{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:XEMQ3K6TKY6LQUFNZEVK2XXBY2","short_pith_number":"pith:XEMQ3K6T","canonical_record":{"source":{"id":"1206.4726","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-20T21:34:03Z","cross_cats_sorted":[],"title_canon_sha256":"c7db82524ae86d1b9c9a5c4c9709ce2d038be9963cef249c5acc67ef4b8e8986","abstract_canon_sha256":"2dd21a3eb66222296b46508c4644966504ffd96e33690a3796e8ba8e1762c67e"},"schema_version":"1.0"},"canonical_sha256":"b9190dabd3563cb850adc92aad5ee1c6aec9ac134a06283ab02c5c2042f4a109","source":{"kind":"arxiv","id":"1206.4726","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4726","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4726v1","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4726","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"XEMQ3K6TKY6L","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XEMQ3K6TKY6LQUFN","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XEMQ3K6T","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:XEMQ3K6TKY6LQUFNZEVK2XXBY2","target":"record","payload":{"canonical_record":{"source":{"id":"1206.4726","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-20T21:34:03Z","cross_cats_sorted":[],"title_canon_sha256":"c7db82524ae86d1b9c9a5c4c9709ce2d038be9963cef249c5acc67ef4b8e8986","abstract_canon_sha256":"2dd21a3eb66222296b46508c4644966504ffd96e33690a3796e8ba8e1762c67e"},"schema_version":"1.0"},"canonical_sha256":"b9190dabd3563cb850adc92aad5ee1c6aec9ac134a06283ab02c5c2042f4a109","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:53:03.892697Z","signature_b64":"6CJF/iRSYio09kRnOk58CNmHd0W8EBy4W52ldqsk4oY9cC+zabkFjzRq3RUwcDmoe8SbcdLGuJGJfGE7IISkDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9190dabd3563cb850adc92aad5ee1c6aec9ac134a06283ab02c5c2042f4a109","last_reissued_at":"2026-05-18T03:53:03.892011Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:53:03.892011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1206.4726","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":"2026-05-18T03:53:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j00LTI34Q7XhLRZ5UylFPMNpK7SGBiUB32u/bCbqE4PSOaih/4DDz2AQT8nAsUYvaBAPy6ynkgaZUkC8AogOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:53:52.358923Z"},"content_sha256":"1e8aca78e6c8613859489cc7645f1cacdebc92398103459507fd6772e016adad","schema_version":"1.0","event_id":"sha256:1e8aca78e6c8613859489cc7645f1cacdebc92398103459507fd6772e016adad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:XEMQ3K6TKY6LQUFNZEVK2XXBY2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Symmetric Regularized-Long-Wave Equation: Ill-posedness and Long Period Limit","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carlos Banquet Brango","submitted_at":"2012-06-20T21:34:03Z","abstract_excerpt":"In the present work we obtain two important results for the Symmetric Regulraized-Long-Wave equation. First we prove that the initial value problem for this equation is ill-posed for data in $H^s(\\mathbb{R})\\times H^{s-1}(\\mathbb{R}),$ if $s< 0,$ in the sense that the flow-map cannot be continuous at the origin from $H^s(\\mathbb{R})\\times H^{s-1}(\\mathbb{R})$ to even $(\\mathcal{D}'(\\mathbb{R}))^2.$ We also establish an exact theory of convergence of the periodic solutions to the continuous one, in Sobolev spaces, as the period goes to infinity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4726","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":"2026-05-18T03:53:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cbr0m1FN6LSJ/0/FZnX/WH4NjgPIRqPhVYql5QjxwmQlfKbp3Z4Jtrc1j/oOxsoV1knm7MvJ4lAKMO7IEZNUDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T23:53:52.359567Z"},"content_sha256":"adcfa433c6531c585f19c268f08145b1da5597f2fd3f099fb0e2d36793389911","schema_version":"1.0","event_id":"sha256:adcfa433c6531c585f19c268f08145b1da5597f2fd3f099fb0e2d36793389911"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XEMQ3K6TKY6LQUFNZEVK2XXBY2/bundle.json","state_url":"https://pith.science/pith/XEMQ3