{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:TY3AFAZI74OVIT3PCZTVBCLF5X","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":"7f7a246316c964b22c7c0761af94973b24db7fdc75acf768c51d9c93c0e516c2","cross_cats_sorted":["math-ph","math.MP","nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-29T12:01:47Z","title_canon_sha256":"0a251f2317afdc2a46bb360dafa4898cd17ba7ad9cddc3d6dad7246fb4055dfe"},"schema_version":"1.0","source":{"id":"1903.12460","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.12460","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"arxiv_version","alias_value":"1903.12460v1","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.12460","created_at":"2026-05-17T23:49:53Z"},{"alias_kind":"pith_short_12","alias_value":"TY3AFAZI74OV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"TY3AFAZI74OVIT3P","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"TY3AFAZI","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:2f54ca8e8625c88fa5790867a870f9a8085aa91b3fd4ca21de590392817ba076","target":"graph","created_at":"2026-05-17T23:49:53Z","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":"We consider the dynamics of even solutions of the one-dimensional nonlinear Klein-Gordon equation $\\partial_t^2 \\phi - \\partial_x^2 \\phi + \\phi - |\\phi|^{2\\alpha} \\phi =0$ for $\\alpha>1$, in the vicinity of the unstable soliton $Q$. Our main result is that stability in the energy space $H^1(\\mathbb R)\\times L^2(\\mathbb R)$ implies asymptotic stability in a local energy norm. In particular, there exists a Lipschitz graph of initial data leading to stable and asymptotically stable trajectories.\n  The condition $\\alpha>1$ corresponds to cases where the linearized operator around $Q$ has no resona","authors_text":"Claudio Mu\\~noz, Michal Kowalczyk, Yvan Martel","cross_cats":["math-ph","math.MP","nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-29T12:01:47Z","title":"Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.12460","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":"sha256:6152cad56262f3ef1e7652e96f61c1cc631bea7e4514d5cba4742b091999c0d7","target":"record","created_at":"2026-05-17T23:49:53Z","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":"7f7a246316c964b22c7c0761af94973b24db7fdc75acf768c51d9c93c0e516c2","cross_cats_sorted":["math-ph","math.MP","nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-03-29T12:01:47Z","title_canon_sha256":"0a251f2317afdc2a46bb360dafa4898cd17ba7ad9cddc3d6dad7246fb4055dfe"},"schema_version":"1.0","source":{"id":"1903.12460","kind":"arxiv","version":1}},"canonical_sha256":"9e36028328ff1d544f6f1667508965edd546dde772a8259adfd796306c5e2ef8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e36028328ff1d544f6f1667508965edd546dde772a8259adfd796306c5e2ef8","first_computed_at":"2026-05-17T23:49:53.969225Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:49:53.969225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+0nAzClcQydXdX/C/dxZeingYSwf0bnL9qeOmiqriKQ1XBWeTx6mrWaXgI+6Wn7x+l2TVXQHtqrZkcAwP3S+Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:49:53.969631Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.12460","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6152cad56262f3ef1e7652e96f61c1cc631bea7e4514d5cba4742b091999c0d7","sha256:2f54ca8e8625c88fa5790867a870f9a8085aa91b3fd4ca21de590392817ba076"],"state_sha256":"965e9a98ca7caecc8d5f4147b752d32e90761bea39276cbea638ba4f151a1c20"}