{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:JWI7RA7CTCBZ66XSQ7YQWMEGOU","short_pith_number":"pith:JWI7RA7C","canonical_record":{"source":{"id":"1011.2441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-10T17:31:57Z","cross_cats_sorted":[],"title_canon_sha256":"c9cec5e2c28201e7a20dbe55a776507f4047c7bea1c4d004a8a36a7758e1380f","abstract_canon_sha256":"11c7e7c7ad741bc00a95bdc8380b54c539dfefaf0dee397570297c1334cd8e32"},"schema_version":"1.0"},"canonical_sha256":"4d91f883e298839f7af287f10b308675390709fddce4296b955bcb60a9da267c","source":{"kind":"arxiv","id":"1011.2441","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2441","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2441v1","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2441","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"JWI7RA7CTCBZ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JWI7RA7CTCBZ66XS","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JWI7RA7C","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:JWI7RA7CTCBZ66XSQ7YQWMEGOU","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2441","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-10T17:31:57Z","cross_cats_sorted":[],"title_canon_sha256":"c9cec5e2c28201e7a20dbe55a776507f4047c7bea1c4d004a8a36a7758e1380f","abstract_canon_sha256":"11c7e7c7ad741bc00a95bdc8380b54c539dfefaf0dee397570297c1334cd8e32"},"schema_version":"1.0"},"canonical_sha256":"4d91f883e298839f7af287f10b308675390709fddce4296b955bcb60a9da267c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:36.823285Z","signature_b64":"J8ucAenYpmmQdV1WH5WTZ+P+d30MojQSAY07xLCNGEYozKOE+wx1mECrp1oDtjHBnBK/ZEoETq4OiU4NzN/XCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d91f883e298839f7af287f10b308675390709fddce4296b955bcb60a9da267c","last_reissued_at":"2026-05-17T23:53:36.822649Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:36.822649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2441","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":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2Ho0cdPdxF7b6iyw1f6Yg5UczyBBMnaOSYTEiydKT1G9kJqQgYvcfbzBy4uBtpa+FGnmQhwkjwAWrEdNK5/8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:06:27.975593Z"},"content_sha256":"955a0f9a9b1e371d48368a4282ae4598e6ed4acd14ec483766bde879f90712c0","schema_version":"1.0","event_id":"sha256:955a0f9a9b1e371d48368a4282ae4598e6ed4acd14ec483766bde879f90712c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:JWI7RA7CTCBZ66XSQ7YQWMEGOU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A lower bound for topological entropy of generic non Anosov symplectic diffeomorphisms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ali Tahzibi, Thiago Catalan","submitted_at":"2010-11-10T17:31:57Z","abstract_excerpt":"We prove that a $C^1-$generic symplectic diffeomorphism is either Anosov or the topological entropy is bounded from below by the supremum over the smallest positive Lyapunov exponent of the periodic points. We also prove that $C^1-$generic symplectic diffeomorphisms outside the Anosov ones do not admit symbolic extension and finally we give examples of volume preserving diffeomorphisms which are not point of upper semicontinuity of entropy function in $C^1-$topology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2441","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":"2026-05-17T23:53:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1ld/qeXAz8WhZeoxkloCI4L2WzIHxfOSiKpTL5AxPi853EzTzYLOZmo8a015bMgNhohibQJ16Pbb5c2frxOgBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:06:27.976404Z"},"content_sha256":"7a2a716f0f731d05e4fb69d81d42279593546b420035d62084198eb93a93cacd","schema_version":"1.0","event_id":"sha256:7a2a716f0f731d05e4fb69d81d42279593546b420035d62084198eb93a93cacd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JWI7RA7CTCBZ66XSQ7YQWMEGOU/bundle.json","state_url":"https://pith.science/pith/JWI7RA7CTCBZ66XSQ7YQWMEGOU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JWI7RA7CTCBZ66XSQ7YQWMEGOU/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":"2026-06-07T21:06:27Z","links":{"resolver":"https://pith.science/pith/JWI7RA7CTCBZ66XSQ7YQWMEGOU","bundle":"https://pith.science/pith/JWI7RA7CTCBZ66XSQ7YQWMEGOU/bundle.json","state":"https://pith.science/pith/JWI7RA7CTCBZ66XSQ7YQWMEGOU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JWI7RA7CTCBZ66XSQ7YQWMEGOU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:JWI7RA7CTCBZ66XSQ7YQWMEGOU","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":"11c7e7c7ad741bc00a95bdc8380b54c539dfefaf0dee397570297c1334cd8e32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-10T17:31:57Z","title_canon_sha256":"c9cec5e2c28201e7a20dbe55a776507f4047c7bea1c4d004a8a36a7758e1380f"},"schema_version":"1.0","source":{"id":"1011.2441","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2441","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2441v1","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2441","created_at":"2026-05-17T23:53:36Z"},{"alias_kind":"pith_short_12","alias_value":"JWI7RA7CTCBZ","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"JWI7RA7CTCBZ66XS","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"JWI7RA7C","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:7a2a716f0f731d05e4fb69d81d42279593546b420035d62084198eb93a93cacd","target":"graph","created_at":"2026-05-17T23:53:36Z","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 prove that a $C^1-$generic symplectic diffeomorphism is either Anosov or the topological entropy is bounded from below by the supremum over the smallest positive Lyapunov exponent of the periodic points. We also prove that $C^1-$generic symplectic diffeomorphisms outside the Anosov ones do not admit symbolic extension and finally we give examples of volume preserving diffeomorphisms which are not point of upper semicontinuity of entropy function in $C^1-$topology.","authors_text":"Ali Tahzibi, Thiago Catalan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-10T17:31:57Z","title":"A lower bound for topological entropy of generic non Anosov symplectic diffeomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2441","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":"sha256:955a0f9a9b1e371d48368a4282ae4598e6ed4acd14ec483766bde879f90712c0","target":"record","created_at":"2026-05-17T23:53:36Z","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":"11c7e7c7ad741bc00a95bdc8380b54c539dfefaf0dee397570297c1334cd8e32","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-11-10T17:31:57Z","title_canon_sha256":"c9cec5e2c28201e7a20dbe55a776507f4047c7bea1c4d004a8a36a7758e1380f"},"schema_version":"1.0","source":{"id":"1011.2441","kind":"arxiv","version":1}},"canonical_sha256":"4d91f883e298839f7af287f10b308675390709fddce4296b955bcb60a9da267c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d91f883e298839f7af287f10b308675390709fddce4296b955bcb60a9da267c","first_computed_at":"2026-05-17T23:53:36.822649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:36.822649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J8ucAenYpmmQdV1WH5WTZ+P+d30MojQSAY07xLCNGEYozKOE+wx1mECrp1oDtjHBnBK/ZEoETq4OiU4NzN/XCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:36.823285Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2441","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:955a0f9a9b1e371d48368a4282ae4598e6ed4acd14ec483766bde879f90712c0","sha256:7a2a716f0f731d05e4fb69d81d42279593546b420035d62084198eb93a93cacd"],"state_sha256":"327fa8595a811e56b72166e7db83b23a006afd00daf39c01be8d56987a0cb569"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YNZoRi9uNyKi6cOoZO3CBPa8Xg/gqnyd2CuXol88JSOQxMzshGyJIaJUwNx/U6Is9qgbkpHL4q4gJ6bJGh2oCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:06:27.980464Z","bundle_sha256":"92a4131fb7b1b2b179958569df4051b4881126a506f12e800ee2a38462ff924d"}}