{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QD5RBTPBEV76IPAMZYK5B7V2JA","short_pith_number":"pith:QD5RBTPB","canonical_record":{"source":{"id":"1505.07177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-27T02:25:26Z","cross_cats_sorted":[],"title_canon_sha256":"25783cb94ae0d0a9b6b8b9bcb033b5ab8e4b899b36717d28956e1d58c72ec707","abstract_canon_sha256":"b65863d835916676d9d82f2834e2c65eb8fdf174696a056338e6cc643a14dcec"},"schema_version":"1.0"},"canonical_sha256":"80fb10cde1257fe43c0cce15d0feba480899ea6fde1dfa045ecceed747d68814","source":{"kind":"arxiv","id":"1505.07177","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07177","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07177v1","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07177","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"pith_short_12","alias_value":"QD5RBTPBEV76","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QD5RBTPBEV76IPAM","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QD5RBTPB","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QD5RBTPBEV76IPAMZYK5B7V2JA","target":"record","payload":{"canonical_record":{"source":{"id":"1505.07177","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-27T02:25:26Z","cross_cats_sorted":[],"title_canon_sha256":"25783cb94ae0d0a9b6b8b9bcb033b5ab8e4b899b36717d28956e1d58c72ec707","abstract_canon_sha256":"b65863d835916676d9d82f2834e2c65eb8fdf174696a056338e6cc643a14dcec"},"schema_version":"1.0"},"canonical_sha256":"80fb10cde1257fe43c0cce15d0feba480899ea6fde1dfa045ecceed747d68814","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:07.250733Z","signature_b64":"vt6Hk9HAiM6xSwRNo4uTi1nbAD7xAJTHY36lHjEtawS1QX+cVIEp1t6+raMFfV5K62pLAiSSaHOY5P63ZA8FCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80fb10cde1257fe43c0cce15d0feba480899ea6fde1dfa045ecceed747d68814","last_reissued_at":"2026-05-18T02:02:07.250190Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:07.250190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.07177","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:02:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0biGR07BPGrdFC7OyIm8cngLl6+P3ok70XOgsVDxZAoyevZMfuf+vcZcouw27Z54Tu8Ls4v7p9NYxNjZXdvmBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:32:38.842295Z"},"content_sha256":"899504be7c0f83639633888fd3997c1d822467f173553823be706d2ffb32926d","schema_version":"1.0","event_id":"sha256:899504be7c0f83639633888fd3997c1d822467f173553823be706d2ffb32926d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QD5RBTPBEV76IPAMZYK5B7V2JA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Center Specification Property and Entropy for Partially Hyperbolic Diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Lin Wang, Yujun Zhu","submitted_at":"2015-05-27T02:25:26Z","abstract_excerpt":"Let $f$ be a partially hyperbolic diffeomorphism on a closed (i.e., compact and boundaryless) Riemannian manifold $M$ with a uniformly compact center foliation $\\mathcal{W}^{c}$. The relationship among topological entropy $h(f)$, entropy of the restriction of $f$ on the center foliation $h(f, \\mathcal{W}^{c})$ and the growth rate of periodic center leaves $p^{c}(f)$ is investigated. It is first shown that if a compact locally maximal invariant center set $\\Lambda$ is center topologically mixing then $f|_{\\Lambda}$ has the center specification property, i.e., any specification with a large spac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07177","kind":"arxiv","version":1},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:02:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q9Pq1VH6SrC3bv7qoZrjWZvV21pMAV1d4BA4aDEcOFfgHlMRKPR8uvJfa5/pBvRnijPwm6PFyduNuXmz3ptZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:32:38.842647Z"},"content_sha256":"f38a7690af07d2323059d1fa04221b40e86998a33628c29e823576a5da2b5824","schema_version":"1.0","event_id":"sha256:f38a7690af07d2323059d1fa04221b40e86998a33628c29e823576a5da2b5824"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QD5RBTPBEV76IPAMZYK5B7V2JA/bundle.json","state_url":"https://pith.science/pith/QD5RBTPBEV76