrJ33pN3ZQ9LKTflHSapUYwtMof59OqfopVkd9A67YgUGp061uzPYBrYe4+Ay6dXghwkMBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T17:10:18.039371Z","bundle_sha256":"eadad82201b6ba0971dfaa9a18eb848e7938ba396f8fd646eecacb42bd354c0f"}}