{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:FFOHNZ7Z3QD35UF7ICQWA24ZRM","short_pith_number":"pith:FFOHNZ7Z","canonical_record":{"source":{"id":"2303.01738","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-03-03T06:43:50Z","cross_cats_sorted":[],"title_canon_sha256":"a8aeededee518b22f861f0f4d6fad3a19038750f774680c08092afaa022bccbb","abstract_canon_sha256":"404afad194eba680c7454bf72fd266345ab97a826205e8dbfc147c68c1f04bc7"},"schema_version":"1.0"},"canonical_sha256":"295c76e7f9dc07bed0bf40a1606b998b1baed00e14080f2707463564402f1fd2","source":{"kind":"arxiv","id":"2303.01738","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.01738","created_at":"2026-07-05T08:01:58Z"},{"alias_kind":"arxiv_version","alias_value":"2303.01738v3","created_at":"2026-07-05T08:01:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.01738","created_at":"2026-07-05T08:01:58Z"},{"alias_kind":"pith_short_12","alias_value":"FFOHNZ7Z3QD3","created_at":"2026-07-05T08:01:58Z"},{"alias_kind":"pith_short_16","alias_value":"FFOHNZ7Z3QD35UF7","created_at":"2026-07-05T08:01:58Z"},{"alias_kind":"pith_short_8","alias_value":"FFOHNZ7Z","created_at":"2026-07-05T08:01:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:FFOHNZ7Z3QD35UF7ICQWA24ZRM","target":"record","payload":{"canonical_record":{"source":{"id":"2303.01738","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-03-03T06:43:50Z","cross_cats_sorted":[],"title_canon_sha256":"a8aeededee518b22f861f0f4d6fad3a19038750f774680c08092afaa022bccbb","abstract_canon_sha256":"404afad194eba680c7454bf72fd266345ab97a826205e8dbfc147c68c1f04bc7"},"schema_version":"1.0"},"canonical_sha256":"295c76e7f9dc07bed0bf40a1606b998b1baed00e14080f2707463564402f1fd2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:01:58.436009Z","signature_b64":"NNR7URKf6phTntknXKEd5a/sEZpzhYMrdA3VRTbh51hag8oU5fEULPIFqe0SwRiTNPa+WdqH8QFAFa6597VWCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"295c76e7f9dc07bed0bf40a1606b998b1baed00e14080f2707463564402f1fd2","last_reissued_at":"2026-07-05T08:01:58.435456Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:01:58.435456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2303.01738","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:01:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IesIog+knGZHUjhKxNvS2Tyq3c1+DGEGBX+CFvjOh9B6oETRlnpWtu7hLU3xhDP68nLvd42fvzi97+jBLF5sCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:38:35.269916Z"},"content_sha256":"7d3b55652ca5ddd89bdd12455f3290a5c3aa484d22f96c8fb4d01adb543a24ad","schema_version":"1.0","event_id":"sha256:7d3b55652ca5ddd89bdd12455f3290a5c3aa484d22f96c8fb4d01adb543a24ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:FFOHNZ7Z3QD35UF7ICQWA24ZRM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational principle for neutralized Bowen topological entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ercai Chen, Rui Yang, Xiaoyao Zhou","submitted_at":"2023-03-03T06:43:50Z","abstract_excerpt":"Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as $$B_n(x,e^{-n\\epsilon})=\\{y\\in X: d(T^jx, T^jy)<e^{-n\\epsilon}, \\forall 0\\leq j\\leq n-1\\}.$$ We introduce the notion of neutralized Bowen topological entropy of subsets by neutralized Bowen open ball, and establish variational principles for neutralized Bowen topological entropy of compact subsets in terms of neutralized Brin-Katok local entropy and neutralized Katok's entropy."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01738","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.01738/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T08:01:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x1LrVx6cAZcm8iKk2CfGZrNUflN3ZzdhCetI03FgGdJAsvpPGPMtVvXwynIXuYkuaGj5+BRCxqFYHWMiib8wDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-12T22:38:35.270416Z"},"content_sha256":"9b78e081e74d7767f61ee82b88149e071845f75a712861124106cbcf33f2fa57","schema_version":"1.0","event_id":"sha256:9b78e081e74d7767f61ee82b88149e071845f75a712861124106cbcf33f2fa57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FFOHNZ7Z3QD35UF7ICQWA24ZRM/bundle.json","state_url":"https://pith.science