{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Y2UHIKL4VAQJMCDGW35U5PAEDP","short_pith_number":"pith:Y2UHIKL4","canonical_record":{"source":{"id":"1306.2136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-10T08:38:00Z","cross_cats_sorted":[],"title_canon_sha256":"631544fd767e12be4f8de6b34d7f6c3bb2d228fa38bea59ae003c9242c4067c4","abstract_canon_sha256":"15a51ed61be1e95c6da0dfb110d6bccbd17ebaf63cce578367c4f57acd15eb52"},"schema_version":"1.0"},"canonical_sha256":"c6a874297ca820960866b6fb4ebc041bf7ad31f4562e407b2989ba4b4e49ec38","source":{"kind":"arxiv","id":"1306.2136","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2136","created_at":"2026-05-18T03:21:22Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2136v1","created_at":"2026-05-18T03:21:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2136","created_at":"2026-05-18T03:21:22Z"},{"alias_kind":"pith_short_12","alias_value":"Y2UHIKL4VAQJ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y2UHIKL4VAQJMCDG","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y2UHIKL4","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Y2UHIKL4VAQJMCDGW35U5PAEDP","target":"record","payload":{"canonical_record":{"source":{"id":"1306.2136","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-10T08:38:00Z","cross_cats_sorted":[],"title_canon_sha256":"631544fd767e12be4f8de6b34d7f6c3bb2d228fa38bea59ae003c9242c4067c4","abstract_canon_sha256":"15a51ed61be1e95c6da0dfb110d6bccbd17ebaf63cce578367c4f57acd15eb52"},"schema_version":"1.0"},"canonical_sha256":"c6a874297ca820960866b6fb4ebc041bf7ad31f4562e407b2989ba4b4e49ec38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:22.242375Z","signature_b64":"mvQv5vmblrdUvesDmreQDqcDUg5b+XudzM7Y95upyRbU4HkKzdnmLLiLrre6CS3i8tqg+WERRCc/koeWGqqCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6a874297ca820960866b6fb4ebc041bf7ad31f4562e407b2989ba4b4e49ec38","last_reissued_at":"2026-05-18T03:21:22.241645Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:22.241645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1306.2136","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":"2026-05-18T03:21:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VPgqQQ53VxasBK1L2pDESV0OxNBcOVzDHA1Cw46dEpWYLU1DAaQ3MBqgqy8MFr1EoVeSurFGDqhC2zPZTNwbCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:35:43.144545Z"},"content_sha256":"4946f6ebc1383ebfa5fe9af57a33a8863798815f5e4ee945a64d2fd1a10f8572","schema_version":"1.0","event_id":"sha256:4946f6ebc1383ebfa5fe9af57a33a8863798815f5e4ee945a64d2fd1a10f8572"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Y2UHIKL4VAQJMCDGW35U5PAEDP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hao Jia, Vladim\\'ir \\v{S}ver\\'ak","submitted_at":"2013-06-10T08:38:00Z","abstract_excerpt":"An important open problem in the theory of the Navier-Stokes equations is the uniqueness of the Leray-Hopf weak solutions with $L^2$ initial data.\n  In this paper we give sufficient conditions for non-uniqueness in terms of spectral properties of a natural linear operator associated to scale-invariant solutions recently constructed in \\cite{JiaSverak}. If the spectral conditions are satisfied, non-uniqueness and ill-posedness can appear for quite benign compactly supported data, just at the borderline of applicability of the classical perturbation theory. The verification of the spectral condi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2136","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":"2026-05-18T03:21:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7a9oSO+uINvGGRShumm+sYIVwhzFGBB4XfzQC+bhyafC31LE44wVDXPAnl+wX9OpGZx8kyQlEysa1ANALBMOBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T05:35:43.145171Z"},"content_sha256":"1655b7ce482c592c9af1769bce9f9f7b4d9216fc198230860f43485b08a6b4f8","schema_version":"1.0","event_id":"sha256:1655b7ce482c592c9af1769bce9f9f7b4d9216fc198230860f43485b08a6b4f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2UHIKL4VAQJMCDGW35U5PAEDP/bundle.json","state_url":"https://pith.science