{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RYT4IDDM7CBIYR26BPI5WZEAYG","short_pith_number":"pith:RYT4IDDM","canonical_record":{"source":{"id":"1308.4884","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-22T14:47:27Z","cross_cats_sorted":[],"title_canon_sha256":"e66a0ff48e6c20715c000640a58a5cf0ed77586ae747b5d37a7489cb4ce8567c","abstract_canon_sha256":"9a5820ab4a1b77077131f6104d0f4fb27f134088e6200d393bdb502152a0c90f"},"schema_version":"1.0"},"canonical_sha256":"8e27c40c6cf8828c475e0bd1db6480c19c4253ce631cc5de5fe229394fc70863","source":{"kind":"arxiv","id":"1308.4884","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4884","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4884v5","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4884","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"pith_short_12","alias_value":"RYT4IDDM7CBI","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RYT4IDDM7CBIYR26","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RYT4IDDM","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RYT4IDDM7CBIYR26BPI5WZEAYG","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4884","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-22T14:47:27Z","cross_cats_sorted":[],"title_canon_sha256":"e66a0ff48e6c20715c000640a58a5cf0ed77586ae747b5d37a7489cb4ce8567c","abstract_canon_sha256":"9a5820ab4a1b77077131f6104d0f4fb27f134088e6200d393bdb502152a0c90f"},"schema_version":"1.0"},"canonical_sha256":"8e27c40c6cf8828c475e0bd1db6480c19c4253ce631cc5de5fe229394fc70863","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:25.458526Z","signature_b64":"QUyBwp0WFQHxBoZBSKrVqKUHTGqfsOx+ZtYlkJrrcMVwL8CkSy0F6ptIpAa2Foy9SwCbqh5iMe4rBuznKuY7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e27c40c6cf8828c475e0bd1db6480c19c4253ce631cc5de5fe229394fc70863","last_reissued_at":"2026-05-17T23:56:25.458101Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:25.458101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4884","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wDlCsWJU8/IxO3MUdDSUVu8xcwCpUTOPl30HEHceisvnxOXZIa3LGsoPzCNLO6HCFPMg9PRQ28fYI19rgmpPCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T00:19:58.137259Z"},"content_sha256":"5f521ec1520660941ddb94d55dcbad14ef0e843f615d88786b02def1d2981d09","schema_version":"1.0","event_id":"sha256:5f521ec1520660941ddb94d55dcbad14ef0e843f615d88786b02def1d2981d09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RYT4IDDM7CBIYR26BPI5WZEAYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ergodicity of a Generalized Jacobi's Equation and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Nicolas Marie","submitted_at":"2013-08-22T14:47:27Z","abstract_excerpt":"Consider a $1$-dimensional centered Gaussian process $W$ with $\\alpha$-H\\\"older continuous paths on the compact intervals of $\\mathbb R_+$ ($\\alpha\\in ]0,1[$) and $W_0 = 0$, and $X$ the local solution in rough paths sense of Jacobi's equation driven by the signal $W$. The global existence and the uniqueness of the solution are proved via a change of variable taking into account the singularities of the vector field, because it doesn't satisfy the non-explosion condition. The regularity of the associated It\\^o map is studied. By using these deterministic results, Jacobi's equation is studied on"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4884","kind":"arxiv","version":5},"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":"2026-05-17T23:56:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0ygr68DSIBiTxqe/2MFyz+nYojBNA4tljXdW/C+9ewHlFNzNspaRn84EX7Scfeea9jC9tB0ULgTbICzvbFFyCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T00:19:58.137616Z"},"content_sha256":"d110e1c36cc7fd6bc35eba34e766f853124fd5675162f0396c93162e31f48482","schema_version":"1.0","event_id":"sha256:d110e1c36cc7fd6bc35eba34e766f853124fd5675162f0396c93162e31f48482"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RYT4IDDM7CBIYR26BPI5WZEAYG/bundle.json","state_url":"https://pith.science/pith/RYT4IDDM7CBIYR26BPI5WZEAYