{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:AD5IMDRTF2NY2Z2HBGZFGVGYYQ","short_pith_number":"pith:AD5IMDRT","canonical_record":{"source":{"id":"1110.4211","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-19T08:56:28Z","cross_cats_sorted":[],"title_canon_sha256":"ca6c98519f2c37ad6d53fc83defbcbb80149d98e4d63a5a7de90051e5d2c06d3","abstract_canon_sha256":"b1db15da1f9cf44ee327ec9f4195c3abe37ceb2b05053a0f881f44abe3e6a5a1"},"schema_version":"1.0"},"canonical_sha256":"00fa860e332e9b8d674709b25354d8c431774b21e1762160e581be32e6d376ae","source":{"kind":"arxiv","id":"1110.4211","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4211","created_at":"2026-05-18T04:10:37Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4211v1","created_at":"2026-05-18T04:10:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4211","created_at":"2026-05-18T04:10:37Z"},{"alias_kind":"pith_short_12","alias_value":"AD5IMDRTF2NY","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AD5IMDRTF2NY2Z2H","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AD5IMDRT","created_at":"2026-05-18T12:26:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:AD5IMDRTF2NY2Z2HBGZFGVGYYQ","target":"record","payload":{"canonical_record":{"source":{"id":"1110.4211","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-19T08:56:28Z","cross_cats_sorted":[],"title_canon_sha256":"ca6c98519f2c37ad6d53fc83defbcbb80149d98e4d63a5a7de90051e5d2c06d3","abstract_canon_sha256":"b1db15da1f9cf44ee327ec9f4195c3abe37ceb2b05053a0f881f44abe3e6a5a1"},"schema_version":"1.0"},"canonical_sha256":"00fa860e332e9b8d674709b25354d8c431774b21e1762160e581be32e6d376ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:10:37.931998Z","signature_b64":"gNSsWcZWVq5Bp9ckMV5siU+u/Ki9yPT81oCFJKqC2XMogMYpMoREcLKbiRc5iHke+RcyMRnt+hF4s951sREdBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00fa860e332e9b8d674709b25354d8c431774b21e1762160e581be32e6d376ae","last_reissued_at":"2026-05-18T04:10:37.931482Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:10:37.931482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.4211","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":"2026-05-18T04:10:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zr9WLiZLwFYXTXi9f1QV+ZSIJt2dNM8ZFJILO+uGGWqRCCnsIvGAqJSrVpIgcowgwhzGxg5lsNf1rg/7r6/GAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:42:56.150045Z"},"content_sha256":"cc3b123111429d2812a39df074bd8eeaccfc9c2c74314fd731d928a0048e7abe","schema_version":"1.0","event_id":"sha256:cc3b123111429d2812a39df074bd8eeaccfc9c2c74314fd731d928a0048e7abe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:AD5IMDRTF2NY2Z2HBGZFGVGYYQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Well-posedness and stability results for the Gardner equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Miguel A. Alejo","submitted_at":"2011-10-19T08:56:28Z","abstract_excerpt":"In this article we present local well-posedness results in the classical Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of the loss of the scaling property of this equation. We also cover the energy space H^1(R) where global well-posedness follows from the conservation laws of the system. Moreover, we construct solitons of the Gardner equation explicitly and prove that, under certain conditions, this family is orbitally stable in the energy space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4211","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":"2026-05-18T04:10:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dyeRnMvzgDZ/WIfBcMsQXpxi686pPMBlD76nA9on4yPIGRyYOpHSfrX4eK42j81k9xHdpxknijdXMbxQnNdDCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T23:42:56.150398Z"},"content_sha256":"53275aa151d42bd39b1022204e954b6c269ff8183a0993b82018bc86e7dc7daf","schema_version":"1.0","event_id":"sha256:53275aa151d42bd39b1022204e954b6c269ff8183a0993b82018bc86e7dc7daf"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AD5IMDRTF2NY2Z2HBGZFGVGYYQ/bundle.json","state_url":"https://pith.science/