{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:6KSKWTVFYIQNNBBYIKUNOAUVAT","short_pith_number":"pith:6KSKWTVF","canonical_record":{"source":{"id":"2608.03390","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-08-04T09:40:14Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fc80346b0b1577cf3b1f398210f6f6b653b5d1bc3ca22a25623a2402a73d7b86","abstract_canon_sha256":"a89821868db45e33dfc9cc5aab048f267ef45ab4d2b6b6b9f097aa89ab370ea5"},"schema_version":"1.0"},"canonical_sha256":"f2a4ab4ea5c220d6843842a8d7029504ef9bd82eb9098e9c19c1954410816fbf","source":{"kind":"arxiv","id":"2608.03390","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.03390","created_at":"2026-08-05T01:35:39Z"},{"alias_kind":"arxiv_version","alias_value":"2608.03390v1","created_at":"2026-08-05T01:35:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.03390","created_at":"2026-08-05T01:35:39Z"},{"alias_kind":"pith_short_12","alias_value":"6KSKWTVFYIQN","created_at":"2026-08-05T01:35:39Z"},{"alias_kind":"pith_short_16","alias_value":"6KSKWTVFYIQNNBBY","created_at":"2026-08-05T01:35:39Z"},{"alias_kind":"pith_short_8","alias_value":"6KSKWTVF","created_at":"2026-08-05T01:35:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:6KSKWTVFYIQNNBBYIKUNOAUVAT","target":"record","payload":{"canonical_record":{"source":{"id":"2608.03390","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-08-04T09:40:14Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"fc80346b0b1577cf3b1f398210f6f6b653b5d1bc3ca22a25623a2402a73d7b86","abstract_canon_sha256":"a89821868db45e33dfc9cc5aab048f267ef45ab4d2b6b6b9f097aa89ab370ea5"},"schema_version":"1.0"},"canonical_sha256":"f2a4ab4ea5c220d6843842a8d7029504ef9bd82eb9098e9c19c1954410816fbf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-05T01:35:39.790522Z","signature_b64":"54zfk0DRSHJRuh8FqnFFuHtalAW72QFCWs3l42uRS/9XcdXA2IjYwtB6lWB5HUivUMuzrXEWnk4K4ZLHCtEuCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2a4ab4ea5c220d6843842a8d7029504ef9bd82eb9098e9c19c1954410816fbf","last_reissued_at":"2026-08-05T01:35:39.789129Z","signature_status":"signed_v1","first_computed_at":"2026-08-05T01:35:39.789129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.03390","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":"2026-08-05T01:35:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i2GnZ74vuE+Tq7BZSxjHlhLQaG2pjxKIu64rC/8WlnTUpk59k2qXvakYVEG3CEKuAUEHCcyZwm1HS5Seql8fBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T19:54:44.910157Z"},"content_sha256":"e7a0fe0bb0112c1f6553c0ae2368df2cf9389a6ea1bd870c5294a1bf3169dbb3","schema_version":"1.0","event_id":"sha256:e7a0fe0bb0112c1f6553c0ae2368df2cf9389a6ea1bd870c5294a1bf3169dbb3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:6KSKWTVFYIQNNBBYIKUNOAUVAT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The geometry of absolute separability and other convex matrix properties from spectrum","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Andreas Winter, Jennifer Ahiable, Naga Bhavya Teja Kothakonda","submitted_at":"2026-08-04T09:40:14Z","abstract_excerpt":"We investigate the geometric structure of the set of spectra of bipartite absolute separable states ($\\mathrm{ASEP}_{m,n}$) and absolute positive partial transpose states ($\\mathrm{APPT}_{m,n}$), i.e., bipartite quantum states that remain separable or PPT respectively, under all global unitary transformations. First, we establish general geometric properties of absolute convex sets of matrices, their spectra and extreme points. Regarding absolute separability, we present a permutation-symmetric reformulation of the absolute PPT criterion and use it to demonstrate that $\\mathrm{APPT}_{m,n}$ is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03390","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2608.03390/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":"2026-08-05T01:35:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DnH9qAuUR7LW0KkDXTVSeEQrfvH1EPBB7WlDPOl8gPUXBLfyUpRDocyqKnT7UWFAEDbxD+8VeenlV5dKV3dCBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T19:54:44.910857Z"},"content_sha256":"9be3da2ea607a6b0d17707e38c00b2afabad9a476ceeb81830285e0063da7f4e","schema_version":"1.0","event_id":"sha256:9be3da2ea607a6b0d17707e38c00b2afabad9a476ceeb81830285e0063da7f4e"},{"event_type":"integrity_finding","subject_pith_number":"pith:2026:6KSKWTVFYIQNNBBYIKUNOAUVAT","target":"integrity","payload":{"note":"DOI is split by whitespace or line breaks in the printed bibliography. Reconstructed DOI 10.1103/PhysRevA.66.062311 resolves to 'Largest separable balls around the maximally mixed bipartite quantum state'. A reader following the printed text alone cannot reach it.","snippet":"L. Gurvits and H. N. Barnum, “Largest separable balls around the maximally mixed bipartite quantum state,”Physical Review A, vol. 66, 6 Dec. 2002, Art. no. 062311.doi:10.1103/PhysRevA. 66.062311","arxiv_id":"2608.03390","detector":"doi_compliance","evidence":{"ref_index":38,"verdict_class":"incontrovertible","resolved_title":"Largest separable balls around the maximally mixed bipartite quantum state","printed_excerpt":"10.1103/physreva","reconstructed_doi":"10.1103/PhysRevA.66.062311"},"severity":"advisory","ref_index":38,"audited_at":"2026-08-05T19:58:20.550297Z","event_type":"pith.integrity.v1","detected_doi":"10.1103/PhysRevA.66.062311","detector_url":"https://pith.science/pith-integrity-protocol#doi_compliance","external_url":null,"finding_type":"recoverable_identifier","evidence_hash":"76fa7451013390dac3b119d7a82aea46635c5f08d1c7882f692c5a3f36c69fb3","paper_version":1,"verdict_class":"incontrovertible","resolved_title":"Largest separable balls around the maximally mixed bipartite quantum state","detector_version":"1.1.0","detected_arxiv_id":null,"integrity_event_id":18137,"payload_sha256":"1440277753e1ddc2c912abd4c81566bd5d209584fd99f6dbef7b4f3aaa69d20f","signature_b64":"gQ1HGGgPUcq9wf16Ocl1xxc8yLrd2jbiIQ8vWWSwCfRd3R888IU7EGz3ZluFxHehD6Hp5nadjgipbMJm4JPZBw==","signing_key_id":"pith-v1-2026-05"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-08-05T19:58:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EKOQ82iLUyOjjhYaz/b/QrFngrgNPngUbWQ/53FSqrwQASRWHTlClOpbMho015c6P5zISCAMyFlow5LyZcvJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T19:54:44.915055Z"},"content_sha256":"e21b390798002016c4e55353b724b2606375e0bb1af93d077d61943681f76d3d","schema_version":"1.0","event_id":"sha256:e21b390798002016c4e55353b724b2606375e0bb1af93d077d61943681f76d3d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6KSKWTVFYIQNNBBYIKUNOAUVAT/bundle.json","state_url":"https://pith.science/pith/6KSKWTVFYIQNNBBYIKUNOAUVAT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6KSKWTVFYIQNNBBYIKUNOAUVAT/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":"2026-08-12T19:54:44Z","links":{"resolver":"https://pith.science/pith/6KSKWTVFYIQNNBBYIKUNOAUVAT","bundle":"https://pith.science/pith/6KSKWTVFYIQNNBBYIKUNOAUVAT/bundle.json","state":"https://pith.science/pith/6KSKWTVFYIQNNBBYIKUNOAUVAT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6KSKWTVFYIQNNBBYIKUNOAUVAT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6KSKWTVFYIQNNBBYIKUNOAUVAT","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a89821868db45e33dfc9cc5aab048f267ef45ab4d2b6b6b9f097aa89ab370ea5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-08-04T09:40