{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2KDCWBUTSTG7ZAYMTAZUD2MTSJ","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":"b810553f2d904e4a469ea7bdb48b13561a506ada41d1901b4ff2fee246a2f1d7","cross_cats_sorted":["math.MP","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-29T22:08:28Z","title_canon_sha256":"2fd7b159014011b4f792f18115fe5f8501b81aa75f5a82f8f5348b8583fd1279"},"schema_version":"1.0","source":{"id":"1011.0029","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.0029","created_at":"2026-05-18T04:23:56Z"},{"alias_kind":"arxiv_version","alias_value":"1011.0029v1","created_at":"2026-05-18T04:23:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.0029","created_at":"2026-05-18T04:23:56Z"},{"alias_kind":"pith_short_12","alias_value":"2KDCWBUTSTG7","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2KDCWBUTSTG7ZAYM","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2KDCWBUT","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:3a88cc02a6e57507474d955ecf12ce69eb6722323fc849fecc988c3edd51a310","target":"graph","created_at":"2026-05-18T04:23:56Z","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 spectral problem for matrices with a block-hierarchical structure is often considered in context of the theory of complex systems. In the present article, a new class of matrices with a block-rectangular non-symmetric hierarchical structure is introduced and the corresponding spectral problem is investigated. Using these results we study a model of error generation in information sequence where such block-rectangular hierarchical matrices appear in a natural way.","authors_text":"B. Gutkin, V.Al. Osipov","cross_cats":["math.MP","math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-29T22:08:28Z","title":"Spectral problem of block-rectangular hierarchical matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0029","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:af72d13558a1f9278498a77f48cde15142b7bd50e7ebcded081b61795c308064","target":"record","created_at":"2026-05-18T04:23:56Z","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":"b810553f2d904e4a469ea7bdb48b13561a506ada41d1901b4ff2fee246a2f1d7","cross_cats_sorted":["math.MP","math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-10-29T22:08:28Z","title_canon_sha256":"2fd7b159014011b4f792f18115fe5f8501b81aa75f5a82f8f5348b8583fd1279"},"schema_version":"1.0","source":{"id":"1011.0029","kind":"arxiv","version":1}},"canonical_sha256":"d2862b069394cdfc830c983341e993927416a7f0a927c0c40f66a7c73552a359","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2862b069394cdfc830c983341e993927416a7f0a927c0c40f66a7c73552a359","first_computed_at":"2026-05-18T04:23:56.495722Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:56.495722Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fwlV/6IMKEmYkuInv1Z9IKcsdy1bWtO8u/Yra7U6kJJQhy5PKcuCN1FB5vYYg8L7o+pFBT3DqnTnAGcwaOuCBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:56.496235Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.0029","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af72d13558a1f9278498a77f48cde15142b7bd50e7ebcded081b61795c308064","sha256:3a88cc02a6e57507474d955ecf12ce69eb6722323fc849fecc988c3edd51a310"],"state_sha256":"6b02919e97769a518e49f932d7999de3bc27fc681415c947924e7fecb34938fa"}