pith/AD5IMDRTF2NY2Z2HBGZFGVGYYQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AD5IMDRTF2NY2Z2HBGZFGVGYYQ/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":"2026-06-25T23:42:56Z","links":{"resolver":"https://pith.science/pith/AD5IMDRTF2NY2Z2HBGZFGVGYYQ","bundle":"https://pith.science/pith/AD5IMDRTF2NY2Z2HBGZFGVGYYQ/bundle.json","state":"https://pith.science/pith/AD5IMDRTF2NY2Z2HBGZFGVGYYQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AD5IMDRTF2NY2Z2HBGZFGVGYYQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:AD5IMDRTF2NY2Z2HBGZFGVGYYQ","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":"b1db15da1f9cf44ee327ec9f4195c3abe37ceb2b05053a0f881f44abe3e6a5a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-19T08:56:28Z","title_canon_sha256":"ca6c98519f2c37ad6d53fc83defbcbb80149d98e4d63a5a7de90051e5d2c06d3"},"schema_version":"1.0","source":{"id":"1110.4211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.4211","created_at":"2026-05-18T04:10:37Z"},{"alias_kind":"arxiv_version","alias_value":"1110.4211v1","created_at":"2026-05-18T04:10:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.4211","created_at":"2026-05-18T04:10:37Z"},{"alias_kind":"pith_short_12","alias_value":"AD5IMDRTF2NY","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"AD5IMDRTF2NY2Z2H","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"AD5IMDRT","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:53275aa151d42bd39b1022204e954b6c269ff8183a0993b82018bc86e7dc7daf","target":"graph","created_at":"2026-05-18T04:10:37Z","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 article we present local well-posedness results in the classical Sobolev space H^s(R) with s > 1/4 for the Cauchy problem of the Gardner equation, overcoming the problem of the loss of the scaling property of this equation. We also cover the energy space H^1(R) where global well-posedness follows from the conservation laws of the system. Moreover, we construct solitons of the Gardner equation explicitly and prove that, under certain conditions, this family is orbitally stable in the energy space.","authors_text":"Miguel A. Alejo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-19T08:56:28Z","title":"Well-posedness and stability results for the Gardner equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4211","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:cc3b123111429d2812a39df074bd8eeaccfc9c2c74314fd731d928a0048e7abe","target":"record","created_at":"2026-05-18T04:10:37Z","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":"b1db15da1f9cf44ee327ec9f4195c3abe37ceb2b05053a0f881f44abe3e6a5a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-10-19T08:56:28Z","title_canon_sha256":"ca6c98519f2c37ad6d53fc83defbcbb80149d98e4d63a5a7de90051e5d2c06d3"},"schema_version":"1.0","source":{"id":"1110.4211","kind":"arxiv","version":1}},"canonical_sha256":"00fa860e332e9b8d674709b25354d8c431774b21e1762160e581be32e6d376ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"00fa860e332e9b8d674709b25354d8c431774b21e1762160e581be32e6d376ae","first_computed_at":"2026-05-18T04:10:37.931482Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:10:37.931482Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gNSsWcZWVq5Bp9ckMV5siU+u/Ki9yPT81oCFJKqC2XMogMYpMoREcLKbiRc5iHke+RcyMRnt+hF4s951sREdBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:10:37.931998Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.4211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cc3b123111429d2812a39df074bd8eeaccfc9c2c74314fd731d928a0048e7abe","sha256:53275aa151d42bd39b1022204e954b6c269ff8183a0993b82018bc86e7dc7daf"],"state_sha256":"ad93320272fd91477da7f66e25f2dcd25aededd9a18674deed367913a8655dbe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SlOuYVV9HUCLnGp5V+0C1afSh9I/jsF08Wykdc/N98eeW/Tuh+Bbon4Lch4wQNrk3KfiFrWS7ThqJwxWgu/qBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T23:42:56.152310Z","bundle_sha256":"32da17ee6a602e46dcd483d12be0cf0c67bf7ef6d35a0f58633962e435515b34"}}