{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4AMC3BPK27ZKSNF7QLAJXWH5HH","short_pith_number":"pith:4AMC3BPK","schema_version":"1.0","canonical_sha256":"e0182d85ead7f2a934bf82c09bd8fd39ce8e761e212d7f51a38e05b3b2bc9e2c","source":{"kind":"arxiv","id":"1503.01036","version":2},"attestation_state":"computed","paper":{"title":"Amorphic complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"G. Fuhrmann, M. Gr\\\"oger, T. J\\\"ager","submitted_at":"2015-03-03T18:22:55Z","abstract_excerpt":"We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For instance, it gives positive value to Denjoy examples on the circle and Sturmian subshifts, while being zero for all isometries and Morse-Smale systems. After discussing basic properties and examples, we show that amorphic complexity and the underlying asymptotic separation numbers can be used to distinguish almost automorphic minimal systems from equicontinuous o"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.01036","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-03T18:22:55Z","cross_cats_sorted":[],"title_canon_sha256":"68d59205262d3cf16a75ff64e89bbd4548aec117989c93c7128807ae54940be9","abstract_canon_sha256":"744672fc41f127f31c90b80888334532105cd22a0a792bcb7731f5ed34b834ef"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:36.768477Z","signature_b64":"crdAXhUshFGmE49BQbjncs3kxeItI41h3zVPGoNmpqjO4sGOVHPdExnR4Ng10lG3Uv0txLvU5mDUC8pdStJvCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0182d85ead7f2a934bf82c09bd8fd39ce8e761e212d7f51a38e05b3b2bc9e2c","last_reissued_at":"2026-05-18T01:20:36.767965Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:36.767965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Amorphic complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"G. Fuhrmann, M. Gr\\\"oger, T. J\\\"ager","submitted_at":"2015-03-03T18:22:55Z","abstract_excerpt":"We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For instance, it gives positive value to Denjoy examples on the circle and Sturmian subshifts, while being zero for all isometries and Morse-Smale systems. After discussing basic properties and examples, we show that amorphic complexity and the underlying asymptotic separation numbers can be used to distinguish almost automorphic minimal systems from equicontinuous o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01036","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.01036","created_at":"2026-05-18T01:20:36.768044+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.01036v2","created_at":"2026-05-18T01:20:36.768044+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01036","created_at":"2026-05-18T01:20:36.768044+00:00"},{"alias_kind":"pith_short_12","alias_value":"4AMC3BPK27ZK","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4AMC3BPK27ZKSNF7","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4AMC3BPK","created_at":"2026-05-18T12:29:05.191682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4AMC3BPK27ZKSNF7QLAJXWH5HH","json":"https://pith.science/pith/4AMC3BPK27ZKSNF7QLAJXWH5HH.json","graph_json":"https://pith.science/api/pith-number/4AMC3BPK27ZKSNF7QLAJXWH5HH/graph.json","events_json":"https://pith.science/api/pith-number/4AMC3BPK27ZKSNF7QLAJXWH5HH/events.json","paper":"https://pith.science/paper/4AMC3BPK"},"agent_actions":{"view_html":"https://pith.science/pith/4AMC3BPK27ZKSNF7QLAJXWH5HH","download_json":"https://pith.science/pith/4AMC3BPK27ZKSNF7QLAJXWH5HH.json","view_paper":"https://pith.science/paper/4AMC3BPK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.01036&json=true","fetch_graph":"https://pith.science/api/pith-number/4AMC3BPK27ZKSNF7QLAJXWH5HH/graph.json","fetch_events":"https://pith.science/api/pith-number/4AMC3BPK27ZKSNF7QLAJXWH5HH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4AMC3BPK27ZKSNF7QLAJXWH5HH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4AMC3BPK27ZKSNF7QLAJXWH5HH/action/storage_attestation","attest_author":"https://pith.science/pith/4AMC3BPK27ZKSNF7QLAJXWH5HH/action/author_attestation","sign_citation":"https://pith.science/pith/4AMC3BPK27ZKSNF7QLAJXWH5HH/action/citation_signature","submit_replication":"https://pith.science/pith/4AMC3BPK27ZKSNF7QLAJXWH5HH/action/replication_record"}},"created_at":"2026-05-18T01:20:36.768044+00:00","updated_at":"2026-05-18T01:20:36.768044+00:00"}