{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IJS2E56ROWCPSDUUXZXBEGSBWU","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":"3fce68284c2ee98ee53b6d830e0b5a2dc2f8f59876782968bea5271af49ad10c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-05T15:25:55Z","title_canon_sha256":"44bf64904c774f5dded8b9a6a108bd499976db42d2ab0a99a8e14aee5414df18"},"schema_version":"1.0","source":{"id":"1703.01609","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01609","created_at":"2026-05-18T00:03:32Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01609v4","created_at":"2026-05-18T00:03:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01609","created_at":"2026-05-18T00:03:32Z"},{"alias_kind":"pith_short_12","alias_value":"IJS2E56ROWCP","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IJS2E56ROWCPSDUU","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IJS2E56R","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:ef90bff97d6f025cf545853b36d853f474aa1d2fca4b9bbf94a4d66ba86ccf11","target":"graph","created_at":"2026-05-18T00:03:32Z","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":"The nonlinear Klein-Gordon (NLKG) equation on a manifold $M$ in the nonrelativistic limit, namely as the speed of light $c$ tends to infinity, is considered. In particular, a higher-order normalized approximation of NLKG (which corresponds to the NLS at order $r=1$) is constructed, and when $M$ is a smooth compact manifold or $\\mathbb{R}^d$ it is proved that the solution of the approximating equation approximates the solution of the NLKG locally uniformly in time. When $M=\\mathbb{R}^d$, $d \\geq 3$, it is proved that solutions of the linearized order $r$ normalized equation approximate solution","authors_text":"Stefano Pasquali","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-05T15:25:55Z","title":"Dynamics of the nonlinear Klein-Gordon equation in the nonrelativistic limit, I"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01609","kind":"arxiv","version":4},"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":"sha256:21addeafada536297a08c7419b497c23098e1e0cf24d188cb8ffb2fc471dd537","target":"record","created_at":"2026-05-18T00:03:32Z","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":"3fce68284c2ee98ee53b6d830e0b5a2dc2f8f59876782968bea5271af49ad10c","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-05T15:25:55Z","title_canon_sha256":"44bf64904c774f5dded8b9a6a108bd499976db42d2ab0a99a8e14aee5414df18"},"schema_version":"1.0","source":{"id":"1703.01609","kind":"arxiv","version":4}},"canonical_sha256":"4265a277d17584f90e94be6e121a41b50bf5c32a9695a4651755e00c11572f78","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4265a277d17584f90e94be6e121a41b50bf5c32a9695a4651755e00c11572f78","first_computed_at":"2026-05-18T00:03:32.673088Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:32.673088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JZt2mTCqEmw9RopgUWuFpjW3SiopFi3hGgScxpfHP2jl7XkIP93o+pp/zL+Gwtj5ILgHHyH7DqioSZ1NssBaDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:32.673582Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01609","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:21addeafada536297a08c7419b497c23098e1e0cf24d188cb8ffb2fc471dd537","sha256:ef90bff97d6f025cf545853b36d853f474aa1d2fca4b9bbf94a4d66ba86ccf11"],"state_sha256":"9a1ade5418ff595322afbe906bf022102a628691156f83df110d5350e901e4ba"}