{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:QDR6R5KVZ37DPW7OI3Q52CQW2H","short_pith_number":"pith:QDR6R5KV","canonical_record":{"source":{"id":"1112.4657","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-20T11:35:41Z","cross_cats_sorted":[],"title_canon_sha256":"5b9962b63fe682e75bb94ab856b8bf90e33e1cac0a41215ce8821cfa585f5c88","abstract_canon_sha256":"c31d5e57af9a2d0633c04a08647ac06acd5ca2980c01b41465aa0f08a0465d51"},"schema_version":"1.0"},"canonical_sha256":"80e3e8f555cefe37dbee46e1dd0a16d1d1dde3d052ae57c5977805561846e0fe","source":{"kind":"arxiv","id":"1112.4657","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4657","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4657v2","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4657","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"QDR6R5KVZ37D","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QDR6R5KVZ37DPW7O","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QDR6R5KV","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:QDR6R5KVZ37DPW7OI3Q52CQW2H","target":"record","payload":{"canonical_record":{"source":{"id":"1112.4657","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-20T11:35:41Z","cross_cats_sorted":[],"title_canon_sha256":"5b9962b63fe682e75bb94ab856b8bf90e33e1cac0a41215ce8821cfa585f5c88","abstract_canon_sha256":"c31d5e57af9a2d0633c04a08647ac06acd5ca2980c01b41465aa0f08a0465d51"},"schema_version":"1.0"},"canonical_sha256":"80e3e8f555cefe37dbee46e1dd0a16d1d1dde3d052ae57c5977805561846e0fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:50.365903Z","signature_b64":"XOyYrW7872wxHnFMLlyYMzcaZ0TW/+IdbC4HvHSymavBT8HiJAT3tN920ozcib5VB+KwuxAXqA+kdW7g4UmFBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80e3e8f555cefe37dbee46e1dd0a16d1d1dde3d052ae57c5977805561846e0fe","last_reissued_at":"2026-05-18T03:50:50.365404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:50.365404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.4657","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:50:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3IfHfTtCkVU/F/GdH/+K49doahsE+juJAMShjV2Qa8sZJfojnOnxnF0PjjglOPnthy++1wAcJxL9th3uM33LAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:34:20.952983Z"},"content_sha256":"3315bff00195e36be2d5f4191d0d1554456b8fe6ea34782345571ac86fadf998","schema_version":"1.0","event_id":"sha256:3315bff00195e36be2d5f4191d0d1554456b8fe6ea34782345571ac86fadf998"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:QDR6R5KVZ37DPW7OI3Q52CQW2H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Korteweg-de-Vries equation at H^{-1} regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Herbert Koch, Tristan Buckmaster","submitted_at":"2011-12-20T11:35:41Z","abstract_excerpt":"In this paper we will prove the existence of weak solutions to the Korteweg-de Vries initial value problem on the real line with H^{-1} initial data; moreover, we will study the problem of orbital and asymptotic H^{s} stability of solitons for integers s\\ge -1; finally, we will also prove new a priori H^{-1} bounds for solutions to the Korteweg-de Vries equation. The paper will utilise the Miura transformation to link the Korteweg-de Vries equation to the modified Korteweg-de Vries equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4657","kind":"arxiv","version":2},"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":"2026-05-18T03:50:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"luFjXSEgx0CC/QkYgJFs/RzxW0zzkQnK0FbtazxY+mTZD0l4ryJFtWo6nXVm+j/lFQNYLmqNLI3k0jdqV5WqBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:34:20.953605Z"},"content_sha256":"2685943660176530c11c19c72116fcdf03d50ae3624866d38737baaa57ff42c9","schema_version":"1.0","event_id":"sha256:2685943660176530c11c19c72116fcdf03d50ae3624866d38737baaa57ff42c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QDR6R5KVZ37DPW7OI3Q52CQW2H/bundle.json","state_url":"https://pith.science/pith/QDR6R5KVZ37DPW7OI3Q52CQW2H