{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:J33UKUTEQE6UNH7WSQIHMYYNO3","short_pith_number":"pith:J33UKUTE","canonical_record":{"source":{"id":"1304.6640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-24T16:00:44Z","cross_cats_sorted":[],"title_canon_sha256":"381edd4b9f1bac9e131cc659576a342acd7d15d817a4f3fdc605ca5982d295b6","abstract_canon_sha256":"48194ec2804c4bdff96d802e9e91f27ea77f422715d18aa7bf2ae57d53dc8cf2"},"schema_version":"1.0"},"canonical_sha256":"4ef7455264813d469ff6941076630d76cc4efbc86de66ce0ac61d2e71a2abece","source":{"kind":"arxiv","id":"1304.6640","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6640","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6640v2","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6640","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"pith_short_12","alias_value":"J33UKUTEQE6U","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J33UKUTEQE6UNH7W","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J33UKUTE","created_at":"2026-05-18T12:27:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:J33UKUTEQE6UNH7WSQIHMYYNO3","target":"record","payload":{"canonical_record":{"source":{"id":"1304.6640","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-24T16:00:44Z","cross_cats_sorted":[],"title_canon_sha256":"381edd4b9f1bac9e131cc659576a342acd7d15d817a4f3fdc605ca5982d295b6","abstract_canon_sha256":"48194ec2804c4bdff96d802e9e91f27ea77f422715d18aa7bf2ae57d53dc8cf2"},"schema_version":"1.0"},"canonical_sha256":"4ef7455264813d469ff6941076630d76cc4efbc86de66ce0ac61d2e71a2abece","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:26.569510Z","signature_b64":"1bHE9RNy3GcvUeyGZg4TGgQlXpB6Jpi47cq2KOXac1tGJtRKO4VNnn7EtPsW1NYsfvk/5sd9XDxkZExgNEYACw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ef7455264813d469ff6941076630d76cc4efbc86de66ce0ac61d2e71a2abece","last_reissued_at":"2026-05-18T03:10:26.568902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:26.568902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.6640","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":"2026-05-18T03:10:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X+KMK6hPb5rlXtsCFjmlfsfeASERWo8peN7zag6lnwTJyUcWiZyrCV32RyUFbfFrQjjDrRbna293Im9nS2tcBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:37:56.725430Z"},"content_sha256":"919ed1a858ea85620321f4b3f8ee29e09afcfbe4b960c3a9a95930af5620d74b","schema_version":"1.0","event_id":"sha256:919ed1a858ea85620321f4b3f8ee29e09afcfbe4b960c3a9a95930af5620d74b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:J33UKUTEQE6UNH7WSQIHMYYNO3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sharp local well-posedness of KdV type equations with dissipative perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mahendra Panthee, Xavier Carvajal","submitted_at":"2013-04-24T16:00:44Z","abstract_excerpt":"In this work, we study the initial value problems associated to some linear perturbations of KdV equations. Our focus is in the well-posedness issues for initial data given in the $L^2$-based Sobolev spaces. We derive bilinear estimate in a space with weight in the time variable and obtain sharp local well-posedness results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6640","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":"2026-05-18T03:10:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T2kLOxmZY0sELXon7KrQ1kA2+RUh39vA5o6aBw5akXdWWzKbcNYLAtDXynqjb4darHYmBFx7rF50o00pluDMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T20:37:56.725798Z"},"content_sha256":"1187d76f1bbb60e22efa9693b597c10469bd817c5720b72ee2ce15a2ea5d8853","schema_version":"1.0","event_id":"sha256:1187d76f1bbb60e22efa9693b597c10469bd817c5720b72ee2ce15a2ea5d8853"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J33UKUTEQE6UNH7WSQIHMYYNO3/bundle.json","state_url":"https://pith.science/pith/J33UKUTEQE6UNH7WSQIHMYYNO3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J33UKUTEQE6UNH7WSQIHMYYNO3/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":"2026-06-24T20:37:56Z","links":{"resolver":"https://pith.science/pith/J33UKUTEQE6UNH7WSQIHMYYNO3","bundle":"https://pith.science/pith/J33UKUTEQE6UNH7WSQIHMYYNO3/bundle.json","state":"https://pith.science/pith/J33UKUTEQE6UNH7WSQIHMYYNO3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J33UKUTEQE6UNH7WSQIHMYYNO3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:J33UKUTEQE6UNH7WSQIHMYYNO3","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":"48194ec2804c4bdff96d802e9e91f27ea77f422715d18aa7bf2ae57d53dc8cf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-24T16:00:44Z","title_canon_sha256":"381edd4b9f1bac9e131cc659576a342acd7d15d817a4f3fdc605ca5982d295b6"},"schema_version":"1.0","source":{"id":"1304.6640","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.6640","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"arxiv_version","alias_value":"1304.6640v2","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.6640","created_at":"2026-05-18T03:10:26Z"},{"alias_kind":"pith_short_12","alias_value":"J33UKUTEQE6U","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"J33UKUTEQE6UNH7W","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"J33UKUTE","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:1187d76f1bbb60e22efa9693b597c10469bd817c5720b72ee2ce15a2ea5d8853","target":"graph","created_at":"2026-05-18T03:10:26Z","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 work, we study the initial value problems associated to some linear perturbations of KdV equations. Our focus is in the well-posedness issues for initial data given in the $L^2$-based Sobolev spaces. We derive bilinear estimate in a space with weight in the time variable and obtain sharp local well-posedness results.","authors_text":"Mahendra Panthee, Xavier Carvajal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-24T16:00:44Z","title":"Sharp local well-posedness of KdV type equations with dissipative perturbations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.6640","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":"sha256:919ed1a858ea85620321f4b3f8ee29e09afcfbe4b960c3a9a95930af5620d74b","target":"record","created_at":"2026-05-18T03:10:26Z","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":"48194ec2804c4bdff96d802e9e91f27ea77f422715d18aa7bf2ae57d53dc8cf2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-04-24T16:00:44Z","title_canon_sha256":"381edd4b9f1bac9e131cc659576a342acd7d15d817a4f3fdc605ca5982d295b6"},"schema_version":"1.0","source":{"id":"1304.6640","kind":"arxiv","version":2}},"canonical_sha256":"4ef7455264813d469ff6941076630d76cc4efbc86de66ce0ac61d2e71a2abece","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ef7455264813d469ff6941076630d76cc4efbc86de66ce0ac61d2e71a2abece","first_computed_at":"2026-05-18T03:10:26.568902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:26.568902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1bHE9RNy3GcvUeyGZg4TGgQlXpB6Jpi47cq2KOXac1tGJtRKO4VNnn7EtPsW1NYsfvk/5sd9XDxkZExgNEYACw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:26.569510Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.6640","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:919ed1a858ea85620321f4b3f8ee29e09afcfbe4b960c3a9a95930af5620d74b","sha256:1187d76f1bbb60e22efa9693b597c10469bd817c5720b72ee2ce15a2ea5d8853"],"state_sha256":"929648152b0cc51f301e404c14a2a50144299473f251d4af6206bd6f8226f894"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y+ITK0Rbd5eQnUZDzZQBSFHjhBtvY/kEsPA4FMRBLy8cgJhFEAmwoguZc7O7wvVF66AxMrvgPo/IdojKNNFLAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T20:37:56.727765Z","bundle_sha256":"a24144fb9094b0f42d9ad1e080b1f74c2167f8771ffe03b4d5021f3eee0ee3d4"}}