{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6RAIHQ6NBVH7IMEWD6667AXUYD","short_pith_number":"pith:6RAIHQ6N","schema_version":"1.0","canonical_sha256":"f44083c3cd0d4ff430961fbdef82f4c0fd6d25b3a3cba0e155bc7443e7042a9c","source":{"kind":"arxiv","id":"2607.12470","version":1},"attestation_state":"computed","paper":{"title":"Sparse anisotropic positive maps for qutrit entanglement: exact indecomposability and PPT geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Massimiliano F. Sacchi","submitted_at":"2026-07-14T07:55:02Z","abstract_excerpt":"Positive but not completely positive maps provide one of the most direct ways to detect entanglement beyond the positive-partial-transpose (PPT) criterion. We introduce and analyze an exactly solvable two-parameter family of sparse bistochastic positive maps on qutrits, in which two coherence channels are independently tuned by parameters $w$ and $z$. The sparse structure makes the full phase diagram analytic: positivity holds exactly on the square $0\\le w,z\\le2/3$, complete positivity on the smaller square $0\\le w,z\\le1/3$, and decomposability is lost precisely outside a quarter circle in the"},"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":"2607.12470","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2026-07-14T07:55:02Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e37ec57a4e3f8ad7a3f03fe8e9dd786705df470383aa1ab90fb177f8274c2f49","abstract_canon_sha256":"34d3e4e9711335dce281cf9b0850949294456e0a0e7232dd101ac84af82d695a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-15T01:21:36.796896Z","signature_b64":"SVmF3o5YAN7nXPeGQaBZ7U5D8tOVKHzw4AoOtgcaKuqk++ovztHJuchoDgesd9MVD8j2XXLwE96qb2f+bjQpAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f44083c3cd0d4ff430961fbdef82f4c0fd6d25b3a3cba0e155bc7443e7042a9c","last_reissued_at":"2026-07-15T01:21:36.796057Z","signature_status":"signed_v1","first_computed_at":"2026-07-15T01:21:36.796057Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sparse anisotropic positive maps for qutrit entanglement: exact indecomposability and PPT geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Massimiliano F. Sacchi","submitted_at":"2026-07-14T07:55:02Z","abstract_excerpt":"Positive but not completely positive maps provide one of the most direct ways to detect entanglement beyond the positive-partial-transpose (PPT) criterion. We introduce and analyze an exactly solvable two-parameter family of sparse bistochastic positive maps on qutrits, in which two coherence channels are independently tuned by parameters $w$ and $z$. The sparse structure makes the full phase diagram analytic: positivity holds exactly on the square $0\\le w,z\\le2/3$, complete positivity on the smaller square $0\\le w,z\\le1/3$, and decomposability is lost precisely outside a quarter circle in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.12470","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/2607.12470/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.12470","created_at":"2026-07-15T01:21:36.796499+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.12470v1","created_at":"2026-07-15T01:21:36.796499+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.12470","created_at":"2026-07-15T01:21:36.796499+00:00"},{"alias_kind":"pith_short_12","alias_value":"6RAIHQ6NBVH7","created_at":"2026-07-15T01:21:36.796499+00:00"},{"alias_kind":"pith_short_16","alias_value":"6RAIHQ6NBVH7IMEW","created_at":"2026-07-15T01:21:36.796499+00:00"},{"alias_kind":"pith_short_8","alias_value":"6RAIHQ6N","created_at":"2026-07-15T01:21:36.796499+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/6RAIHQ6NBVH7IMEWD6667AXUYD","json":"https://pith.science/pith/6RAIHQ6NBVH7IMEWD6667AXUYD.json","graph_json":"https://pith.science/api/pith-number/6RAIHQ6NBVH7IMEWD6667AXUYD/graph.json","events_json":"https://pith.science/api/pith-number/6RAIHQ6NBVH7IMEWD6667AXUYD/events.json","paper":"https://pith.science/paper/6RAIHQ6N"},"agent_actions":{"view_html":"https://pith.science/pith/6RAIHQ6NBVH7IMEWD6667AXUYD","download_json":"https://pith.science/pith/6RAIHQ6NBVH7IMEWD6667AXUYD.json","view_paper":"https://pith.science/paper/6RAIHQ6N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.12470&json=true","fetch_graph":"https://pith.science/api/pith-number/6RAIHQ6NBVH7IMEWD6667AXUYD/graph.json","fetch_events":"https://pith.science/api/pith-number/6RAIHQ6NBVH7IMEWD6667AXUYD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6RAIHQ6NBVH7IMEWD6667AXUYD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6RAIHQ6NBVH7IMEWD6667AXUYD/action/storage_attestation","attest_author":"https://pith.science/pith/6RAIHQ6NBVH7IMEWD6667AXUYD/action/author_attestation","sign_citation":"https://pith.science/pith/6RAIHQ6NBVH7IMEWD6667AXUYD/action/citation_signature","submit_replication":"https://pith.science/pith/6RAIHQ6NBVH7IMEWD6667AXUYD/action/replication_record"}},"created_at":"2026-07-15T01:21:36.796499+00:00","updated_at":"2026-07-15T01:21:36.796499+00:00"}