{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:SRI3YKBB4DA3O23FTPF5WXMQQK","short_pith_number":"pith:SRI3YKBB","canonical_record":{"source":{"id":"1604.06352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-21T15:15:22Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"2acf44a05b2a0691ed76487a4d4b76423ceba1bfbc2c55e765f600747679afb5","abstract_canon_sha256":"1affba482903aa6b3368863cb44277eb394de7ab7207dc06537c133f8e4317c9"},"schema_version":"1.0"},"canonical_sha256":"9451bc2821e0c1b76b659bcbdb5d9082a52d191b0457f934dd66204bc2da74ee","source":{"kind":"arxiv","id":"1604.06352","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06352","created_at":"2026-05-18T01:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06352v1","created_at":"2026-05-18T01:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06352","created_at":"2026-05-18T01:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"SRI3YKBB4DA3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SRI3YKBB4DA3O23F","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SRI3YKBB","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:SRI3YKBB4DA3O23FTPF5WXMQQK","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06352","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-21T15:15:22Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"2acf44a05b2a0691ed76487a4d4b76423ceba1bfbc2c55e765f600747679afb5","abstract_canon_sha256":"1affba482903aa6b3368863cb44277eb394de7ab7207dc06537c133f8e4317c9"},"schema_version":"1.0"},"canonical_sha256":"9451bc2821e0c1b76b659bcbdb5d9082a52d191b0457f934dd66204bc2da74ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:31.978231Z","signature_b64":"vRyANHiKnqPBtPiDSQaC/CXdO8SWtLSOBsT7b0gGaE9NdBoddDO8bhu6I1LuZ0lMWdFnIr5L8ntKQiXTq3dIDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9451bc2821e0c1b76b659bcbdb5d9082a52d191b0457f934dd66204bc2da74ee","last_reissued_at":"2026-05-18T01:16:31.977575Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:31.977575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06352","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":"2026-05-18T01:16:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uA2tIZU5woK1jNjENr4otkSRv9YNINeaHOv2GZRAmxOCTSrCBr2fTf8siPOYwL2P3/TV1e5xyPa6JpciPfwDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:21:30.058427Z"},"content_sha256":"8d882e32f9d73d47a945da3fff4daefd33d6cf32f4e20b6dbe1856c23cf1793a","schema_version":"1.0","event_id":"sha256:8d882e32f9d73d47a945da3fff4daefd33d6cf32f4e20b6dbe1856c23cf1793a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:SRI3YKBB4DA3O23FTPF5WXMQQK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Analysis for Randomly Forced MHD","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Geordie Richards, Juraj F\\\"oldes, Nathan Glatt-Holtz, Susan Friedlander","submitted_at":"2016-04-21T15:15:22Z","abstract_excerpt":"We consider the three-dimensional magnetohydrodynamics (MHD) equations in the presence of a spatially degenerate stochastic forcing as a model for magnetostrophic turbulence in the Earth's fluid core. We examine the multi-parameter singular limit of vanishing Rossby number $\\epsilon$ and magnetic Reynold's number $\\delta$, and establish that: (i) the limiting stochastically driven active scalar equation (with $\\epsilon =\\delta=0$) possesses a unique ergodic invariant measure, and (ii) any suitable sequence of statistically invariant states of the full MHD system converge weakly, as $\\epsilon,\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06352","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":"2026-05-18T01:16:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fkai+p/Pf8NJlEtS6g18wKyATEGne6k8vmcCadgSuCeDT3nFrI6c8nDVHbkv/Zwu8u7w6zGaFMlZbbeJB4DJBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T17:21:30.058829Z"},"content_sha256":"eccd37d4524dfc7dc2ed99997ed586316229f0e35d8c040c7d81521d44ae0f82","schema_version":"1.0","event_id":"sha256:eccd37d4524dfc7dc2ed99997ed586316229f0e35d8c040c7d81521d44ae0f82"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SRI3YKBB4DA3O23FTPF5WXMQQK/bundle.json","state_url":"https://pith.science/pith/SRI3YKBB4DA3O23FTPF5WXMQQK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SRI3YKBB4DA3O23FTPF5WXMQQK/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":"2026-05-26T17:21:30Z","links":{"resolver":"https://pith.science/pith/SRI3YKBB4DA3O23FTPF5WXMQQK","bundle":"https://pith.science/pith/SRI3YKBB4DA3O23FTPF5WXMQQK/bundle.json","state":"https://pith.science/pith/SRI3YKBB4DA3O23FTPF5WXMQQK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SRI3YKBB4DA3O23FTPF5WXMQQK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:SRI3YKBB4DA3O23FTPF5WXMQQK","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":"1affba482903aa6b3368863cb44277eb394de7ab7207dc06537c133f8e4317c9","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-21T15:15:22Z","title_canon_sha256":"2acf44a05b2a0691ed76487a4d4b76423ceba1bfbc2c55e765f600747679afb5"},"schema_version":"1.0","source":{"id":"1604.06352","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06352","created_at":"2026-05-18T01:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06352v1","created_at":"2026-05-18T01:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06352","created_at":"2026-05-18T01:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"SRI3YKBB4DA3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"SRI3YKBB4DA3O23F","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"SRI3YKBB","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:eccd37d4524dfc7dc2ed99997ed586316229f0e35d8c040c7d81521d44ae0f82","target":"graph","created_at":"2026-05-18T01:16:31Z","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 three-dimensional magnetohydrodynamics (MHD) equations in the presence of a spatially degenerate stochastic forcing as a model for magnetostrophic turbulence in the Earth's fluid core. We examine the multi-parameter singular limit of vanishing Rossby number $\\epsilon$ and magnetic Reynold's number $\\delta$, and establish that: (i) the limiting stochastically driven active scalar equation (with $\\epsilon =\\delta=0$) possesses a unique ergodic invariant measure, and (ii) any suitable sequence of statistically invariant states of the full MHD system converge weakly, as $\\epsilon,\\","authors_text":"Geordie Richards, Juraj F\\\"oldes, Nathan Glatt-Holtz, Susan Friedlander","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-21T15:15:22Z","title":"Asymptotic Analysis for Randomly Forced MHD"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06352","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":"sha256:8d882e32f9d73d47a945da3fff4daefd33d6cf32f4e20b6dbe1856c23cf1793a","target":"record","created_at":"2026-05-18T01:16:31Z","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":"1affba482903aa6b3368863cb44277eb394de7ab7207dc06537c133f8e4317c9","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-04-21T15:15:22Z","title_canon_sha256":"2acf44a05b2a0691ed76487a4d4b76423ceba1bfbc2c55e765f600747679afb5"},"schema_version":"1.0","source":{"id":"1604.06352","kind":"arxiv","version":1}},"canonical_sha256":"9451bc2821e0c1b76b659bcbdb5d9082a52d191b0457f934dd66204bc2da74ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9451bc2821e0c1b76b659bcbdb5d9082a52d191b0457f934dd66204bc2da74ee","first_computed_at":"2026-05-18T01:16:31.977575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:16:31.977575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vRyANHiKnqPBtPiDSQaC/CXdO8SWtLSOBsT7b0gGaE9NdBoddDO8bhu6I1LuZ0lMWdFnIr5L8ntKQiXTq3dIDw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:16:31.978231Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06352","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d882e32f9d73d47a945da3fff4daefd33d6cf32f4e20b6dbe1856c23cf1793a","sha256:eccd37d4524dfc7dc2ed99997ed586316229f0e35d8c040c7d81521d44ae0f82"],"state_sha256":"539187a3b0f7765ba7f2de7cc0309b564def4af06519a7a32ee6f398bcd9409e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9HQJ0ZkgMmVA4ZhwX8hUovhY17n0QhheQ/dvtj4igyvRv2V3jBIUx/HfpvGmDjQcxVzmr+IFHHqcWA86MZH+CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T17:21:30.061825Z","bundle_sha256":"637faf8dd89b7740b81824f9489195c9cc711e2d978cfdb1e36c8a966af8c0a8"}}