{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZRHS2XXIGAC6QLRANDVHAQRLKD","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":"251a0edbff57f4a4d8c4172cba097920c518d85e6f6c6c5885c811eb62be655b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-31T11:19:20Z","title_canon_sha256":"a42688be3c31688410453376467b97ad65bd646f023c252d125b5a5b97b64258"},"schema_version":"1.0","source":{"id":"1508.07766","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07766","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07766v2","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07766","created_at":"2026-05-18T00:55:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZRHS2XXIGAC6","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZRHS2XXIGAC6QLRA","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZRHS2XXI","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:75a77da40c62b3d6d820f11c51caf5d20addcfc8abdff0303a22eb1d1ccfb29f","target":"graph","created_at":"2026-05-18T00:55:34Z","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":"For any measurable set $E$ of a measure space $(X, \\mu)$, let $P_E$ be the (orthogonal) projection on the Hilbert space $L^2(X, \\mu)$ with the range $ran \\, P_E = \\{f \\in L^2(X, \\mu) : f = 0 \\ \\ a.e. \\ on \\ E^c\\}$ that is called a standard subspace of $L^2(X, \\mu)$. Let $T$ be an operator on $L^2(X, \\mu)$ having increasing spectrum relative to standard compressions, that is, for any measurable sets $E$ and $F$ with $E \\subseteq F$, the spectrum of the operator $P_E T|_{ran \\, P_E}$ is contained in the spectrum of the operator $P_F T|_{ran \\, P_F}$. In 2009, Marcoux, Mastnak and Radjavi asked w","authors_text":"Roman Drnov\\v{s}ek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-31T11:19:20Z","title":"Triangularizability of trace-class operators with increasing spectrum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07766","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":"sha256:358ee7e88c7a455a481379c0e0472883b22b930c4a9e84435a5e45d57df86b52","target":"record","created_at":"2026-05-18T00:55:34Z","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":"251a0edbff57f4a4d8c4172cba097920c518d85e6f6c6c5885c811eb62be655b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-08-31T11:19:20Z","title_canon_sha256":"a42688be3c31688410453376467b97ad65bd646f023c252d125b5a5b97b64258"},"schema_version":"1.0","source":{"id":"1508.07766","kind":"arxiv","version":2}},"canonical_sha256":"cc4f2d5ee83005e82e2068ea70422b50dbba646c523d68542370a74f5ed080da","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cc4f2d5ee83005e82e2068ea70422b50dbba646c523d68542370a74f5ed080da","first_computed_at":"2026-05-18T00:55:34.457390Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:55:34.457390Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VDizJ/ZchMcKTVOy51IFz8Qt3w+b+JLQSkhTTzlLNwdf8wGOXZmqgRJjT+39+lxab1yaIN+A5ycPhJ8II0jgBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:55:34.458077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07766","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:358ee7e88c7a455a481379c0e0472883b22b930c4a9e84435a5e45d57df86b52","sha256:75a77da40c62b3d6d820f11c51caf5d20addcfc8abdff0303a22eb1d1ccfb29f"],"state_sha256":"42c24e4a3f77b10a29176768a7f0b39af5e41d09a13b50dd3e5ea12afb8d6c3c"}