{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:3CBMA5OR4YFEAJQ5HGSAF7X3NQ","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":"878afc94d504d5e7f427f2f08197d13f0ac16bc240e9fb493cccf2045c1cf928","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-20T03:53:14Z","title_canon_sha256":"610ed1032a158d40fe193d6be46df7dca430316ccee20770c16e53af821eb204"},"schema_version":"1.0","source":{"id":"1709.06717","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.06717","created_at":"2026-05-18T00:34:40Z"},{"alias_kind":"arxiv_version","alias_value":"1709.06717v1","created_at":"2026-05-18T00:34:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.06717","created_at":"2026-05-18T00:34:40Z"},{"alias_kind":"pith_short_12","alias_value":"3CBMA5OR4YFE","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_16","alias_value":"3CBMA5OR4YFEAJQ5","created_at":"2026-05-18T12:30:58Z"},{"alias_kind":"pith_short_8","alias_value":"3CBMA5OR","created_at":"2026-05-18T12:30:58Z"}],"graph_snapshots":[{"event_id":"sha256:38bc7bdde7d3b9c32dc36c31bdf6e74bd04adfc95b1a7728628a928779115f33","target":"graph","created_at":"2026-05-18T00:34:40Z","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 establish the relationship between the growth rate of periodic orbits and the topological entropy for $C^1$ generic vector fields: this extends a classical result of Katok for $C^{1+\\alpha}(\\alpha>0)$ surface diffeomorphisms to $C^1$ generic vector fields of any dimension. The main difficulty comes from the existence of singularities and the shear of the flow.","authors_text":"Dawei Yang, Wanlou Wu, Yong Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-20T03:53:14Z","title":"On the growth rate of periodic orbits for vector fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06717","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:af3b4d456c806047ba3ede3e4d04ab8c34bc9ac05adbdcf38e28651fe41ef026","target":"record","created_at":"2026-05-18T00:34:40Z","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":"878afc94d504d5e7f427f2f08197d13f0ac16bc240e9fb493cccf2045c1cf928","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-09-20T03:53:14Z","title_canon_sha256":"610ed1032a158d40fe193d6be46df7dca430316ccee20770c16e53af821eb204"},"schema_version":"1.0","source":{"id":"1709.06717","kind":"arxiv","version":1}},"canonical_sha256":"d882c075d1e60a40261d39a402fefb6c10ad3cbd9e6b2494102bdf210d681669","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d882c075d1e60a40261d39a402fefb6c10ad3cbd9e6b2494102bdf210d681669","first_computed_at":"2026-05-18T00:34:40.706110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:34:40.706110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LbBpwxn08V3JLPi8uxM57ra+By2a/Rf5tTo+EaA4k6Yke4WvPDJnqSQM4Hzo9dPBq0sGOWcgugs9Viwga4+MBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:34:40.706726Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.06717","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af3b4d456c806047ba3ede3e4d04ab8c34bc9ac05adbdcf38e28651fe41ef026","sha256:38bc7bdde7d3b9c32dc36c31bdf6e74bd04adfc95b1a7728628a928779115f33"],"state_sha256":"28861ce41439189f9431f8d58c80981ebb8950143edbc8307d6913853b1ae475"}