{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:6VBCCXFM7AEIRAGYKOQP4TZHQZ","short_pith_number":"pith:6VBCCXFM","schema_version":"1.0","canonical_sha256":"f542215cacf8088880d853a0fe4f278645c9758f8363f0e4cd835bd7c48d0062","source":{"kind":"arxiv","id":"2607.08401","version":1},"attestation_state":"computed","paper":{"title":"Nonlinear stability of periodic waves in the Korteweg-de Vries equation under localized perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bj\\\"orn de Rijk, Emile Bukieda","submitted_at":"2026-07-09T12:27:49Z","abstract_excerpt":"We investigate the stability and asymptotic behavior of spatially periodic cnoidal waves in the Korteweg-de Vries equation subject to localized perturbations. Standard stability arguments in Hamiltonian systems break down in this setting, since localized perturbations preclude a characterization of stable periodic waves as strict minimizers of a suitable energy functional subject to finitely many constraints. As a result, the nonlinear stability of periodic waves under localized perturbations has remained a long-standing open problem in Hamiltonian systems, with previous results only addressin"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":1,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2607.08401","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-09T12:27:49Z","cross_cats_sorted":[],"title_canon_sha256":"2fae7a1012ddab5f72d59b2d6a3c4cda2a3f508c838589aa59cce7046e4eb4fc","abstract_canon_sha256":"3f8c53138799e061a3ab7e97ce699cf7bfac7cdf3ebb70e403e01b3fe338af0f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-10T01:19:49.300866Z","signature_b64":"Fhb7ADCehbkI48r2/T0CNPWcfbt2uXpeW5Jaa8h8fPjT3UWQO2g9bBkEj+Ci6PmnqvJvkdmXPdHa5sQYZXTVAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f542215cacf8088880d853a0fe4f278645c9758f8363f0e4cd835bd7c48d0062","last_reissued_at":"2026-07-10T01:19:49.300405Z","signature_status":"signed_v1","first_computed_at":"2026-07-10T01:19:49.300405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Nonlinear stability of periodic waves in the Korteweg-de Vries equation under localized perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Bj\\\"orn de Rijk, Emile Bukieda","submitted_at":"2026-07-09T12:27:49Z","abstract_excerpt":"We investigate the stability and asymptotic behavior of spatially periodic cnoidal waves in the Korteweg-de Vries equation subject to localized perturbations. Standard stability arguments in Hamiltonian systems break down in this setting, since localized perturbations preclude a characterization of stable periodic waves as strict minimizers of a suitable energy functional subject to finitely many constraints. As a result, the nonlinear stability of periodic waves under localized perturbations has remained a long-standing open problem in Hamiltonian systems, with previous results only addressin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08401","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.08401/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2607.08401","created_at":"2026-07-10T01:19:49.300481+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.08401v1","created_at":"2026-07-10T01:19:49.300481+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08401","created_at":"2026-07-10T01:19:49.300481+00:00"},{"alias_kind":"pith_short_12","alias_value":"6VBCCXFM7AEI","created_at":"2026-07-10T01:19:49.300481+00:00"},{"alias_kind":"pith_short_16","alias_value":"6VBCCXFM7AEIRAGY","created_at":"2026-07-10T01:19:49.300481+00:00"},{"alias_kind":"pith_short_8","alias_value":"6VBCCXFM","created_at":"2026-07-10T01:19:49.300481+00:00"}],"events":[],"event_summary":{},"paper_claims":[{"claim_id":"aeb1df2b-bab2-4d34-a813-8e20f9849d91","handle":"jonathanwashburn","display_name":"Jonathan Washburn","verification":"self_claimed","verification_note":null,"role_label":null,"open_disputes":0}],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6VBCCXFM7AEIRAGYKOQP4TZHQZ","json":"https://pith.science/pith/6VBCCXFM7AEIRAGYKOQP4TZHQZ.json","graph_json":"https://pith.science/api/pith-number/6VBCCXFM7AEIRAGYKOQP4TZHQZ/graph.json","events_json":"https://pith.science/api/pith-number/6VBCCXFM7AEIRAGYKOQP4TZHQZ/events.json","paper":"https://pith.science/paper/6VBCCXFM"},"agent_actions":{"view_html":"https://pith.science/pith/6VBCCXFM7AEIRAGYKOQP4TZHQZ","download_json":"https://pith.science/pith/6VBCCXFM7AEIRAGYKOQP4TZHQZ.json","view_paper":"https://pith.science/paper/6VBCCXFM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.08401&json=true","fetch_graph":"https://pith.science/api/pith-number/6VBCCXFM7AEIRAGYKOQP4TZHQZ/graph.json","fetch_events":"https://pith.science/api/pith-number/6VBCCXFM7AEIRAGYKOQP4TZHQZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6VBCCXFM7AEIRAGYKOQP4TZHQZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6VBCCXFM7AEIRAGYKOQP4TZHQZ/action/storage_attestation","attest_author":"https://pith.science/pith/6VBCCXFM7AEIRAGYKOQP4TZHQZ/action/author_attestation","sign_citation":"https://pith.science/pith/6VBCCXFM7AEIRAGYKOQP4TZHQZ/action/citation_signature","submit_replication":"https://pith.science/pith/6VBCCXFM7AEIRAGYKOQP4TZHQZ/action/replication_record"}},"created_at":"2026-07-10T01:19:49.300481+00:00","updated_at":"2026-07-10T01:19:49.300481+00:00"}