{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PN62KMPTHQWBQKH6U6QQWX7RHU","short_pith_number":"pith:PN62KMPT","canonical_record":{"source":{"id":"1102.0612","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-03T07:53:25Z","cross_cats_sorted":[],"title_canon_sha256":"96fc5931b494dcfea7e38ebafcd5c0b0df6652856bd288938a0d06c7ff12dcc8","abstract_canon_sha256":"0d5b64867e69e0c00b58504758792386973366d73571fc7e7724d6c6e0ca2e15"},"schema_version":"1.0"},"canonical_sha256":"7b7da531f33c2c1828fea7a10b5ff13d1f78d139aff4f3e0cc611b4271a608f2","source":{"kind":"arxiv","id":"1102.0612","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0612","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0612v1","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0612","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"pith_short_12","alias_value":"PN62KMPTHQWB","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PN62KMPTHQWBQKH6","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PN62KMPT","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PN62KMPTHQWBQKH6U6QQWX7RHU","target":"record","payload":{"canonical_record":{"source":{"id":"1102.0612","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-03T07:53:25Z","cross_cats_sorted":[],"title_canon_sha256":"96fc5931b494dcfea7e38ebafcd5c0b0df6652856bd288938a0d06c7ff12dcc8","abstract_canon_sha256":"0d5b64867e69e0c00b58504758792386973366d73571fc7e7724d6c6e0ca2e15"},"schema_version":"1.0"},"canonical_sha256":"7b7da531f33c2c1828fea7a10b5ff13d1f78d139aff4f3e0cc611b4271a608f2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:04.373094Z","signature_b64":"1EjwDyB2FFTZXZC4CkVd1ScgXfzUkf5sdnJWaHGQSxQTJP3IOTTL0+SmxCF6gVVGBxP1U6WURl1YXqCLQty1Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b7da531f33c2c1828fea7a10b5ff13d1f78d139aff4f3e0cc611b4271a608f2","last_reissued_at":"2026-05-18T04:30:04.372466Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:04.372466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.0612","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":"2026-05-18T04:30:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Git90rNRr7VIJ5FBr1VZXaERBdNtF8Z0f4/evflHuLWSUJd5//HsPDaUTUdg7SMW68u3K6irJG81kdTS/iWSBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:38:50.135511Z"},"content_sha256":"ace265e6d32f19a6928514781587b97952b0b69369dbbec4a7e1550803b31022","schema_version":"1.0","event_id":"sha256:ace265e6d32f19a6928514781587b97952b0b69369dbbec4a7e1550803b31022"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PN62KMPTHQWBQKH6U6QQWX7RHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dimensional entropies and semi-uniform hyperbolicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jerome Buzzi (LM-Orsay)","submitted_at":"2011-02-03T07:53:25Z","abstract_excerpt":"We describe dimensional entropies introduced in a previous work list some of their properties and give some new proofs. These entropies allowed the definition of entropy-expanding maps. We introduce a new notion of entropy-hyperbolicity for diffeomorphisms. We indicate some simple sufficient conditions (some of them new) for these properties. We conclude by some work in progress and more questions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0612","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":"2026-05-18T04:30:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CrDmGigm4qPUl2wll01huLXw1jGvQqsiEI62oW2jiMqq2EbtTgOJsqn2QW4/WkYCCT0lBlszFo295A5KKehlBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T01:38:50.136255Z"},"content_sha256":"015509db65f4cfd0a5747ab0f25296c409ddae198838cf31586273d0879e7abe","schema_version":"1.0","event_id":"sha256:015509db65f4cfd0a5747ab0f25296c409ddae198838cf31586273d0879e7abe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PN62KMPTHQWBQKH6U6QQWX7RHU/bundle.json","state_url":"https://pith.science/pith/PN62KMPTHQWBQKH6U6QQWX7RHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PN62KMPTHQWBQKH6U6QQWX7RHU/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":"2026-06-07T01:38:50Z","links":{"resolver":"https://pith.science/pith/PN62KMPTHQWBQKH6U6QQWX7RHU","bundle":"https://pith.science/pith/PN62KMPTHQWBQKH6U6QQWX7RHU/bundle.json","state":"https://pith.science/pith/PN62KMPTHQWBQKH6U6QQWX7RHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PN62KMPTHQWBQKH6U6QQWX7RHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PN62KMPTHQWBQKH6U6QQWX7RHU","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":"0d5b64867e69e0c00b58504758792386973366d73571fc7e7724d6c6e0ca2e15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-03T07:53:25Z","title_canon_sha256":"96fc5931b494dcfea7e38ebafcd5c0b0df6652856bd288938a0d06c7ff12dcc8"},"schema_version":"1.0","source":{"id":"1102.0612","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.0612","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"arxiv_version","alias_value":"1102.0612v1","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.0612","created_at":"2026-05-18T04:30:04Z"},{"alias_kind":"pith_short_12","alias_value":"PN62KMPTHQWB","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PN62KMPTHQWBQKH6","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PN62KMPT","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:015509db65f4cfd0a5747ab0f25296c409ddae198838cf31586273d0879e7abe","target":"graph","created_at":"2026-05-18T04:30:04Z","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 describe dimensional entropies introduced in a previous work list some of their properties and give some new proofs. These entropies allowed the definition of entropy-expanding maps. We introduce a new notion of entropy-hyperbolicity for diffeomorphisms. We indicate some simple sufficient conditions (some of them new) for these properties. We conclude by some work in progress and more questions.","authors_text":"Jerome Buzzi (LM-Orsay)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-03T07:53:25Z","title":"Dimensional entropies and semi-uniform hyperbolicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.0612","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:ace265e6d32f19a6928514781587b97952b0b69369dbbec4a7e1550803b31022","target":"record","created_at":"2026-05-18T04:30:04Z","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":"0d5b64867e69e0c00b58504758792386973366d73571fc7e7724d6c6e0ca2e15","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-02-03T07:53:25Z","title_canon_sha256":"96fc5931b494dcfea7e38ebafcd5c0b0df6652856bd288938a0d06c7ff12dcc8"},"schema_version":"1.0","source":{"id":"1102.0612","kind":"arxiv","version":1}},"canonical_sha256":"7b7da531f33c2c1828fea7a10b5ff13d1f78d139aff4f3e0cc611b4271a608f2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b7da531f33c2c1828fea7a10b5ff13d1f78d139aff4f3e0cc611b4271a608f2","first_computed_at":"2026-05-18T04:30:04.372466Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:04.372466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1EjwDyB2FFTZXZC4CkVd1ScgXfzUkf5sdnJWaHGQSxQTJP3IOTTL0+SmxCF6gVVGBxP1U6WURl1YXqCLQty1Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:04.373094Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.0612","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ace265e6d32f19a6928514781587b97952b0b69369dbbec4a7e1550803b31022","sha256:015509db65f4cfd0a5747ab0f25296c409ddae198838cf31586273d0879e7abe"],"state_sha256":"4710ef57df8fb8589044b6d7fef04265480399c75d48b8ebe5edbc1021d1587f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x2pFvSorJ1EFOtG7I4nFfFb0C+o1yeqySpM9MF3glKU+cX2pj8+1y410QwyGJft7P//nJ91LPsYvzJ/MtuqFDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T01:38:50.143896Z","bundle_sha256":"326c87ba8ffefeba5c62ca08ae2511bbe696f38a44817ae7d039abc011d81e02"}}