K6TKY6LQUFNZEVK2XXBY2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XEMQ3K6TKY6LQUFNZEVK2XXBY2/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":"2026-06-06T23:53:52Z","links":{"resolver":"https://pith.science/pith/XEMQ3K6TKY6LQUFNZEVK2XXBY2","bundle":"https://pith.science/pith/XEMQ3K6TKY6LQUFNZEVK2XXBY2/bundle.json","state":"https://pith.science/pith/XEMQ3K6TKY6LQUFNZEVK2XXBY2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XEMQ3K6TKY6LQUFNZEVK2XXBY2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XEMQ3K6TKY6LQUFNZEVK2XXBY2","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":"2dd21a3eb66222296b46508c4644966504ffd96e33690a3796e8ba8e1762c67e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-20T21:34:03Z","title_canon_sha256":"c7db82524ae86d1b9c9a5c4c9709ce2d038be9963cef249c5acc67ef4b8e8986"},"schema_version":"1.0","source":{"id":"1206.4726","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4726","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4726v1","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4726","created_at":"2026-05-18T03:53:03Z"},{"alias_kind":"pith_short_12","alias_value":"XEMQ3K6TKY6L","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XEMQ3K6TKY6LQUFN","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XEMQ3K6T","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:adcfa433c6531c585f19c268f08145b1da5597f2fd3f099fb0e2d36793389911","target":"graph","created_at":"2026-05-18T03:53:03Z","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 the present work we obtain two important results for the Symmetric Regulraized-Long-Wave equation. First we prove that the initial value problem for this equation is ill-posed for data in $H^s(\\mathbb{R})\\times H^{s-1}(\\mathbb{R}),$ if $s< 0,$ in the sense that the flow-map cannot be continuous at the origin from $H^s(\\mathbb{R})\\times H^{s-1}(\\mathbb{R})$ to even $(\\mathcal{D}'(\\mathbb{R}))^2.$ We also establish an exact theory of convergence of the periodic solutions to the continuous one, in Sobolev spaces, as the period goes to infinity.","authors_text":"Carlos Banquet Brango","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-20T21:34:03Z","title":"The Symmetric Regularized-Long-Wave Equation: Ill-posedness and Long Period Limit"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4726","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":"sha256:1e8aca78e6c8613859489cc7645f1cacdebc92398103459507fd6772e016adad","target":"record","created_at":"2026-05-18T03:53:03Z","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":"2dd21a3eb66222296b46508c4644966504ffd96e33690a3796e8ba8e1762c67e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-06-20T21:34:03Z","title_canon_sha256":"c7db82524ae86d1b9c9a5c4c9709ce2d038be9963cef249c5acc67ef4b8e8986"},"schema_version":"1.0","source":{"id":"1206.4726","kind":"arxiv","version":1}},"canonical_sha256":"b9190dabd3563cb850adc92aad5ee1c6aec9ac134a06283ab02c5c2042f4a109","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9190dabd3563cb850adc92aad5ee1c6aec9ac134a06283ab02c5c2042f4a109","first_computed_at":"2026-05-18T03:53:03.892011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:53:03.892011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6CJF/iRSYio09kRnOk58CNmHd0W8EBy4W52ldqsk4oY9cC+zabkFjzRq3RUwcDmoe8SbcdLGuJGJfGE7IISkDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:53:03.892697Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.4726","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e8aca78e6c8613859489cc7645f1cacdebc92398103459507fd6772e016adad","sha256:adcfa433c6531c585f19c268f08145b1da5597f2fd3f099fb0e2d36793389911"],"state_sha256":"9be737bad1cc1e99eb28575cd04fa32b2076d967489c35ff94b688000e554fd6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KlOAK8FhjxxnfRA7T+L53ye35UVeVbuo/nRQraFrlyWoyhjLfo4EOjvXeh3dkzFwd2GpEa8F0MFUqMW8bum2AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T23:53:52.363329Z","bundle_sha256":"a06aaaaec3fe3d71a727c4a4bba640c874d57fea3201110e1ea45bda19b65e8a"}}