{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:7XJZB7FRK7E4CQHN2SQTQYXRPN","short_pith_number":"pith:7XJZB7FR","canonical_record":{"source":{"id":"2409.18948","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-09-27T17:49:59Z","cross_cats_sorted":["math.AG","math.OC"],"title_canon_sha256":"b4de19cdb8f015491087b63a0273b97d622920af8d66eef90ee8d91526f42c55","abstract_canon_sha256":"b01d39d7af4bbca751b0eebe2000f2a975be7d8f706fbfa8320b92b7d4ed1adc"},"schema_version":"1.0"},"canonical_sha256":"fdd390fcb157c9c140edd4a13862f17b42224b817d3491f840d35f6937871e89","source":{"kind":"arxiv","id":"2409.18948","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.18948","created_at":"2026-07-05T09:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"2409.18948v2","created_at":"2026-07-05T09:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.18948","created_at":"2026-07-05T09:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"7XJZB7FRK7E4","created_at":"2026-07-05T09:36:14Z"},{"alias_kind":"pith_short_16","alias_value":"7XJZB7FRK7E4CQHN","created_at":"2026-07-05T09:36:14Z"},{"alias_kind":"pith_short_8","alias_value":"7XJZB7FR","created_at":"2026-07-05T09:36:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:7XJZB7FRK7E4CQHN2SQTQYXRPN","target":"record","payload":{"canonical_record":{"source":{"id":"2409.18948","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-09-27T17:49:59Z","cross_cats_sorted":["math.AG","math.OC"],"title_canon_sha256":"b4de19cdb8f015491087b63a0273b97d622920af8d66eef90ee8d91526f42c55","abstract_canon_sha256":"b01d39d7af4bbca751b0eebe2000f2a975be7d8f706fbfa8320b92b7d4ed1adc"},"schema_version":"1.0"},"canonical_sha256":"fdd390fcb157c9c140edd4a13862f17b42224b817d3491f840d35f6937871e89","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:36:14.818540Z","signature_b64":"qgPN2k0EPcFpW+ODqrZHVtHmg+REjZJ1GIQhF5vqp9X+gbzY8+p1rWDSUICjWkHcLKdM8UY/z+jANwZS6xKECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdd390fcb157c9c140edd4a13862f17b42224b817d3491f840d35f6937871e89","last_reissued_at":"2026-07-05T09:36:14.818033Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:36:14.818033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.18948","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:36:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fn0MHYJqIZzkVnwFe/C4YL/g2Ih4c3uCytG6mqXmZSPIXplBFEgLm+2ENojezUhLmfQTkXXVPGXxJp80d2lqDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T07:44:06.628645Z"},"content_sha256":"b80ae24ab592313c1205177a6e193dcb6730912542227232ca6d1415e82cc2a3","schema_version":"1.0","event_id":"sha256:b80ae24ab592313c1205177a6e193dcb6730912542227232ca6d1415e82cc2a3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:7XJZB7FRK7E4CQHN2SQTQYXRPN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"X-arability of mixed quantum states","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.OC"],"primary_cat":"quant-ph","authors_text":"Benjamin Lovitz, Harm Derksen, Nathaniel Johnston","submitted_at":"2024-09-27T17:49:59Z","abstract_excerpt":"The problem of determining when entanglement is present in a quantum system is one of the most active areas of research in quantum physics. Depending on the setting at hand, different notions of entanglement (or lack thereof) become relevant. Examples include separability (of bosons, fermions, and distinguishable particles), Schmidt number, biseparability, entanglement depth, and bond dimension. In this work, we propose and study a unified notion of separability, which we call X-arability, that captures a wide range of applications including these. For a subset (more specifically, an algebraic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.18948","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.18948/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:36:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UcSKD3sd8Ukkm4RwxBt48fWg64fFHYtEDTVUjsVXtNQWrXmKi4dB/EdAXWphLLGNHruzGV8F+frGUmkyrC/NBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T07:44:06.629165Z"},"content_sha256":"cc1c6974c4832eae263e9321ce99b913a9df0abe60a4745d6b52b659160bc8ec","schema_version":"1.0","event_id":"sha256:cc1c6974c4832eae263e9321ce99b913a9df0abe60a4745d6b52b659160bc8ec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7XJZB7FRK7E4CQHN2SQTQYXRPN/bundle.json","state_url":"https://pith.science/pith/7XJZB7FRK7E4CQHN2SQTQYXRPN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7XJZB7FRK7E4CQHN2SQTQYXRPN/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":"2026-08-19T07:44:06Z","links":{"resolver":"https://pith.science/pith/7XJZB7FRK7E4CQHN2SQTQYXRPN","bundle":"https://pith.science/pith/7XJZB7FRK7E4CQHN2SQTQYXRPN/bundle.json","state":"https://pith.science/pith/7XJZB7FRK7E4CQHN2SQTQYXRPN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7XJZB7FRK7E4CQHN2SQTQYXRPN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:7XJZB7FRK7E4CQHN2SQTQYXRPN","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":"b01d39d7af4bbca751b0eebe2000f2a975be7d8f706fbfa8320b92b7d4ed1adc","cross_cats_sorted":["math.AG","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-09-27T17:49:59Z","title_canon_sha256":"b4de19cdb8f015491087b63a0273b97d622920af8d66eef90ee8d91526f42c55"},"schema_version":"1.0","source":{"id":"2409.18948","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.18948","created_at":"2026-07-05T09:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"2409.18948v2","created_at":"2026-07-05T09:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.18948","created_at":"2026-07-05T09:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"7XJZB7FRK7E4","created_at":"2026-07-05T09:36:14Z"},{"alias_kind":"pith_short_16","alias_value":"7XJZB7FRK7E4CQHN","created_at":"2026-07-05T09:36:14Z"},{"alias_kind":"pith_short_8","alias_value":"7XJZB7FR","created_at":"2026-07-05T09:36:14Z"}],"graph_snapshots":[{"event_id":"sha256:cc1c6974c4832eae263e9321ce99b913a9df0abe60a4745d6b52b659160bc8ec","target":"graph","created_at":"2026-07-05T09:36:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2409.18948/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The problem of determining when entanglement is present in a quantum system is one of the most active areas of research in quantum physics. Depending on the setting at hand, different notions of entanglement (or lack thereof) become relevant. Examples include separability (of bosons, fermions, and distinguishable particles), Schmidt number, biseparability, entanglement depth, and bond dimension. In this work, we propose and study a unified notion of separability, which we call X-arability, that captures a wide range of applications including these. For a subset (more specifically, an algebraic","authors_text":"Benjamin Lovitz, Harm Derksen, Nathaniel Johnston","cross_cats":["math.AG","math.OC"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-09-27T17:49:59Z","title":"X-arability of mixed quantum states"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.18948","kind":"arxiv","version":2},"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:b80ae24ab592313c1205177a6e193dcb6730912542227232ca6d1415e82cc2a3","target":"record","created_at":"2026-07-05T09:36:14Z","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":"b01d39d7af4bbca751b0eebe2000f2a975be7d8f706fbfa8320b92b7d4ed1adc","cross_cats_sorted":["math.AG","math.OC"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2024-09-27T17:49:59Z","title_canon_sha256":"b4de19cdb8f015491087b63a0273b97d622920af8d66eef90ee8d91526f42c55"},"schema_version":"1.0","source":{"id":"2409.18948","kind":"arxiv","version":2}},"canonical_sha256":"fdd390fcb157c9c140edd4a13862f17b42224b817d3491f840d35f6937871e89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fdd390fcb157c9c140edd4a13862f17b42224b817d3491f840d35f6937871e89","first_computed_at":"2026-07-05T09:36:14.818033Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:36:14.818033Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qgPN2k0EPcFpW+ODqrZHVtHmg+REjZJ1GIQhF5vqp9X+gbzY8+p1rWDSUICjWkHcLKdM8UY/z+jANwZS6xKECA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:36:14.818540Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.18948","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b80ae24ab592313c1205177a6e193dcb6730912542227232ca6d1415e82cc2a3","sha256:cc1c6974c4832eae263e9321ce99b913a9df0abe60a4745d6b52b659160bc8ec"],"state_sha256":"8766a2084a1cd9c169154dac08cb5672b7401cccee1b8d8609fafabe8d59d646"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tuCtnFeXAs1hC+vFslJhoEPq8CD39SJhGpj0op00i9WNnj/YVKk56CSKcnqL32cATUzHqXKGVO5OvI74yXjgBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T07:44:06.632884Z","bundle_sha256":"4a6fc12d1dee2af6f8604d05050526da38238fa62ddd0ab707e0109ff3a18eb7"}}