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QDR6R5KVZ37DPW7OI3Q52CQW2H/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":"2026-06-02T07:34:20Z","links":{"resolver":"https://pith.science/pith/QDR6R5KVZ37DPW7OI3Q52CQW2H","bundle":"https://pith.science/pith/QDR6R5KVZ37DPW7OI3Q52CQW2H/bundle.json","state":"https://pith.science/pith/QDR6R5KVZ37DPW7OI3Q52CQW2H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QDR6R5KVZ37DPW7OI3Q52CQW2H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:QDR6R5KVZ37DPW7OI3Q52CQW2H","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":"c31d5e57af9a2d0633c04a08647ac06acd5ca2980c01b41465aa0f08a0465d51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-20T11:35:41Z","title_canon_sha256":"5b9962b63fe682e75bb94ab856b8bf90e33e1cac0a41215ce8821cfa585f5c88"},"schema_version":"1.0","source":{"id":"1112.4657","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.4657","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"arxiv_version","alias_value":"1112.4657v2","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4657","created_at":"2026-05-18T03:50:50Z"},{"alias_kind":"pith_short_12","alias_value":"QDR6R5KVZ37D","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"QDR6R5KVZ37DPW7O","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"QDR6R5KV","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:2685943660176530c11c19c72116fcdf03d50ae3624866d38737baaa57ff42c9","target":"graph","created_at":"2026-05-18T03:50:50Z","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":"In this paper we will prove the existence of weak solutions to the Korteweg-de Vries initial value problem on the real line with H^{-1} initial data; moreover, we will study the problem of orbital and asymptotic H^{s} stability of solitons for integers s\\ge -1; finally, we will also prove new a priori H^{-1} bounds for solutions to the Korteweg-de Vries equation. The paper will utilise the Miura transformation to link the Korteweg-de Vries equation to the modified Korteweg-de Vries equation.","authors_text":"Herbert Koch, Tristan Buckmaster","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-20T11:35:41Z","title":"The Korteweg-de-Vries equation at H^{-1} regularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4657","kind":"arxiv","version":2},"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":"sha256:3315bff00195e36be2d5f4191d0d1554456b8fe6ea34782345571ac86fadf998","target":"record","created_at":"2026-05-18T03:50:50Z","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":"c31d5e57af9a2d0633c04a08647ac06acd5ca2980c01b41465aa0f08a0465d51","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-12-20T11:35:41Z","title_canon_sha256":"5b9962b63fe682e75bb94ab856b8bf90e33e1cac0a41215ce8821cfa585f5c88"},"schema_version":"1.0","source":{"id":"1112.4657","kind":"arxiv","version":2}},"canonical_sha256":"80e3e8f555cefe37dbee46e1dd0a16d1d1dde3d052ae57c5977805561846e0fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80e3e8f555cefe37dbee46e1dd0a16d1d1dde3d052ae57c5977805561846e0fe","first_computed_at":"2026-05-18T03:50:50.365404Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:50.365404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XOyYrW7872wxHnFMLlyYMzcaZ0TW/+IdbC4HvHSymavBT8HiJAT3tN920ozcib5VB+KwuxAXqA+kdW7g4UmFBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:50.365903Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.4657","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3315bff00195e36be2d5f4191d0d1554456b8fe6ea34782345571ac86fadf998","sha256:2685943660176530c11c19c72116fcdf03d50ae3624866d38737baaa57ff42c9"],"state_sha256":"1785fef6b270050899a9c989524ff541813ff30d7f3a746e7fd98c4d34907412"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BLs24wvGQfO8eIHbjnmS8Aeki/Zl75ZuWyRg0fnfPyWrVzr5pm20erN0W+phyhZt96gs9W9+d1x9+x/I1eNtDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:34:20.956519Z","bundle_sha256":"099aa7baae49a2ae0eaa3e77d53060d7e3cbc5546ffa5f61d6ae5ef2fad10d0b"}}