/pith/FFOHNZ7Z3QD35UF7ICQWA24ZRM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FFOHNZ7Z3QD35UF7ICQWA24ZRM/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":"2026-08-12T22:38:35Z","links":{"resolver":"https://pith.science/pith/FFOHNZ7Z3QD35UF7ICQWA24ZRM","bundle":"https://pith.science/pith/FFOHNZ7Z3QD35UF7ICQWA24ZRM/bundle.json","state":"https://pith.science/pith/FFOHNZ7Z3QD35UF7ICQWA24ZRM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FFOHNZ7Z3QD35UF7ICQWA24ZRM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:FFOHNZ7Z3QD35UF7ICQWA24ZRM","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":"404afad194eba680c7454bf72fd266345ab97a826205e8dbfc147c68c1f04bc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-03-03T06:43:50Z","title_canon_sha256":"a8aeededee518b22f861f0f4d6fad3a19038750f774680c08092afaa022bccbb"},"schema_version":"1.0","source":{"id":"2303.01738","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.01738","created_at":"2026-07-05T08:01:58Z"},{"alias_kind":"arxiv_version","alias_value":"2303.01738v3","created_at":"2026-07-05T08:01:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.01738","created_at":"2026-07-05T08:01:58Z"},{"alias_kind":"pith_short_12","alias_value":"FFOHNZ7Z3QD3","created_at":"2026-07-05T08:01:58Z"},{"alias_kind":"pith_short_16","alias_value":"FFOHNZ7Z3QD35UF7","created_at":"2026-07-05T08:01:58Z"},{"alias_kind":"pith_short_8","alias_value":"FFOHNZ7Z","created_at":"2026-07-05T08:01:58Z"}],"graph_snapshots":[{"event_id":"sha256:9b78e081e74d7767f61ee82b88149e071845f75a712861124106cbcf33f2fa57","target":"graph","created_at":"2026-07-05T08:01:58Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2303.01738/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as $$B_n(x,e^{-n\\epsilon})=\\{y\\in X: d(T^jx, T^jy)<e^{-n\\epsilon}, \\forall 0\\leq j\\leq n-1\\}.$$ We introduce the notion of neutralized Bowen topological entropy of subsets by neutralized Bowen open ball, and establish variational principles for neutralized Bowen topological entropy of compact subsets in terms of neutralized Brin-Katok local entropy and neutralized Katok's entropy.","authors_text":"Ercai Chen, Rui Yang, Xiaoyao Zhou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-03-03T06:43:50Z","title":"Variational principle for neutralized Bowen topological entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.01738","kind":"arxiv","version":3},"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":"sha256:7d3b55652ca5ddd89bdd12455f3290a5c3aa484d22f96c8fb4d01adb543a24ad","target":"record","created_at":"2026-07-05T08:01:58Z","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":"404afad194eba680c7454bf72fd266345ab97a826205e8dbfc147c68c1f04bc7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2023-03-03T06:43:50Z","title_canon_sha256":"a8aeededee518b22f861f0f4d6fad3a19038750f774680c08092afaa022bccbb"},"schema_version":"1.0","source":{"id":"2303.01738","kind":"arxiv","version":3}},"canonical_sha256":"295c76e7f9dc07bed0bf40a1606b998b1baed00e14080f2707463564402f1fd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"295c76e7f9dc07bed0bf40a1606b998b1baed00e14080f2707463564402f1fd2","first_computed_at":"2026-07-05T08:01:58.435456Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:01:58.435456Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NNR7URKf6phTntknXKEd5a/sEZpzhYMrdA3VRTbh51hag8oU5fEULPIFqe0SwRiTNPa+WdqH8QFAFa6597VWCg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:01:58.436009Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.01738","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d3b55652ca5ddd89bdd12455f3290a5c3aa484d22f96c8fb4d01adb543a24ad","sha256:9b78e081e74d7767f61ee82b88149e071845f75a712861124106cbcf33f2fa57"],"state_sha256":"d4b9cca0eec9b4c8e1b27aae669159bf484b2ff63dacfa3242ca84c4a49baa12"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bt44KEiA2vc9j/6AXNVTpIttLHG5iqAJtYyrYe58O2tAsY0Ze29dTZ3eclpK2hBPevKh3oRZ8imV/F3LLAktCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-12T22:38:35.277070Z","bundle_sha256":"d8b12a7ed0b6ad9ed80d91f3582e064bc755da1c8502d40395f3c76147c5d556"}}