{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:V6N6PDY2MORP23KW5UJ4A3HZAS","short_pith_number":"pith:V6N6PDY2","canonical_record":{"source":{"id":"1708.07545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-24T20:29:08Z","cross_cats_sorted":[],"title_canon_sha256":"492473e2d0a279b29013be0cacb3f43bd56cfa890f105d98a0b6376b5c60980c","abstract_canon_sha256":"ecd39ff08e817670e1d9db58ab3520c2c1d52ff85f4fbc4af73422f63b2bea4b"},"schema_version":"1.0"},"canonical_sha256":"af9be78f1a63a2fd6d56ed13c06cf904bfabff2f780ffd6e1b47eaee659cafa0","source":{"kind":"arxiv","id":"1708.07545","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07545","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07545v1","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07545","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"pith_short_12","alias_value":"V6N6PDY2MORP","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V6N6PDY2MORP23KW","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V6N6PDY2","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:V6N6PDY2MORP23KW5UJ4A3HZAS","target":"record","payload":{"canonical_record":{"source":{"id":"1708.07545","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-24T20:29:08Z","cross_cats_sorted":[],"title_canon_sha256":"492473e2d0a279b29013be0cacb3f43bd56cfa890f105d98a0b6376b5c60980c","abstract_canon_sha256":"ecd39ff08e817670e1d9db58ab3520c2c1d52ff85f4fbc4af73422f63b2bea4b"},"schema_version":"1.0"},"canonical_sha256":"af9be78f1a63a2fd6d56ed13c06cf904bfabff2f780ffd6e1b47eaee659cafa0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:36:42.716366Z","signature_b64":"Ks4z1sxegY2p92VGx/TAmEUNgt+t0LiizxlCZmxdakXXJbpshGozG5Wx7HvNZaBBEW0wPDxel90+PuhNnWhhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af9be78f1a63a2fd6d56ed13c06cf904bfabff2f780ffd6e1b47eaee659cafa0","last_reissued_at":"2026-05-18T00:36:42.715875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:36:42.715875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1708.07545","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":"2026-05-18T00:36:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d5f6UaBIggP0tNfFTJvdXl6EMwXACYCc7ZWSFMLLE5jBxAVj2hcsSni6sVUkhoBCBEmIFyEk3+t4BgN63hJhBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T15:45:04.949597Z"},"content_sha256":"d3b44254b34bc3a7f2d618f2a23436c73f61036508c386d210dcf654ab7d4858","schema_version":"1.0","event_id":"sha256:d3b44254b34bc3a7f2d618f2a23436c73f61036508c386d210dcf654ab7d4858"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:V6N6PDY2MORP23KW5UJ4A3HZAS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Asymptotic Stability of the Landau-Lifshitz Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Amenda Chow","submitted_at":"2017-08-24T20:29:08Z","abstract_excerpt":"The Landau--Lifshitz equation describes the behaviour of magnetic domains in ferromagnetic structures. Recently such structures have been found to be favourable for storing digital data. Stability of magnetic domains is important for this. Consequently, asymptotic stability of the equilibrium points in the Landau--Lifshitz equation are established. A suitable Lyapunov function is presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07545","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":"2026-05-18T00:36:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"goAt3NVaWrQUdIZ8dtKfWNmyr2RO3/qGq2e0vkDrN4Ak3nmbb0eSTZgn3VYDb7E+N0DuYhoidq9tyNabP9bSCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T15:45:04.949933Z"},"content_sha256":"a1b04150a0760d85fb042142c469622a597e9eac8f8978f16864b10813c4d670","schema_version":"1.0","event_id":"sha256:a1b04150a0760d85fb042142c469622a597e9eac8f8978f16864b10813c4d670"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V6N6PDY2MORP23KW5UJ4A3HZAS/bundle.json","state_url":"https://pith.science/pith/V6N6PDY2MORP23KW5UJ4A3HZAS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V6N6PDY2MORP23KW5UJ4A3HZAS/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":"2026-06-28T15:45:04Z","links":{"resolver":"https://pith.science/pith/V6N6PDY2MORP23KW5UJ4A3HZAS","bundle":"https://pith.science/pith/V6N6PDY2MORP23KW5UJ4A3HZAS/bundle.json","state":"https://pith.science/pith/V6N6PDY2MORP23KW5UJ4A3HZAS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V6N6PDY2MORP23KW5UJ4A3HZAS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V6N6PDY2MORP23KW5UJ4A3HZAS","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":"ecd39ff08e817670e1d9db58ab3520c2c1d52ff85f4fbc4af73422f63b2bea4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-24T20:29:08Z","title_canon_sha256":"492473e2d0a279b29013be0cacb3f43bd56cfa890f105d98a0b6376b5c60980c"},"schema_version":"1.0","source":{"id":"1708.07545","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07545","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07545v1","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07545","created_at":"2026-05-18T00:36:42Z"},{"alias_kind":"pith_short_12","alias_value":"V6N6PDY2MORP","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V6N6PDY2MORP23KW","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V6N6PDY2","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:a1b04150a0760d85fb042142c469622a597e9eac8f8978f16864b10813c4d670","target":"graph","created_at":"2026-05-18T00:36:42Z","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 Landau--Lifshitz equation describes the behaviour of magnetic domains in ferromagnetic structures. Recently such structures have been found to be favourable for storing digital data. Stability of magnetic domains is important for this. Consequently, asymptotic stability of the equilibrium points in the Landau--Lifshitz equation are established. A suitable Lyapunov function is presented.","authors_text":"Amenda Chow","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-24T20:29:08Z","title":"Asymptotic Stability of the Landau-Lifshitz Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07545","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:d3b44254b34bc3a7f2d618f2a23436c73f61036508c386d210dcf654ab7d4858","target":"record","created_at":"2026-05-18T00:36:42Z","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":"ecd39ff08e817670e1d9db58ab3520c2c1d52ff85f4fbc4af73422f63b2bea4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-24T20:29:08Z","title_canon_sha256":"492473e2d0a279b29013be0cacb3f43bd56cfa890f105d98a0b6376b5c60980c"},"schema_version":"1.0","source":{"id":"1708.07545","kind":"arxiv","version":1}},"canonical_sha256":"af9be78f1a63a2fd6d56ed13c06cf904bfabff2f780ffd6e1b47eaee659cafa0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af9be78f1a63a2fd6d56ed13c06cf904bfabff2f780ffd6e1b47eaee659cafa0","first_computed_at":"2026-05-18T00:36:42.715875Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:42.715875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ks4z1sxegY2p92VGx/TAmEUNgt+t0LiizxlCZmxdakXXJbpshGozG5Wx7HvNZaBBEW0wPDxel90+PuhNnWhhBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:42.716366Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07545","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d3b44254b34bc3a7f2d618f2a23436c73f61036508c386d210dcf654ab7d4858","sha256:a1b04150a0760d85fb042142c469622a597e9eac8f8978f16864b10813c4d670"],"state_sha256":"6b3ba317915ed42c73b15b9bcf9890bcb89627a32fad92adc8856d5c7c9d3c04"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jXmTtrFA9KiLE1Pv4Klz9iH1yEmvNxaqdGISUCaY2I1D6yt3whaJMvQXxDGqVksq7M3aIgp9NXNx1jG3b7JOBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T15:45:04.951843Z","bundle_sha256":"f82b9f9ef66ea19d444bbfef41c16711bd7bbbde0685c3071e239002f5ddf553"}}