{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HP74VE57TYPNNUNIIEA3CDMFXJ","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":"ad60d9c0adff18bcf668b3cdabd486f8f9f16910f453b66ca696b72e420712c1","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-24T12:36:31Z","title_canon_sha256":"c548477cd635a951ce32ed6b6ba3ad3393b7ea39a8c6c0451648802562d19b87"},"schema_version":"1.0","source":{"id":"1706.07945","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07945","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07945v2","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07945","created_at":"2026-05-18T00:40:53Z"},{"alias_kind":"pith_short_12","alias_value":"HP74VE57TYPN","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_16","alias_value":"HP74VE57TYPNNUNI","created_at":"2026-05-18T12:31:18Z"},{"alias_kind":"pith_short_8","alias_value":"HP74VE57","created_at":"2026-05-18T12:31:18Z"}],"graph_snapshots":[{"event_id":"sha256:2853e816a53df86b064102fd59d2d5300ff1e5e8071688cb707815d05aaf53a0","target":"graph","created_at":"2026-05-18T00:40:53Z","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 Radon-Nikodym formalism is used to study the structure of the set of positive maps from $\\mathcal{B}(\\mathcal{H})$ into itself, where $\\mathcal{H}$ is a finite dimensional Hilbert space. In particular, this formalism was employed to formulate simple criteria which ensure that certain maps are non decomposable. In that way, a recipe for construction of non decomposable maps was obtained.","authors_text":"W. A. Majewski","cross_cats":["math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-24T12:36:31Z","title":"On the origin of non-decomposable maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07945","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":"sha256:96563cc19629edff31d8a8dc1fe295276b202ef6c40139d6b4858caf8246204a","target":"record","created_at":"2026-05-18T00:40:53Z","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":"ad60d9c0adff18bcf668b3cdabd486f8f9f16910f453b66ca696b72e420712c1","cross_cats_sorted":["math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-06-24T12:36:31Z","title_canon_sha256":"c548477cd635a951ce32ed6b6ba3ad3393b7ea39a8c6c0451648802562d19b87"},"schema_version":"1.0","source":{"id":"1706.07945","kind":"arxiv","version":2}},"canonical_sha256":"3bffca93bf9e1ed6d1a84101b10d85ba5870a39a645c201dff1b3caafb716f6a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3bffca93bf9e1ed6d1a84101b10d85ba5870a39a645c201dff1b3caafb716f6a","first_computed_at":"2026-05-18T00:40:53.700645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:53.700645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7cu9yU0LhopJ8lxHBegIT3L0HF9W4HCXFuSszWGEpkWgW6jOTIisvsZUQG5quJmzEzCJwdquI5Q5OorlHRvdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:53.701173Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07945","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:96563cc19629edff31d8a8dc1fe295276b202ef6c40139d6b4858caf8246204a","sha256:2853e816a53df86b064102fd59d2d5300ff1e5e8071688cb707815d05aaf53a0"],"state_sha256":"b15f8a8c596c3d4e9be580be92087de7f6dfd2db04ba91d0f726b4e9fa3a8595"}