{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:XJMPPAN5D3F4FW7ZVZDYGW3SHX","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":"79acb5a408acfd9dc795f1b0c89427ad6e857bfc255249ef5f2caa729ee974f3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-01-14T19:24:39Z","title_canon_sha256":"78fa6f13aa0729e3feeddcf030811c1d1fe7b5f635915bff75a99f73e481c006"},"schema_version":"1.0","source":{"id":"2601.09817","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2601.09817","created_at":"2026-05-20T00:05:40Z"},{"alias_kind":"arxiv_version","alias_value":"2601.09817v2","created_at":"2026-05-20T00:05:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2601.09817","created_at":"2026-05-20T00:05:40Z"},{"alias_kind":"pith_short_12","alias_value":"XJMPPAN5D3F4","created_at":"2026-05-20T00:05:40Z"},{"alias_kind":"pith_short_16","alias_value":"XJMPPAN5D3F4FW7Z","created_at":"2026-05-20T00:05:40Z"},{"alias_kind":"pith_short_8","alias_value":"XJMPPAN5","created_at":"2026-05-20T00:05:40Z"}],"graph_snapshots":[{"event_id":"sha256:096546862630f7fb3b0523e0be9ef19a9f98f99d0efc0254c69dfeb3dfb5bc7a","target":"graph","created_at":"2026-05-20T00:05:40Z","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/2601.09817/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This work introduces a rigorous notion of localization probability of a quantum state within a given subspace of its Hilbert space. A non-negative operator A is uniquely decomposed as A=B+C, where B is the maximal positive operator supported inside the chosen subspace and C has support disjoint from it. The localized component B can be expressed via the Schur complement and characterized through an A-dependent inner product and suitable trace inequalities. For quantum states, this yields a probability lambda that a state rho be completely contained in a subspace, which is strictly more restric","authors_text":"L. L. Salcedo","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-01-14T19:24:39Z","title":"Localization of quantum states within subspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2601.09817","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":"sha256:64bc66243621b2691d45e87e394ce342ed68094a39c794678928c65976fc5ee8","target":"record","created_at":"2026-05-20T00:05:40Z","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":"79acb5a408acfd9dc795f1b0c89427ad6e857bfc255249ef5f2caa729ee974f3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2026-01-14T19:24:39Z","title_canon_sha256":"78fa6f13aa0729e3feeddcf030811c1d1fe7b5f635915bff75a99f73e481c006"},"schema_version":"1.0","source":{"id":"2601.09817","kind":"arxiv","version":2}},"canonical_sha256":"ba58f781bd1ecbc2dbf9ae47835b723dd290474198f740dd56fafae02d7ac772","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba58f781bd1ecbc2dbf9ae47835b723dd290474198f740dd56fafae02d7ac772","first_computed_at":"2026-05-20T00:05:40.548268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:40.548268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KvzPH2xQOVHhKjyPlLmR2ZpbA8hQtjHYNWgQ16E1Vy1QPHZe4QAnli3XUcV4O9lIq7Hy6vMTWMJRRmL/2k6fBw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:40.548941Z","signed_message":"canonical_sha256_bytes"},"source_id":"2601.09817","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:64bc66243621b2691d45e87e394ce342ed68094a39c794678928c65976fc5ee8","sha256:096546862630f7fb3b0523e0be9ef19a9f98f99d0efc0254c69dfeb3dfb5bc7a"],"state_sha256":"c03b8a7fdeb1ad5c3cc77efd509961c7a7721c08dd5ffcc1d9b1cca94e3c7359"}