{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:4TUPQVMYRBJFRYMA2XQIYNLSOY","short_pith_number":"pith:4TUPQVMY","canonical_record":{"source":{"id":"1209.6504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-28T12:54:09Z","cross_cats_sorted":[],"title_canon_sha256":"709beec6a8716d79e9b4090eae826cbf4fd5eabca48263692fda0ffe85ae5473","abstract_canon_sha256":"22062f50df01990f39853c6db7a841ca309bc5c633e8b2b4f4712038df78c730"},"schema_version":"1.0"},"canonical_sha256":"e4e8f85598885258e180d5e08c3572762e392ffacb409334c30e46b033afb0af","source":{"kind":"arxiv","id":"1209.6504","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.6504","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"1209.6504v2","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6504","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"4TUPQVMYRBJF","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4TUPQVMYRBJFRYMA","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4TUPQVMY","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:4TUPQVMYRBJFRYMA2XQIYNLSOY","target":"record","payload":{"canonical_record":{"source":{"id":"1209.6504","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-28T12:54:09Z","cross_cats_sorted":[],"title_canon_sha256":"709beec6a8716d79e9b4090eae826cbf4fd5eabca48263692fda0ffe85ae5473","abstract_canon_sha256":"22062f50df01990f39853c6db7a841ca309bc5c633e8b2b4f4712038df78c730"},"schema_version":"1.0"},"canonical_sha256":"e4e8f85598885258e180d5e08c3572762e392ffacb409334c30e46b033afb0af","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:28.427896Z","signature_b64":"gh0bGbQn0WL9svVdn9i49lc8g/S2Pr5mvQPP/ZRVks/MZBeZ8/PpvM6KdpzBqQNRUifgntM+mj+diAuNl/CeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4e8f85598885258e180d5e08c3572762e392ffacb409334c30e46b033afb0af","last_reissued_at":"2026-05-18T03:05:28.427386Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:28.427386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.6504","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gESydiKK6ykth6fsdMhm/KADtmnzJNt8u+zEG0ve5OleB40CzPegMjqERaODTv3QXDobZqKFi9nosUW7NcCyDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:15:04.678010Z"},"content_sha256":"4415992451688bb5cb5f15a483058d6c28fcb27b648fca0e21741b01d87b0f67","schema_version":"1.0","event_id":"sha256:4415992451688bb5cb5f15a483058d6c28fcb27b648fca0e21741b01d87b0f67"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:4TUPQVMYRBJFRYMA2XQIYNLSOY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical stability of Geometric Lorenz attractors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jose F. Alves, Mohammad Soufi","submitted_at":"2012-09-28T12:54:09Z","abstract_excerpt":"We consider the robust family of Geometric Lorenz attractors. These attractors are chaotic in the sense that they are transitive and have sensitive dependence on the initial conditions. Moreover, they support SRB measures whose ergodic basins cover a full Lebesgue measure subset of points in the topological basin of attraction. Here we prove that the SRB measures depend continuously on the dynamics in the weak$^*$ topology."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6504","kind":"arxiv","version":2},"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":"2026-05-18T03:05:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JpHX+W/87EoYA18JbzSL5QzzKt5wY7f3HMrJ+FWTO19r/61/EUFp5RbvawSsiu1DUe5+XABEKvqdAqtmWrT6Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T18:15:04.678355Z"},"content_sha256":"0cddef2d00110d64aa97829ecf43f891605e15d23111a5cc0190f971e3db4d9c","schema_version":"1.0","event_id":"sha256:0cddef2d00110d64aa97829ecf43f891605e15d23111a5cc0190f971e3db4d9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4TUPQVMYRBJFRYMA2XQIYNLSOY/bundle.json","state_url":"https://pith.science/pith/4TUPQVMYRBJFRYMA2XQIYNLSOY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4TUPQVMYRBJFRYMA2XQIYNLSOY/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":"2026-06-03T18:15:04Z","links":{"resolver":"https://pith.science/pith/4TUPQVMYRBJFRYMA2XQIYNLSOY","bundle":"https://pith.science/pith/4TUPQVMYRBJFRYMA2XQIYNLSOY/bundle.json","state":"https://pith.science/pith/4TUPQVMYRBJFRYMA2XQIYNLSOY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4TUPQVMYRBJFRYMA2XQIYNLSOY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:4TUPQVMYRBJFRYMA2XQIYNLSOY","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":"22062f50df01990f39853c6db7a841ca309bc5c633e8b2b4f4712038df78c730","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-28T12:54:09Z","title_canon_sha256":"709beec6a8716d79e9b4090eae826cbf4fd5eabca48263692fda0ffe85ae5473"},"schema_version":"1.0","source":{"id":"1209.6504","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.6504","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"1209.6504v2","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.6504","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"4TUPQVMYRBJF","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"4TUPQVMYRBJFRYMA","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"4TUPQVMY","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:0cddef2d00110d64aa97829ecf43f891605e15d23111a5cc0190f971e3db4d9c","target":"graph","created_at":"2026-05-18T03:05:28Z","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 consider the robust family of Geometric Lorenz attractors. These attractors are chaotic in the sense that they are transitive and have sensitive dependence on the initial conditions. Moreover, they support SRB measures whose ergodic basins cover a full Lebesgue measure subset of points in the topological basin of attraction. Here we prove that the SRB measures depend continuously on the dynamics in the weak$^*$ topology.","authors_text":"Jose F. Alves, Mohammad Soufi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-28T12:54:09Z","title":"Statistical stability of Geometric Lorenz attractors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.6504","kind":"arxiv","version":2},"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":"sha256:4415992451688bb5cb5f15a483058d6c28fcb27b648fca0e21741b01d87b0f67","target":"record","created_at":"2026-05-18T03:05:28Z","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":"22062f50df01990f39853c6db7a841ca309bc5c633e8b2b4f4712038df78c730","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-09-28T12:54:09Z","title_canon_sha256":"709beec6a8716d79e9b4090eae826cbf4fd5eabca48263692fda0ffe85ae5473"},"schema_version":"1.0","source":{"id":"1209.6504","kind":"arxiv","version":2}},"canonical_sha256":"e4e8f85598885258e180d5e08c3572762e392ffacb409334c30e46b033afb0af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4e8f85598885258e180d5e08c3572762e392ffacb409334c30e46b033afb0af","first_computed_at":"2026-05-18T03:05:28.427386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:28.427386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gh0bGbQn0WL9svVdn9i49lc8g/S2Pr5mvQPP/ZRVks/MZBeZ8/PpvM6KdpzBqQNRUifgntM+mj+diAuNl/CeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:28.427896Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.6504","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4415992451688bb5cb5f15a483058d6c28fcb27b648fca0e21741b01d87b0f67","sha256:0cddef2d00110d64aa97829ecf43f891605e15d23111a5cc0190f971e3db4d9c"],"state_sha256":"63e89a79c812dd50e93fe0e189085f37d7226be81bf0472ba91401da900bc7d5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e4Dlc3F0SjT1PZmk9vwouFyan8ya1UTaObFa2Q8LlkFefCUTiLWU8uOoLAVnPSNIiH+Q14fgdzrxz/9QwZ9RCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T18:15:04.680252Z","bundle_sha256":"84fc7a0ada9eba02be91064b66c7160c64372f1f50419fa103271907482b201b"}}