{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:FU6OGB5QIRHQOAH72VCXHHX5T3","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":"9fb21441ed4efa40d698d7e6b7e5f7e3b55080cda46ef250f2213fbfb5ca3442","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-06-25T13:33:46Z","title_canon_sha256":"75677f1b963e28641be7d0dd357aa682ba4927bc94aae8710dddaf072fb9434f"},"schema_version":"1.0","source":{"id":"1206.5676","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.5676","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"arxiv_version","alias_value":"1206.5676v1","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.5676","created_at":"2026-05-18T02:48:10Z"},{"alias_kind":"pith_short_12","alias_value":"FU6OGB5QIRHQ","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"FU6OGB5QIRHQOAH7","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"FU6OGB5Q","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:61e0204db2ae7595069a3de46275a6bd41b9448877aa7d6eff7abeb806f46abf","target":"graph","created_at":"2026-05-18T02:48:10Z","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":"We study the asymptotical behaviour of iterates of piecewise contractive maps of the interval. It is known that Poincar\\'e first return maps induced by some Cherry flows on transverse intervals are, up to topological conjugacy, piecewise contractions. These maps also appear in discretely controlled dynamical systems, describing the time evolution of manufacturing process adopting some decision-making policies. An injective map $f:[0,1)\\to [0,1)$ is a {\\it piecewise contraction of $n$ intervals}, if there exists a partition of the interval $[0,1)$ into $n$ intervals $I_1$,..., $I_n$ such that f","authors_text":"Arnaldo Nogueira, Benito Pires","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-06-25T13:33:46Z","title":"Dynamics of piecewise contractions of the interval"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5676","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":"sha256:3ba68e55f5dec2fc4696291f36a1b5cdbebca41fd932addf2aaa01ed6d017b69","target":"record","created_at":"2026-05-18T02:48:10Z","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":"9fb21441ed4efa40d698d7e6b7e5f7e3b55080cda46ef250f2213fbfb5ca3442","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-06-25T13:33:46Z","title_canon_sha256":"75677f1b963e28641be7d0dd357aa682ba4927bc94aae8710dddaf072fb9434f"},"schema_version":"1.0","source":{"id":"1206.5676","kind":"arxiv","version":1}},"canonical_sha256":"2d3ce307b0444f0700ffd545739efd9effb57cae1c3bf2ec5e2d60cfbcbfc136","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2d3ce307b0444f0700ffd545739efd9effb57cae1c3bf2ec5e2d60cfbcbfc136","first_computed_at":"2026-05-18T02:48:10.182757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:48:10.182757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QNz+XOiWT8aU8rCUHlVSgwYqQhePdyrHFCTiNnt7HbG/mXO0a4GofQ20MOkUHvHlJjf++TPtoiEcA5PUTSA1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:48:10.183239Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.5676","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ba68e55f5dec2fc4696291f36a1b5cdbebca41fd932addf2aaa01ed6d017b69","sha256:61e0204db2ae7595069a3de46275a6bd41b9448877aa7d6eff7abeb806f46abf"],"state_sha256":"09e053c6adcbbac7225783b303a0546e59f9490f52f504940f04d12e441ca9ff"}