{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:TMHQJM63Q32DTFNE3YOZS6TMW7","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":"f595ffc27983939c6f0a7be6c58148ee13e42c6fffe2ba7fe8492dc5b5b83150","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-01-15T02:20:12Z","title_canon_sha256":"a77013b632c9a8a0c486850b1763b48e0254e1b20eddf7017439056abb3720be"},"schema_version":"1.0","source":{"id":"2101.05937","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.05937","created_at":"2026-07-05T02:07:07Z"},{"alias_kind":"arxiv_version","alias_value":"2101.05937v1","created_at":"2026-07-05T02:07:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.05937","created_at":"2026-07-05T02:07:07Z"},{"alias_kind":"pith_short_12","alias_value":"TMHQJM63Q32D","created_at":"2026-07-05T02:07:07Z"},{"alias_kind":"pith_short_16","alias_value":"TMHQJM63Q32DTFNE","created_at":"2026-07-05T02:07:07Z"},{"alias_kind":"pith_short_8","alias_value":"TMHQJM63","created_at":"2026-07-05T02:07:07Z"}],"graph_snapshots":[{"event_id":"sha256:dd9ed2397ecd3a4dbaac8ec22d9bb70ac9635a4023cc732c2f4a9d892d293707","target":"graph","created_at":"2026-07-05T02:07:07Z","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/2101.05937/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the nonlinear Klein-Gordon systems arising from relativistic physics and quantum field theories\n  $$\\left\\{\\begin{array}{lll} u_{tt}- u_{xx} +bu + \\varepsilon v + f(t,x,u) =0,\\; v_{tt}- v_{xx} +bv + \\varepsilon u + g(t,x,v) =0\n  \\end{array}\\right.\n  $$ where $u,v$ satisfy the Dirichlet boundary conditions on spatial interval $[0, \\pi]$, $b>0$ and $f$, $g$ are $2\\pi$-periodic in $t$. We are concerned with the existence, regularity and asymptotic behavior of time-periodic solutions to the linearly coupled problem as $\\varepsilon$ goes to 0. Firstly, under some superlinear","authors_text":"Guijuan Chang, Jianyi Chen, Jing Zhao, Zhitao Zhang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-01-15T02:20:12Z","title":"Periodic solutions to Klein-Gordon systems with linear couplings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.05937","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":"sha256:322fbd3f33e090fe59ebf6cda6bb4e3860aa9cadf3dbdb0a89883c479fe7fd17","target":"record","created_at":"2026-07-05T02:07:07Z","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":"f595ffc27983939c6f0a7be6c58148ee13e42c6fffe2ba7fe8492dc5b5b83150","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2021-01-15T02:20:12Z","title_canon_sha256":"a77013b632c9a8a0c486850b1763b48e0254e1b20eddf7017439056abb3720be"},"schema_version":"1.0","source":{"id":"2101.05937","kind":"arxiv","version":1}},"canonical_sha256":"9b0f04b3db86f43995a4de1d997a6cb7c3b64f9db8a0477e62fb438538474e25","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b0f04b3db86f43995a4de1d997a6cb7c3b64f9db8a0477e62fb438538474e25","first_computed_at":"2026-07-05T02:07:07.908052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:07:07.908052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hGnyHZ74g170fYNlQrs3TBLxtnznY3JjX03FrU5SSIaDjc4AXmcevmHX3FAYOVtpjt2WZodtgnG8S06Gkoh8Ag==","signature_status":"signed_v1","signed_at":"2026-07-05T02:07:07.908609Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.05937","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:322fbd3f33e090fe59ebf6cda6bb4e3860aa9cadf3dbdb0a89883c479fe7fd17","sha256:dd9ed2397ecd3a4dbaac8ec22d9bb70ac9635a4023cc732c2f4a9d892d293707"],"state_sha256":"e7fcd9331469aaee42487fb63a12e3bb3054075f3e8ad12e08da01845a9409bc"}