:14Z","title_canon_sha256":"fc80346b0b1577cf3b1f398210f6f6b653b5d1bc3ca22a25623a2402a73d7b86"},"schema_version":"1.0","source":{"id":"2608.03390","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.03390","created_at":"2026-08-05T01:35:39Z"},{"alias_kind":"arxiv_version","alias_value":"2608.03390v1","created_at":"2026-08-05T01:35:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.03390","created_at":"2026-08-05T01:35:39Z"},{"alias_kind":"pith_short_12","alias_value":"6KSKWTVFYIQN","created_at":"2026-08-05T01:35:39Z"},{"alias_kind":"pith_short_16","alias_value":"6KSKWTVFYIQNNBBY","created_at":"2026-08-05T01:35:39Z"},{"alias_kind":"pith_short_8","alias_value":"6KSKWTVF","created_at":"2026-08-05T01:35:39Z"}],"graph_snapshots":[{"event_id":"sha256:9be3da2ea607a6b0d17707e38c00b2afabad9a476ceeb81830285e0063da7f4e","target":"graph","created_at":"2026-08-05T01:35:39Z","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/2608.03390/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate the geometric structure of the set of spectra of bipartite absolute separable states ($\\mathrm{ASEP}_{m,n}$) and absolute positive partial transpose states ($\\mathrm{APPT}_{m,n}$), i.e., bipartite quantum states that remain separable or PPT respectively, under all global unitary transformations. First, we establish general geometric properties of absolute convex sets of matrices, their spectra and extreme points. Regarding absolute separability, we present a permutation-symmetric reformulation of the absolute PPT criterion and use it to demonstrate that $\\mathrm{APPT}_{m,n}$ is ","authors_text":"Andreas Winter, Jennifer Ahiable, Naga Bhavya Teja Kothakonda","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-08-04T09:40:14Z","title":"The geometry of absolute separability and other convex matrix properties from spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.03390","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:e7a0fe0bb0112c1f6553c0ae2368df2cf9389a6ea1bd870c5294a1bf3169dbb3","target":"record","created_at":"2026-08-05T01:35:39Z","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":"a89821868db45e33dfc9cc5aab048f267ef45ab4d2b6b6b9f097aa89ab370ea5","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-08-04T09:40:14Z","title_canon_sha256":"fc80346b0b1577cf3b1f398210f6f6b653b5d1bc3ca22a25623a2402a73d7b86"},"schema_version":"1.0","source":{"id":"2608.03390","kind":"arxiv","version":1}},"canonical_sha256":"f2a4ab4ea5c220d6843842a8d7029504ef9bd82eb9098e9c19c1954410816fbf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2a4ab4ea5c220d6843842a8d7029504ef9bd82eb9098e9c19c1954410816fbf","first_computed_at":"2026-08-05T01:35:39.789129Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-05T01:35:39.789129Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"54zfk0DRSHJRuh8FqnFFuHtalAW72QFCWs3l42uRS/9XcdXA2IjYwtB6lWB5HUivUMuzrXEWnk4K4ZLHCtEuCw==","signature_status":"signed_v1","signed_at":"2026-08-05T01:35:39.790522Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.03390","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7a0fe0bb0112c1f6553c0ae2368df2cf9389a6ea1bd870c5294a1bf3169dbb3","sha256:9be3da2ea607a6b0d17707e38c00b2afabad9a476ceeb81830285e0063da7f4e","sha256:e21b390798002016c4e55353b724b2606375e0bb1af93d077d61943681f76d3d"],"state_sha256":"2feaa5a48a60c35cebaef3eb88ee32f0c20699902839a963e481807b5547653a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SItYM8+RqG9YseOY9CMmlmlzEl8PVQaaXRpn3G9IwQ/N3zoQXs63f1eW88+dCaf2wRBZX9Wk81WjPa4C4aTCAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T19:54:44.917589Z","bundle_sha256":"c0b45ca0a90fc208924b3bad2ce04ca3c8c3b3274bf03205cd6e996d30042415"}}