{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:B2CFRBA74RD4YJQ6HOVJVPZMI6","short_pith_number":"pith:B2CFRBA7","canonical_record":{"source":{"id":"1709.02347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-07T16:48:29Z","cross_cats_sorted":[],"title_canon_sha256":"5df042f267d25a805350956a6a53e2bf91a3928f225254b9b5b989d128a6d223","abstract_canon_sha256":"af3ca6bd624f221e0cb34a73387ee1793abd5b64fc1eed16ec42a6e93dbb0c76"},"schema_version":"1.0"},"canonical_sha256":"0e8458841fe447cc261e3baa9abf2c47a5556635635cf313b7823b809e6c7cb6","source":{"kind":"arxiv","id":"1709.02347","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02347","created_at":"2026-05-18T00:35:49Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02347v1","created_at":"2026-05-18T00:35:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02347","created_at":"2026-05-18T00:35:49Z"},{"alias_kind":"pith_short_12","alias_value":"B2CFRBA74RD4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B2CFRBA74RD4YJQ6","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B2CFRBA7","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:B2CFRBA74RD4YJQ6HOVJVPZMI6","target":"record","payload":{"canonical_record":{"source":{"id":"1709.02347","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-07T16:48:29Z","cross_cats_sorted":[],"title_canon_sha256":"5df042f267d25a805350956a6a53e2bf91a3928f225254b9b5b989d128a6d223","abstract_canon_sha256":"af3ca6bd624f221e0cb34a73387ee1793abd5b64fc1eed16ec42a6e93dbb0c76"},"schema_version":"1.0"},"canonical_sha256":"0e8458841fe447cc261e3baa9abf2c47a5556635635cf313b7823b809e6c7cb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:49.424594Z","signature_b64":"ZDclYqfcG2ZyxeMLymSKuZ5ANvgtfuIwJ9q00Fsa4QzeNLWUxIPrEnDu8EMu33qbBls9eXR0e/BfLXNr2Ns6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e8458841fe447cc261e3baa9abf2c47a5556635635cf313b7823b809e6c7cb6","last_reissued_at":"2026-05-18T00:35:49.423868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:49.423868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.02347","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":"2026-05-18T00:35:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LfRk+qcASbdbMzRHtoqkYXEzsPmrQMAImA46jLudXxhsrwnSuCCbSzewEBLRjV/+XeDRxAiDt0xBO0iiP6GnCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T23:43:13.959792Z"},"content_sha256":"728cf56a4ec2c94c379431115174b786084dd800cf32fc300649d0dc1b368845","schema_version":"1.0","event_id":"sha256:728cf56a4ec2c94c379431115174b786084dd800cf32fc300649d0dc1b368845"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:B2CFRBA74RD4YJQ6HOVJVPZMI6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Local well-posedness of the Hall-MHD system in $H^s(\\mathbb {R}^n)$ with $s>\\frac n2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mimi Dai","submitted_at":"2017-09-07T16:48:29Z","abstract_excerpt":"We establish local well-posedness of the Hall-magneto-hydrodynamics (Hall-MHD) system in the Sobolev space $\\left(H^s(\\mathbb{R}^n)\\right)^2$ with $s>\\frac n2$. The previously known local well-posedness space was $\\left(H^s(\\mathbb{R}^n)\\right)^2$ with $s>\\frac n2+1$. Thus the result presented here is an improvement."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02347","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":"2026-05-18T00:35:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h0CjfA4Vdizn0e2UYyl+KyxyGKCMx0VcZdGzlza1T/tkI5o4YLsAPplTCiGb2TYiFKhxtTIza1jOvQIa9Sq3Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T23:43:13.960137Z"},"content_sha256":"2c15fbe2811788a2460873c5d8550389475d4042a53cb824ed22c5ff1feffbe7","schema_version":"1.0","event_id":"sha256:2c15fbe2811788a2460873c5d8550389475d4042a53cb824ed22c5ff1feffbe7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B2CFRBA74RD4YJQ6HOVJVPZMI6/bundle.json","state_url":"https://pith.science/pith/B2CFRBA74RD4YJQ6HOVJVPZMI6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B2CFRBA74RD4YJQ6HOVJVPZMI6/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":"2026-08-17T23:43:13Z","links":{"resolver":"https://pith.science/pith/B2CFRBA74RD4YJQ6HOVJVPZMI6","bundle":"https://pith.science/pith/B2CFRBA74RD4YJQ6HOVJVPZMI6/bundle.json","state":"https://pith.science/pith/B2CFRBA74RD4YJQ6HOVJVPZMI6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B2CFRBA74RD4YJQ6HOVJVPZMI6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:B2CFRBA74RD4YJQ6HOVJVPZMI6","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":"af3ca6bd624f221e0cb34a73387ee1793abd5b64fc1eed16ec42a6e93dbb0c76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-07T16:48:29Z","title_canon_sha256":"5df042f267d25a805350956a6a53e2bf91a3928f225254b9b5b989d128a6d223"},"schema_version":"1.0","source":{"id":"1709.02347","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.02347","created_at":"2026-05-18T00:35:49Z"},{"alias_kind":"arxiv_version","alias_value":"1709.02347v1","created_at":"2026-05-18T00:35:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.02347","created_at":"2026-05-18T00:35:49Z"},{"alias_kind":"pith_short_12","alias_value":"B2CFRBA74RD4","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"B2CFRBA74RD4YJQ6","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"B2CFRBA7","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:2c15fbe2811788a2460873c5d8550389475d4042a53cb824ed22c5ff1feffbe7","target":"graph","created_at":"2026-05-18T00:35:49Z","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 establish local well-posedness of the Hall-magneto-hydrodynamics (Hall-MHD) system in the Sobolev space $\\left(H^s(\\mathbb{R}^n)\\right)^2$ with $s>\\frac n2$. The previously known local well-posedness space was $\\left(H^s(\\mathbb{R}^n)\\right)^2$ with $s>\\frac n2+1$. Thus the result presented here is an improvement.","authors_text":"Mimi Dai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-07T16:48:29Z","title":"Local well-posedness of the Hall-MHD system in $H^s(\\mathbb {R}^n)$ with $s>\\frac n2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02347","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":"sha256:728cf56a4ec2c94c379431115174b786084dd800cf32fc300649d0dc1b368845","target":"record","created_at":"2026-05-18T00:35:49Z","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":"af3ca6bd624f221e0cb34a73387ee1793abd5b64fc1eed16ec42a6e93dbb0c76","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-07T16:48:29Z","title_canon_sha256":"5df042f267d25a805350956a6a53e2bf91a3928f225254b9b5b989d128a6d223"},"schema_version":"1.0","source":{"id":"1709.02347","kind":"arxiv","version":1}},"canonical_sha256":"0e8458841fe447cc261e3baa9abf2c47a5556635635cf313b7823b809e6c7cb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e8458841fe447cc261e3baa9abf2c47a5556635635cf313b7823b809e6c7cb6","first_computed_at":"2026-05-18T00:35:49.423868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:49.423868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZDclYqfcG2ZyxeMLymSKuZ5ANvgtfuIwJ9q00Fsa4QzeNLWUxIPrEnDu8EMu33qbBls9eXR0e/BfLXNr2Ns6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:49.424594Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.02347","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:728cf56a4ec2c94c379431115174b786084dd800cf32fc300649d0dc1b368845","sha256:2c15fbe2811788a2460873c5d8550389475d4042a53cb824ed22c5ff1feffbe7"],"state_sha256":"8e11b5feb446a5e8e01e877c845c410b95849f6c1076f48ddc5314330e6a0c99"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tew/O+pvgSTkZwjCD94ir+zwg8PchxWXpTw2m9WaMqxsG03ltTSISDOLGtNSQ0sw1VgewjIftsEcYF/hVBXuAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T23:43:13.962330Z","bundle_sha256":"ec1502523b48dea92e4dc598dce7d127082295f000dbf913402a89fbe96cfc2c"}}