{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QSBBPZPIS556BY2VRET2LRMDA6","short_pith_number":"pith:QSBBPZPI","canonical_record":{"source":{"id":"1908.01220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-03T19:16:50Z","cross_cats_sorted":[],"title_canon_sha256":"67a968081ca9a1dde3b74d06908bb3e6a36cad4e9c94847371437e550c98f8f7","abstract_canon_sha256":"932426fd8946512ced94e9ae23275b9c189a9350e85156af7e26e87800e48af6"},"schema_version":"1.0"},"canonical_sha256":"848217e5e8977be0e3558927a5c58307862e516bd0199723557ad25461c22f36","source":{"kind":"arxiv","id":"1908.01220","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01220","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01220v2","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01220","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"pith_short_12","alias_value":"QSBBPZPIS556","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"pith_short_16","alias_value":"QSBBPZPIS556BY2V","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"pith_short_8","alias_value":"QSBBPZPI","created_at":"2026-07-04T23:55:13Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QSBBPZPIS556BY2VRET2LRMDA6","target":"record","payload":{"canonical_record":{"source":{"id":"1908.01220","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-03T19:16:50Z","cross_cats_sorted":[],"title_canon_sha256":"67a968081ca9a1dde3b74d06908bb3e6a36cad4e9c94847371437e550c98f8f7","abstract_canon_sha256":"932426fd8946512ced94e9ae23275b9c189a9350e85156af7e26e87800e48af6"},"schema_version":"1.0"},"canonical_sha256":"848217e5e8977be0e3558927a5c58307862e516bd0199723557ad25461c22f36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T23:55:13.075427Z","signature_b64":"BP5PoCNm46kqkiQIF22O4M//Dtjdp5MotsUMuD11PzFxDgak4oDxdyfzW5yVssZoiO9azxi/oqb6iG3krsTXBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"848217e5e8977be0e3558927a5c58307862e516bd0199723557ad25461c22f36","last_reissued_at":"2026-07-04T23:55:13.074884Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T23:55:13.074884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.01220","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":"2026-07-04T23:55:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Iyt/yXIsZmeFTp3sTLD0igH8uSJP+m9gN3klA6UTt7XI1RTbFh8ZUAP0xClCzv1IhrRcTA+fRvcKVk6EDV5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T03:22:52.531241Z"},"content_sha256":"65876d2cba3e3f56e11d064fcccd63ca68d6198d2dc0dd74b4bc17ca75b3eb75","schema_version":"1.0","event_id":"sha256:65876d2cba3e3f56e11d064fcccd63ca68d6198d2dc0dd74b4bc17ca75b3eb75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QSBBPZPIS556BY2VRET2LRMDA6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random Attractor for Stochastic Hindmarsh-Rose Equations with Multiplicative Noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Chi Phan","submitted_at":"2019-08-03T19:16:50Z","abstract_excerpt":"The longtime and global pullback dynamics of stochastic Hindmarsh-Rose equations with multiplicative noise on a three-dimensional bounded domain in neurodynamics is investigated in this work. The existence of a random attractor for this random dynamical system is proved through the exponential transformation and uniform estimates showing the pullback absorbing property and the pullback asymptotically compactness of this cocycle in the $L^2$ Hilbert space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01220","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.01220/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":"2026-07-04T23:55:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SKgt0WgkQ69bY5YY7exDg0yujd8fFcDNPTwZLJVT8nU9rUZ8+n6Sj0YXkHbSowBBmtMF+ZRxbW1az3X/aUnaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T03:22:52.531776Z"},"content_sha256":"f841f08fd601a87a413d60105359937c863991706dc7295befa767f7253aaf39","schema_version":"1.0","event_id":"sha256:f841f08fd601a87a413d60105359937c863991706dc7295befa767f7253aaf39"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QSBBPZPIS556BY2VRET2LRMDA6/bundle.json","state_url":"https://pith.