{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:6VBCCXFM7AEIRAGYKOQP4TZHQZ","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"3f8c53138799e061a3ab7e97ce699cf7bfac7cdf3ebb70e403e01b3fe338af0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-09T12:27:49Z","title_canon_sha256":"2fae7a1012ddab5f72d59b2d6a3c4cda2a3f508c838589aa59cce7046e4eb4fc"},"schema_version":"1.0","source":{"id":"2607.08401","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08401","created_at":"2026-07-10T01:19:49Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08401v1","created_at":"2026-07-10T01:19:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08401","created_at":"2026-07-10T01:19:49Z"},{"alias_kind":"pith_short_12","alias_value":"6VBCCXFM7AEI","created_at":"2026-07-10T01:19:49Z"},{"alias_kind":"pith_short_16","alias_value":"6VBCCXFM7AEIRAGY","created_at":"2026-07-10T01:19:49Z"},{"alias_kind":"pith_short_8","alias_value":"6VBCCXFM","created_at":"2026-07-10T01:19:49Z"}],"graph_snapshots":[{"event_id":"sha256:58b7ba7afee3a95ca472ea88b997c7359cccdf2573b5ac2f6b12c43ebc26e4b2","target":"graph","created_at":"2026-07-10T01:19:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.08401/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Bj\\\"orn de Rijk, Emile Bukieda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-09T12:27:49Z","title":"Nonlinear stability of periodic waves in the Korteweg-de Vries equation under localized perturbations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08401","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:dd87e600aa0347df4450ea8f18d4ea4ce05ddf6712032f8656875afb45eb2940","target":"record","created_at":"2026-07-10T01:19:49Z","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":"3f8c53138799e061a3ab7e97ce699cf7bfac7cdf3ebb70e403e01b3fe338af0f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-09T12:27:49Z","title_canon_sha256":"2fae7a1012ddab5f72d59b2d6a3c4cda2a3f508c838589aa59cce7046e4eb4fc"},"schema_version":"1.0","source":{"id":"2607.08401","kind":"arxiv","version":1}},"canonical_sha256":"f542215cacf8088880d853a0fe4f278645c9758f8363f0e4cd835bd7c48d0062","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f542215cacf8088880d853a0fe4f278645c9758f8363f0e4cd835bd7c48d0062","first_computed_at":"2026-07-10T01:19:49.300405Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-10T01:19:49.300405Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fhb7ADCehbkI48r2/T0CNPWcfbt2uXpeW5Jaa8h8fPjT3UWQO2g9bBkEj+Ci6PmnqvJvkdmXPdHa5sQYZXTVAg==","signature_status":"signed_v1","signed_at":"2026-07-10T01:19:49.300866Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.08401","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd87e600aa0347df4450ea8f18d4ea4ce05ddf6712032f8656875afb45eb2940","sha256:58b7ba7afee3a95ca472ea88b997c7359cccdf2573b5ac2f6b12c43ebc26e4b2","sha256:188c28e5d153f91cb4592fa433f2e9e7604b70130f35d095af6020762788cdb7"],"state_sha256":"29cada912b0566de632167d3c8da955ac6ca381d54ad0a3d728ad97740837270"}