/pith/Y2UHIKL4VAQJMCDGW35U5PAEDP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2UHIKL4VAQJMCDGW35U5PAEDP/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":"2026-06-04T05:35:43Z","links":{"resolver":"https://pith.science/pith/Y2UHIKL4VAQJMCDGW35U5PAEDP","bundle":"https://pith.science/pith/Y2UHIKL4VAQJMCDGW35U5PAEDP/bundle.json","state":"https://pith.science/pith/Y2UHIKL4VAQJMCDGW35U5PAEDP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2UHIKL4VAQJMCDGW35U5PAEDP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Y2UHIKL4VAQJMCDGW35U5PAEDP","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":"15a51ed61be1e95c6da0dfb110d6bccbd17ebaf63cce578367c4f57acd15eb52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-10T08:38:00Z","title_canon_sha256":"631544fd767e12be4f8de6b34d7f6c3bb2d228fa38bea59ae003c9242c4067c4"},"schema_version":"1.0","source":{"id":"1306.2136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2136","created_at":"2026-05-18T03:21:22Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2136v1","created_at":"2026-05-18T03:21:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2136","created_at":"2026-05-18T03:21:22Z"},{"alias_kind":"pith_short_12","alias_value":"Y2UHIKL4VAQJ","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"Y2UHIKL4VAQJMCDG","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"Y2UHIKL4","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:1655b7ce482c592c9af1769bce9f9f7b4d9216fc198230860f43485b08a6b4f8","target":"graph","created_at":"2026-05-18T03:21:22Z","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":"An important open problem in the theory of the Navier-Stokes equations is the uniqueness of the Leray-Hopf weak solutions with $L^2$ initial data.\n  In this paper we give sufficient conditions for non-uniqueness in terms of spectral properties of a natural linear operator associated to scale-invariant solutions recently constructed in \\cite{JiaSverak}. If the spectral conditions are satisfied, non-uniqueness and ill-posedness can appear for quite benign compactly supported data, just at the borderline of applicability of the classical perturbation theory. The verification of the spectral condi","authors_text":"Hao Jia, Vladim\\'ir \\v{S}ver\\'ak","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-10T08:38:00Z","title":"Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2136","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":"sha256:4946f6ebc1383ebfa5fe9af57a33a8863798815f5e4ee945a64d2fd1a10f8572","target":"record","created_at":"2026-05-18T03:21:22Z","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":"15a51ed61be1e95c6da0dfb110d6bccbd17ebaf63cce578367c4f57acd15eb52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-10T08:38:00Z","title_canon_sha256":"631544fd767e12be4f8de6b34d7f6c3bb2d228fa38bea59ae003c9242c4067c4"},"schema_version":"1.0","source":{"id":"1306.2136","kind":"arxiv","version":1}},"canonical_sha256":"c6a874297ca820960866b6fb4ebc041bf7ad31f4562e407b2989ba4b4e49ec38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6a874297ca820960866b6fb4ebc041bf7ad31f4562e407b2989ba4b4e49ec38","first_computed_at":"2026-05-18T03:21:22.241645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:22.241645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mvQv5vmblrdUvesDmreQDqcDUg5b+XudzM7Y95upyRbU4HkKzdnmLLiLrre6CS3i8tqg+WERRCc/koeWGqqCAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:22.242375Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4946f6ebc1383ebfa5fe9af57a33a8863798815f5e4ee945a64d2fd1a10f8572","sha256:1655b7ce482c592c9af1769bce9f9f7b4d9216fc198230860f43485b08a6b4f8"],"state_sha256":"ea928cddfe063130d8bec1d1b59e927a5603652d4f9b92d3118579218b3bc05d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v07vCbxCstQtueHig/dDtnkHQnf8OXMJucHWVYgMDQypseW1ChSBMbl6UAkA/MkzSnAgy5tlCD1A0IiFimLzCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T05:35:43.147901Z","bundle_sha256":"f70a884bff34597c211a0fc9529c483cad804cb445aa30c1d9a0102a962d12d8"}}