science/pith/QSBBPZPIS556BY2VRET2LRMDA6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QSBBPZPIS556BY2VRET2LRMDA6/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":"2026-08-16T03:22:52Z","links":{"resolver":"https://pith.science/pith/QSBBPZPIS556BY2VRET2LRMDA6","bundle":"https://pith.science/pith/QSBBPZPIS556BY2VRET2LRMDA6/bundle.json","state":"https://pith.science/pith/QSBBPZPIS556BY2VRET2LRMDA6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QSBBPZPIS556BY2VRET2LRMDA6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QSBBPZPIS556BY2VRET2LRMDA6","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":"932426fd8946512ced94e9ae23275b9c189a9350e85156af7e26e87800e48af6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-03T19:16:50Z","title_canon_sha256":"67a968081ca9a1dde3b74d06908bb3e6a36cad4e9c94847371437e550c98f8f7"},"schema_version":"1.0","source":{"id":"1908.01220","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01220","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01220v2","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01220","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"pith_short_12","alias_value":"QSBBPZPIS556","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"pith_short_16","alias_value":"QSBBPZPIS556BY2V","created_at":"2026-07-04T23:55:13Z"},{"alias_kind":"pith_short_8","alias_value":"QSBBPZPI","created_at":"2026-07-04T23:55:13Z"}],"graph_snapshots":[{"event_id":"sha256:f841f08fd601a87a413d60105359937c863991706dc7295befa767f7253aaf39","target":"graph","created_at":"2026-07-04T23:55:13Z","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/1908.01220/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The longtime and global pullback dynamics of stochastic Hindmarsh-Rose equations with multiplicative noise on a three-dimensional bounded domain in neurodynamics is investigated in this work. The existence of a random attractor for this random dynamical system is proved through the exponential transformation and uniform estimates showing the pullback absorbing property and the pullback asymptotically compactness of this cocycle in the $L^2$ Hilbert space.","authors_text":"Chi Phan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-03T19:16:50Z","title":"Random Attractor for Stochastic Hindmarsh-Rose Equations with Multiplicative Noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01220","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":"sha256:65876d2cba3e3f56e11d064fcccd63ca68d6198d2dc0dd74b4bc17ca75b3eb75","target":"record","created_at":"2026-07-04T23:55:13Z","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":"932426fd8946512ced94e9ae23275b9c189a9350e85156af7e26e87800e48af6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-03T19:16:50Z","title_canon_sha256":"67a968081ca9a1dde3b74d06908bb3e6a36cad4e9c94847371437e550c98f8f7"},"schema_version":"1.0","source":{"id":"1908.01220","kind":"arxiv","version":2}},"canonical_sha256":"848217e5e8977be0e3558927a5c58307862e516bd0199723557ad25461c22f36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"848217e5e8977be0e3558927a5c58307862e516bd0199723557ad25461c22f36","first_computed_at":"2026-07-04T23:55:13.074884Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:55:13.074884Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BP5PoCNm46kqkiQIF22O4M//Dtjdp5MotsUMuD11PzFxDgak4oDxdyfzW5yVssZoiO9azxi/oqb6iG3krsTXBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T23:55:13.075427Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01220","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65876d2cba3e3f56e11d064fcccd63ca68d6198d2dc0dd74b4bc17ca75b3eb75","sha256:f841f08fd601a87a413d60105359937c863991706dc7295befa767f7253aaf39"],"state_sha256":"30112df48f28468b6af0643c8799fb8db2d344f669f7ccf772e2a595332c792e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mDoI8UUkDkRf+ol41gqPI7gwdCXljmf6ylE0NUwEms3IJ189e1IdhKyTo2OcyEcQaykfrfirBHh6CWJq7LprDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T03:22:52.536760Z","bundle_sha256":"4b9146044cd99b5bfdfeec8991e29693eb097cc7c6e2addddc99de4fc79561bb"}}