{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4HRIDBMH6BBD3MP7XHTFQOY64H","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":"5041397398ba9997811441099059988fcc7a591f966d5327f2585fd912b1f861","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-22T15:12:35Z","title_canon_sha256":"f7af421fdb319461110444379473bfad8fe5af1e8f6b211a746ffa148255355d"},"schema_version":"1.0","source":{"id":"2605.23736","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.23736","created_at":"2026-05-25T02:02:29Z"},{"alias_kind":"arxiv_version","alias_value":"2605.23736v1","created_at":"2026-05-25T02:02:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.23736","created_at":"2026-05-25T02:02:29Z"},{"alias_kind":"pith_short_12","alias_value":"4HRIDBMH6BBD","created_at":"2026-05-25T02:02:29Z"},{"alias_kind":"pith_short_16","alias_value":"4HRIDBMH6BBD3MP7","created_at":"2026-05-25T02:02:29Z"},{"alias_kind":"pith_short_8","alias_value":"4HRIDBMH","created_at":"2026-05-25T02:02:29Z"}],"graph_snapshots":[{"event_id":"sha256:c68e51df9acf0e979f1564f32e2375e76ba0a35c8055012c61ee73d7d6fc3741","target":"graph","created_at":"2026-05-25T02:02:29Z","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/2605.23736/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the dynamical properties of composition operators acting on Banach spaces of measurable functions. In particular, we study in some detail the composition operators induced by odometers, which allows us to give a variety of new examples and counter-examples. We also get general statements about supercyclicity and frequent hypercyclicity of composition operators on $L\\_p$-spaces.","authors_text":"Etienne Matheron, Fr\\'ed\\'eric Bayart (LMBP)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-22T15:12:35Z","title":"On the dynamics of composition operators: supercyclicity, odometers and translations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23736","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:e5d0ee7b1dbe50d9f1aa0f9ba2efd1b4e198811b8cda2488fb7cb90ab092e6d7","target":"record","created_at":"2026-05-25T02:02:29Z","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":"5041397398ba9997811441099059988fcc7a591f966d5327f2585fd912b1f861","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-22T15:12:35Z","title_canon_sha256":"f7af421fdb319461110444379473bfad8fe5af1e8f6b211a746ffa148255355d"},"schema_version":"1.0","source":{"id":"2605.23736","kind":"arxiv","version":1}},"canonical_sha256":"e1e2818587f0423db1ffb9e6583b1ee1dc83032edd85c8cb48503c6e467919e8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1e2818587f0423db1ffb9e6583b1ee1dc83032edd85c8cb48503c6e467919e8","first_computed_at":"2026-05-25T02:02:29.226053Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-25T02:02:29.226053Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O/uG/cia08E5Bmy/iZ0C9FlLP7JDcTgpNdq9ipQp9AlG9wetRo5RJVo2A/zbvIpRaO3UAaGg1OEJ0pwtHX1ABw==","signature_status":"signed_v1","signed_at":"2026-05-25T02:02:29.226771Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.23736","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5d0ee7b1dbe50d9f1aa0f9ba2efd1b4e198811b8cda2488fb7cb90ab092e6d7","sha256:c68e51df9acf0e979f1564f32e2375e76ba0a35c8055012c61ee73d7d6fc3741"],"state_sha256":"1abb39d9280d8a2b7cc4121e914179c0a9bbf7c4693b3c9f1f0712e5ee692726"}