{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YKBHQXT6VG4Z3HCNQTKB2WDCXQ","short_pith_number":"pith:YKBHQXT6","canonical_record":{"source":{"id":"1709.01374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-05T13:26:05Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"c7ae9c9b4fbce25799a0b0a786b3778c26779f0f5e8a3bbc66592160d08f8959","abstract_canon_sha256":"837c3c9844487195471c0535897ff978fb110bb47f8e883cd024841dd04892ba"},"schema_version":"1.0"},"canonical_sha256":"c282785e7ea9b99d9c4d84d41d5862bc325bccd2fffaf67b11f168e14f80041d","source":{"kind":"arxiv","id":"1709.01374","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01374","created_at":"2026-05-18T00:36:00Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01374v1","created_at":"2026-05-18T00:36:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01374","created_at":"2026-05-18T00:36:00Z"},{"alias_kind":"pith_short_12","alias_value":"YKBHQXT6VG4Z","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YKBHQXT6VG4Z3HCN","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YKBHQXT6","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YKBHQXT6VG4Z3HCNQTKB2WDCXQ","target":"record","payload":{"canonical_record":{"source":{"id":"1709.01374","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-05T13:26:05Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"c7ae9c9b4fbce25799a0b0a786b3778c26779f0f5e8a3bbc66592160d08f8959","abstract_canon_sha256":"837c3c9844487195471c0535897ff978fb110bb47f8e883cd024841dd04892ba"},"schema_version":"1.0"},"canonical_sha256":"c282785e7ea9b99d9c4d84d41d5862bc325bccd2fffaf67b11f168e14f80041d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:00.278850Z","signature_b64":"OCi7bsdgfg+JJTEgWwCp0hcgjQM09VSKX3UkoMeftAs8eJujdUANP9wXhk3KUyP3NxvIVgvlHFznHqKGIFSvAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c282785e7ea9b99d9c4d84d41d5862bc325bccd2fffaf67b11f168e14f80041d","last_reissued_at":"2026-05-18T00:36:00.278271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:00.278271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.01374","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":"2026-05-18T00:36:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MUvKts7xGgTxuwJiE0b11PXpD7I/hRRjfmVFZpDDVRa/S4u2k7xJ1m0wD1rOLJreYrPyjzzfKsH63e0riHclCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:36:35.484935Z"},"content_sha256":"8ddc9842ca799d10e9ef836aedbffb19f1c64b59a675f41c2efe00396d0e763e","schema_version":"1.0","event_id":"sha256:8ddc9842ca799d10e9ef836aedbffb19f1c64b59a675f41c2efe00396d0e763e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YKBHQXT6VG4Z3HCNQTKB2WDCXQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The magnetization ripple: a nonlocal stochastic PDE perspective","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Felix Otto, Radu Ignat","submitted_at":"2017-09-05T13:26:05Z","abstract_excerpt":"The magnetization ripple is a microstructure formed by the magnetization in a thin-film ferromagnet. It is triggered by the random orientation of the grains in the poly-crystalline material. In an approximation of the micromagnetic model, which is sketched in this paper, this leads to a nonlocal (and strongly anisotropic) elliptic equation in two dimensions with white noise as a right hand side. However, like in singular Stochastic PDE, this right hand side is too rough for the non-linearity in the equation. In order to develop a small-date well-posedness theory, we take inspiration from the r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01374","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":"2026-05-18T00:36:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gt5lQG6fRvIz3loSZFuhwTdgdIALOvT1SC8zFteqwo78xo2RprpxeKWx0Y5ojvOrPifmIi6sYDQ9qOLqoMt0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:36:35.485620Z"},"content_sha256":"a27c7c5866c917a922260e7b58238ab91e09450b75fa328a4e8a7e48acec47b6","schema_version":"1.0","event_id":"sha256:a27c7c5866c917a922260e7b58238ab91e09450b75fa328a4e8a7e48acec47b6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YKBHQXT6VG4Z3HCNQTKB2WDCXQ/bundle.json","state_url":"https://pith.science