IPAMZYK5B7V2JA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QD5RBTPBEV76IPAMZYK5B7V2JA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T23:32:38Z","links":{"resolver":"https://pith.science/pith/QD5RBTPBEV76IPAMZYK5B7V2JA","bundle":"https://pith.science/pith/QD5RBTPBEV76IPAMZYK5B7V2JA/bundle.json","state":"https://pith.science/pith/QD5RBTPBEV76IPAMZYK5B7V2JA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QD5RBTPBEV76IPAMZYK5B7V2JA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QD5RBTPBEV76IPAMZYK5B7V2JA","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":"b65863d835916676d9d82f2834e2c65eb8fdf174696a056338e6cc643a14dcec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-27T02:25:26Z","title_canon_sha256":"25783cb94ae0d0a9b6b8b9bcb033b5ab8e4b899b36717d28956e1d58c72ec707"},"schema_version":"1.0","source":{"id":"1505.07177","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.07177","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"arxiv_version","alias_value":"1505.07177v1","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.07177","created_at":"2026-05-18T02:02:07Z"},{"alias_kind":"pith_short_12","alias_value":"QD5RBTPBEV76","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QD5RBTPBEV76IPAM","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QD5RBTPB","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:f38a7690af07d2323059d1fa04221b40e86998a33628c29e823576a5da2b5824","target":"graph","created_at":"2026-05-18T02:02:07Z","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":"Let $f$ be a partially hyperbolic diffeomorphism on a closed (i.e., compact and boundaryless) Riemannian manifold $M$ with a uniformly compact center foliation $\\mathcal{W}^{c}$. The relationship among topological entropy $h(f)$, entropy of the restriction of $f$ on the center foliation $h(f, \\mathcal{W}^{c})$ and the growth rate of periodic center leaves $p^{c}(f)$ is investigated. It is first shown that if a compact locally maximal invariant center set $\\Lambda$ is center topologically mixing then $f|_{\\Lambda}$ has the center specification property, i.e., any specification with a large spac","authors_text":"Lin Wang, Yujun Zhu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-27T02:25:26Z","title":"Center Specification Property and Entropy for Partially Hyperbolic Diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.07177","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":"sha256:899504be7c0f83639633888fd3997c1d822467f173553823be706d2ffb32926d","target":"record","created_at":"2026-05-18T02:02:07Z","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":"b65863d835916676d9d82f2834e2c65eb8fdf174696a056338e6cc643a14dcec","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-05-27T02:25:26Z","title_canon_sha256":"25783cb94ae0d0a9b6b8b9bcb033b5ab8e4b899b36717d28956e1d58c72ec707"},"schema_version":"1.0","source":{"id":"1505.07177","kind":"arxiv","version":1}},"canonical_sha256":"80fb10cde1257fe43c0cce15d0feba480899ea6fde1dfa045ecceed747d68814","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80fb10cde1257fe43c0cce15d0feba480899ea6fde1dfa045ecceed747d68814","first_computed_at":"2026-05-18T02:02:07.250190Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:07.250190Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vt6Hk9HAiM6xSwRNo4uTi1nbAD7xAJTHY36lHjEtawS1QX+cVIEp1t6+raMFfV5K62pLAiSSaHOY5P63ZA8FCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:07.250733Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.07177","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:899504be7c0f83639633888fd3997c1d822467f173553823be706d2ffb32926d","sha256:f38a7690af07d2323059d1fa04221b40e86998a33628c29e823576a5da2b5824"],"state_sha256":"cbe1075514c77df75ba31230e35933a5161fe41718bf4d31d5c6316f9a145446"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eFkZ1X4N8XLQ0bCPQmu+0sgVSsWyhph53u5RqTfsbI/D4xjvjg2CUwwkaxP7ooeAoHvpjHrgUlayIU8X4aiEAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:32:38.844571Z","bundle_sha256":"023c1e180312ebc59c19f47bffa0d9ce33488760b849a15e0b273ce6447977a1"}}