{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:MFFBXNGZWJSZNNJSF6DW53NUBR","short_pith_number":"pith:MFFBXNGZ","canonical_record":{"source":{"id":"1110.5201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-24T11:19:38Z","cross_cats_sorted":[],"title_canon_sha256":"91333ea3211a97a94e5fd3b388a0300223d8fa79a420e3539fac646f889e76a4","abstract_canon_sha256":"477f321f61784feeb95bd67e2f481f2b5a5f3da75ce93446923b95823f0e4ea0"},"schema_version":"1.0"},"canonical_sha256":"614a1bb4d9b26596b5322f876eedb40c535a456a64250572fb933ffdf7f7d406","source":{"kind":"arxiv","id":"1110.5201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5201","created_at":"2026-05-18T04:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5201v1","created_at":"2026-05-18T04:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5201","created_at":"2026-05-18T04:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"MFFBXNGZWJSZ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MFFBXNGZWJSZNNJS","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MFFBXNGZ","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:MFFBXNGZWJSZNNJSF6DW53NUBR","target":"record","payload":{"canonical_record":{"source":{"id":"1110.5201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-24T11:19:38Z","cross_cats_sorted":[],"title_canon_sha256":"91333ea3211a97a94e5fd3b388a0300223d8fa79a420e3539fac646f889e76a4","abstract_canon_sha256":"477f321f61784feeb95bd67e2f481f2b5a5f3da75ce93446923b95823f0e4ea0"},"schema_version":"1.0"},"canonical_sha256":"614a1bb4d9b26596b5322f876eedb40c535a456a64250572fb933ffdf7f7d406","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:24.444958Z","signature_b64":"uusXZ1W9KPYCmsVOI7f0GgEO0k1fhxku4luUzbfHj62tBGxgbGqiciBMQZ8OY6mz2CPGuCjXOE7pjd4jHKz7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"614a1bb4d9b26596b5322f876eedb40c535a456a64250572fb933ffdf7f7d406","last_reissued_at":"2026-05-18T04:10:24.444276Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:24.444276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.5201","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":"2026-05-18T04:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UxG7tiYTU+7b0N7+K7YZUfLAZoQRCktb+NdUrkkGNpnFgMOrVvXZ6EfiBCda9tqEKT7vk/OOj+sSdwwA+lRRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:33:51.134541Z"},"content_sha256":"384cd5c282e7049de6bebe9d816d8118cce7ab130bf1fa77d755fa7962a884ab","schema_version":"1.0","event_id":"sha256:384cd5c282e7049de6bebe9d816d8118cce7ab130bf1fa77d755fa7962a884ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:MFFBXNGZWJSZNNJSF6DW53NUBR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive topological entropy implies chaos DC2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Tomasz Downarowicz","submitted_at":"2011-10-24T11:19:38Z","abstract_excerpt":"Using methods of ergodic theory we prove as in the title."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5201","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":"2026-05-18T04:10:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ZuFWV8RdMbXMByZ+2zAO6FnSCLgAfencDorZ0HkZYAuZSFCoebLikdssEClGhMzPV2hVWbVMehoRvhQk7O6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T02:33:51.135170Z"},"content_sha256":"f684fa5879a9f5a6583380f985e49329eef92f6b915244487e5a545af31b2fdb","schema_version":"1.0","event_id":"sha256:f684fa5879a9f5a6583380f985e49329eef92f6b915244487e5a545af31b2fdb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MFFBXNGZWJSZNNJSF6DW53NUBR/bundle.json","state_url":"https://pith.science/pith/MFFBXNGZWJSZNNJSF6DW53NUBR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MFFBXNGZWJSZNNJSF6DW53NUBR/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":"2026-06-01T02:33:51Z","links":{"resolver":"https://pith.science/pith/MFFBXNGZWJSZNNJSF6DW53NUBR","bundle":"https://pith.science/pith/MFFBXNGZWJSZNNJSF6DW53NUBR/bundle.json","state":"https://pith.science/pith/MFFBXNGZWJSZNNJSF6DW53NUBR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MFFBXNGZWJSZNNJSF6DW53NUBR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:MFFBXNGZWJSZNNJSF6DW53NUBR","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":"477f321f61784feeb95bd67e2f481f2b5a5f3da75ce93446923b95823f0e4ea0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-24T11:19:38Z","title_canon_sha256":"91333ea3211a97a94e5fd3b388a0300223d8fa79a420e3539fac646f889e76a4"},"schema_version":"1.0","source":{"id":"1110.5201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5201","created_at":"2026-05-18T04:10:24Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5201v1","created_at":"2026-05-18T04:10:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5201","created_at":"2026-05-18T04:10:24Z"},{"alias_kind":"pith_short_12","alias_value":"MFFBXNGZWJSZ","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"MFFBXNGZWJSZNNJS","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"MFFBXNGZ","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:f684fa5879a9f5a6583380f985e49329eef92f6b915244487e5a545af31b2fdb","target":"graph","created_at":"2026-05-18T04:10:24Z","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":"Using methods of ergodic theory we prove as in the title.","authors_text":"Tomasz Downarowicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-24T11:19:38Z","title":"Positive topological entropy implies chaos DC2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5201","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":"sha256:384cd5c282e7049de6bebe9d816d8118cce7ab130bf1fa77d755fa7962a884ab","target":"record","created_at":"2026-05-18T04:10:24Z","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":"477f321f61784feeb95bd67e2f481f2b5a5f3da75ce93446923b95823f0e4ea0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-10-24T11:19:38Z","title_canon_sha256":"91333ea3211a97a94e5fd3b388a0300223d8fa79a420e3539fac646f889e76a4"},"schema_version":"1.0","source":{"id":"1110.5201","kind":"arxiv","version":1}},"canonical_sha256":"614a1bb4d9b26596b5322f876eedb40c535a456a64250572fb933ffdf7f7d406","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"614a1bb4d9b26596b5322f876eedb40c535a456a64250572fb933ffdf7f7d406","first_computed_at":"2026-05-18T04:10:24.444276Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:24.444276Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uusXZ1W9KPYCmsVOI7f0GgEO0k1fhxku4luUzbfHj62tBGxgbGqiciBMQZ8OY6mz2CPGuCjXOE7pjd4jHKz7AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:24.444958Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:384cd5c282e7049de6bebe9d816d8118cce7ab130bf1fa77d755fa7962a884ab","sha256:f684fa5879a9f5a6583380f985e49329eef92f6b915244487e5a545af31b2fdb"],"state_sha256":"3c8b8076effe248ab8a11d5648b13b0c43327c564ee00de72b82137ff5597dda"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rnN9nsfih8TAVhoIUftjQBY2Q7fmhBDM+ZKmRZW4cVaDSJIh+/I1Vn5Cz+LRsqJWYBFrE0L16QlhDVUOUaH3Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T02:33:51.139367Z","bundle_sha256":"5365371c9457df5b8c097099e9aa063e6ae949c15a6e866ade271b93d207da47"}}