/pith/YKBHQXT6VG4Z3HCNQTKB2WDCXQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YKBHQXT6VG4Z3HCNQTKB2WDCXQ/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":"2026-05-30T02:36:35Z","links":{"resolver":"https://pith.science/pith/YKBHQXT6VG4Z3HCNQTKB2WDCXQ","bundle":"https://pith.science/pith/YKBHQXT6VG4Z3HCNQTKB2WDCXQ/bundle.json","state":"https://pith.science/pith/YKBHQXT6VG4Z3HCNQTKB2WDCXQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YKBHQXT6VG4Z3HCNQTKB2WDCXQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YKBHQXT6VG4Z3HCNQTKB2WDCXQ","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":"837c3c9844487195471c0535897ff978fb110bb47f8e883cd024841dd04892ba","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-05T13:26:05Z","title_canon_sha256":"c7ae9c9b4fbce25799a0b0a786b3778c26779f0f5e8a3bbc66592160d08f8959"},"schema_version":"1.0","source":{"id":"1709.01374","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01374","created_at":"2026-05-18T00:36:00Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01374v1","created_at":"2026-05-18T00:36:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01374","created_at":"2026-05-18T00:36:00Z"},{"alias_kind":"pith_short_12","alias_value":"YKBHQXT6VG4Z","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YKBHQXT6VG4Z3HCN","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YKBHQXT6","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:a27c7c5866c917a922260e7b58238ab91e09450b75fa328a4e8a7e48acec47b6","target":"graph","created_at":"2026-05-18T00:36:00Z","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":"The magnetization ripple is a microstructure formed by the magnetization in a thin-film ferromagnet. It is triggered by the random orientation of the grains in the poly-crystalline material. In an approximation of the micromagnetic model, which is sketched in this paper, this leads to a nonlocal (and strongly anisotropic) elliptic equation in two dimensions with white noise as a right hand side. However, like in singular Stochastic PDE, this right hand side is too rough for the non-linearity in the equation. In order to develop a small-date well-posedness theory, we take inspiration from the r","authors_text":"Felix Otto, Radu Ignat","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-05T13:26:05Z","title":"The magnetization ripple: a nonlocal stochastic PDE perspective"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01374","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":"sha256:8ddc9842ca799d10e9ef836aedbffb19f1c64b59a675f41c2efe00396d0e763e","target":"record","created_at":"2026-05-18T00:36:00Z","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":"837c3c9844487195471c0535897ff978fb110bb47f8e883cd024841dd04892ba","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-05T13:26:05Z","title_canon_sha256":"c7ae9c9b4fbce25799a0b0a786b3778c26779f0f5e8a3bbc66592160d08f8959"},"schema_version":"1.0","source":{"id":"1709.01374","kind":"arxiv","version":1}},"canonical_sha256":"c282785e7ea9b99d9c4d84d41d5862bc325bccd2fffaf67b11f168e14f80041d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c282785e7ea9b99d9c4d84d41d5862bc325bccd2fffaf67b11f168e14f80041d","first_computed_at":"2026-05-18T00:36:00.278271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:00.278271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OCi7bsdgfg+JJTEgWwCp0hcgjQM09VSKX3UkoMeftAs8eJujdUANP9wXhk3KUyP3NxvIVgvlHFznHqKGIFSvAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:00.278850Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.01374","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ddc9842ca799d10e9ef836aedbffb19f1c64b59a675f41c2efe00396d0e763e","sha256:a27c7c5866c917a922260e7b58238ab91e09450b75fa328a4e8a7e48acec47b6"],"state_sha256":"e65f9242a7abaa578d50a3245316071f3b9dbf568a1a029a58e3eea97968f5bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YTXGmmnALxO1FYhL/wegTW/+4FD6fQfUyNZLETp6/2PSdVghUzNzlraA8yCPHXiNSbIrwIC2qOKuuh+UC6p8AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:36:35.488610Z","bundle_sha256":"c739e0daed69bfe7b1b17413a5b70f25f41a1856b433b1c64fe3cff2ff35b221"}}