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RYT4IDDM7CBIYR26BPI5WZEAYG/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":"2026-07-03T00:19:58Z","links":{"resolver":"https://pith.science/pith/RYT4IDDM7CBIYR26BPI5WZEAYG","bundle":"https://pith.science/pith/RYT4IDDM7CBIYR26BPI5WZEAYG/bundle.json","state":"https://pith.science/pith/RYT4IDDM7CBIYR26BPI5WZEAYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RYT4IDDM7CBIYR26BPI5WZEAYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RYT4IDDM7CBIYR26BPI5WZEAYG","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":"9a5820ab4a1b77077131f6104d0f4fb27f134088e6200d393bdb502152a0c90f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-22T14:47:27Z","title_canon_sha256":"e66a0ff48e6c20715c000640a58a5cf0ed77586ae747b5d37a7489cb4ce8567c"},"schema_version":"1.0","source":{"id":"1308.4884","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4884","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4884v5","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4884","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"pith_short_12","alias_value":"RYT4IDDM7CBI","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RYT4IDDM7CBIYR26","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RYT4IDDM","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:d110e1c36cc7fd6bc35eba34e766f853124fd5675162f0396c93162e31f48482","target":"graph","created_at":"2026-05-17T23:56:25Z","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":"Consider a $1$-dimensional centered Gaussian process $W$ with $\\alpha$-H\\\"older continuous paths on the compact intervals of $\\mathbb R_+$ ($\\alpha\\in ]0,1[$) and $W_0 = 0$, and $X$ the local solution in rough paths sense of Jacobi's equation driven by the signal $W$. The global existence and the uniqueness of the solution are proved via a change of variable taking into account the singularities of the vector field, because it doesn't satisfy the non-explosion condition. The regularity of the associated It\\^o map is studied. By using these deterministic results, Jacobi's equation is studied on","authors_text":"Nicolas Marie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-22T14:47:27Z","title":"Ergodicity of a Generalized Jacobi's Equation and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4884","kind":"arxiv","version":5},"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":"sha256:5f521ec1520660941ddb94d55dcbad14ef0e843f615d88786b02def1d2981d09","target":"record","created_at":"2026-05-17T23:56:25Z","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":"9a5820ab4a1b77077131f6104d0f4fb27f134088e6200d393bdb502152a0c90f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-22T14:47:27Z","title_canon_sha256":"e66a0ff48e6c20715c000640a58a5cf0ed77586ae747b5d37a7489cb4ce8567c"},"schema_version":"1.0","source":{"id":"1308.4884","kind":"arxiv","version":5}},"canonical_sha256":"8e27c40c6cf8828c475e0bd1db6480c19c4253ce631cc5de5fe229394fc70863","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8e27c40c6cf8828c475e0bd1db6480c19c4253ce631cc5de5fe229394fc70863","first_computed_at":"2026-05-17T23:56:25.458101Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:25.458101Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QUyBwp0WFQHxBoZBSKrVqKUHTGqfsOx+ZtYlkJrrcMVwL8CkSy0F6ptIpAa2Foy9SwCbqh5iMe4rBuznKuY7AQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:25.458526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4884","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5f521ec1520660941ddb94d55dcbad14ef0e843f615d88786b02def1d2981d09","sha256:d110e1c36cc7fd6bc35eba34e766f853124fd5675162f0396c93162e31f48482"],"state_sha256":"213ee696f1e42c03ea7ffdae823d6349252ec05dffcf392af0e79455c128fa88"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WzRooz9mFZuXVismeOmf2TyfuazubJoeIzAR22PRqPCcQ4Ndz8nzuVizsHQ0rIdvezAf7AaD7hkdnRTWEFTfDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T00:19:58.139430Z","bundle_sha256":"c5cb75fbe8043f078f42312850675e98d6f80608a02c8f7709cbd78e682ee099"}}