{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:L5BSF3BUO26R3O3E36N6RFZLZA","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":"72a47558e838279be58aec2b727c943db10a78a0259e230ca4c82854b4c1c5b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-02T10:37:21Z","title_canon_sha256":"081b38dbb8451aeb672a47c9dcf455d10f1e1cea7c2b099ec3a43b2ce4938bcb"},"schema_version":"1.0","source":{"id":"1511.00437","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.00437","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"arxiv_version","alias_value":"1511.00437v3","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.00437","created_at":"2026-05-18T01:24:43Z"},{"alias_kind":"pith_short_12","alias_value":"L5BSF3BUO26R","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"L5BSF3BUO26R3O3E","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"L5BSF3BU","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:5118db73bf3cb9193cf9bb39da5776330d786e9a24fe3bfddd3869b06a4b3d5a","target":"graph","created_at":"2026-05-18T01:24:43Z","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 paper, we proved that if the solution to damped focusing Klein-Gordon equations is global forward in time, then it will decouple into a finite number of equilibrium points with different shifts from the origin. The core ingredient of our proof is the existence of the \"concentration-compact attractor\" which yields a finite number of profiles. Using damping effect, we can prove all the profiles are equilibrium points.","authors_text":"Lifeng Zhao, Ze Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-02T10:37:21Z","title":"Asymptotic decomposition for nonlinear damped Klein-Gordon equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00437","kind":"arxiv","version":3},"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":"sha256:13514e691e113cdbdfffa253a33e3ad56726f41a056cfe4e99ecf204a3fef396","target":"record","created_at":"2026-05-18T01:24:43Z","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":"72a47558e838279be58aec2b727c943db10a78a0259e230ca4c82854b4c1c5b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-11-02T10:37:21Z","title_canon_sha256":"081b38dbb8451aeb672a47c9dcf455d10f1e1cea7c2b099ec3a43b2ce4938bcb"},"schema_version":"1.0","source":{"id":"1511.00437","kind":"arxiv","version":3}},"canonical_sha256":"5f4322ec3476bd1dbb64df9be8972bc83a10cf5f961c5b591699221d7231155c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f4322ec3476bd1dbb64df9be8972bc83a10cf5f961c5b591699221d7231155c","first_computed_at":"2026-05-18T01:24:43.477495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:43.477495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9Bfr/acWQQZPx6Ed/YvmRRKXz/Re276Fg3N2llanusp6/d2Alb9FZNySnpKWSWKcZ2d4uITLBr0ll9f322K4BA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:43.477882Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.00437","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13514e691e113cdbdfffa253a33e3ad56726f41a056cfe4e99ecf204a3fef396","sha256:5118db73bf3cb9193cf9bb39da5776330d786e9a24fe3bfddd3869b06a4b3d5a"],"state_sha256":"a42815c769ca4460940e7a15a6e03a1d3db4762c6d6037d657e9bc9ea1f36b83"}