{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:MOER3U3RVO5S2GCMASORQ7NANI","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":"5427365243d453c8befc8592130914edf74569a4670ec1153d9658ddd5acae29","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.CD","submitted_at":"2023-03-10T19:19:56Z","title_canon_sha256":"0e8a4f03d93db847cd8f77ab606eb14124f5f5b72d525748cbac39ce110b3080"},"schema_version":"1.0","source":{"id":"2303.06176","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.06176","created_at":"2026-06-24T01:14:54Z"},{"alias_kind":"arxiv_version","alias_value":"2303.06176v2","created_at":"2026-06-24T01:14:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.06176","created_at":"2026-06-24T01:14:54Z"},{"alias_kind":"pith_short_12","alias_value":"MOER3U3RVO5S","created_at":"2026-06-24T01:14:54Z"},{"alias_kind":"pith_short_16","alias_value":"MOER3U3RVO5S2GCM","created_at":"2026-06-24T01:14:54Z"},{"alias_kind":"pith_short_8","alias_value":"MOER3U3R","created_at":"2026-06-24T01:14:54Z"}],"graph_snapshots":[{"event_id":"sha256:bc88ee65a7d4efae080aac5cbb196ad89f918ad4c29da5e3038539684cd3c0a1","target":"graph","created_at":"2026-06-24T01:14:54Z","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/2303.06176/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The standard logistic map, $x'=ax(1-x)$, serves as a paradigmatic model to demonstrate how apparently simple non-linear equations lead to complex and chaotic dynamics. In this work we introduce and investigate its matrix analogue defined for an arbitrary matrix $X$ of a given order $N$. We show that for an arbitrary initial ensemble of hermitian random matrices with a continuous level density supported on the interval $[0,1]$, the asymptotic level density converges to the invariant measure of the logistic map. Depending on the parameter $a$ the constructed measure may be either singular, fract","authors_text":"Karol \\.Zyczkowski, {\\L}ukasz Pawela","cross_cats":["quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.CD","submitted_at":"2023-03-10T19:19:56Z","title":"Matrix logistic map: fractal spectral distributions and transfer of chaos"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.06176","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":"sha256:8886b99e59769d84e9ccdb96351951a7f0fa83905c1b7bc9f038587ce722f6dd","target":"record","created_at":"2026-06-24T01:14:54Z","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":"5427365243d453c8befc8592130914edf74569a4670ec1153d9658ddd5acae29","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"nlin.CD","submitted_at":"2023-03-10T19:19:56Z","title_canon_sha256":"0e8a4f03d93db847cd8f77ab606eb14124f5f5b72d525748cbac39ce110b3080"},"schema_version":"1.0","source":{"id":"2303.06176","kind":"arxiv","version":2}},"canonical_sha256":"63891dd371abbb2d184c049d187da06a35a6199084706bb307ba8b4c524734ad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"63891dd371abbb2d184c049d187da06a35a6199084706bb307ba8b4c524734ad","first_computed_at":"2026-06-24T01:14:54.839176Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:14:54.839176Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XePqW3dHdDpyRwrHMJgiBRn6/1oPSQzQJ3iYSp3Shi6rrLPBx+Kk/vDk3LNO0W2ZF8g9V3smk6ju5R5MIINzCw==","signature_status":"signed_v1","signed_at":"2026-06-24T01:14:54.839845Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.06176","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8886b99e59769d84e9ccdb96351951a7f0fa83905c1b7bc9f038587ce722f6dd","sha256:bc88ee65a7d4efae080aac5cbb196ad89f918ad4c29da5e3038539684cd3c0a1"],"state_sha256":"0aef5d4dbe76bf978c17db1fc34218c48500e6ee7a56850924bedd67ca4b658a"}