{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:5M5MY6JKOJ46CM2HOYQUF635DW","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":"469f5b4aaf468a9fa003b70fdce3e6d2233698ebc81ed1ad733f09b7e41a62a4","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2011-09-27T14:49:34Z","title_canon_sha256":"e466e9847fe656f658429d4d02753e5059d8d343ad0dd55c09e067a3a966760d"},"schema_version":"1.0","source":{"id":"1109.5916","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.5916","created_at":"2026-05-18T03:56:22Z"},{"alias_kind":"arxiv_version","alias_value":"1109.5916v1","created_at":"2026-05-18T03:56:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.5916","created_at":"2026-05-18T03:56:22Z"},{"alias_kind":"pith_short_12","alias_value":"5M5MY6JKOJ46","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"5M5MY6JKOJ46CM2H","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"5M5MY6JK","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:7b760aafdda161f81f4951758bb104e44c3bc6196a5bdc88578bb5b1d1757864","target":"graph","created_at":"2026-05-18T03:56:22Z","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 consider the viscoelastic wave equation of Kirchhoff type:\n$$ u_{tt}-M(\\|\\nabla u\\|_{2}^{2})\\Delta u+\\int_{0}^{t}g(t-s)\\Delta u(s){\\rm d}s+u_{t}=|u|^{p-1}u $$\nwith Dirichlet boundary conditions. Under some suitable assumptions on $g$ and the initial data, we established a global nonexistence result for certain solutions with arbitrarily high energy.","authors_text":"Gang Li, Linghui Hong, Wenjun Liu","cross_cats":["math.FA"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2011-09-27T14:49:34Z","title":"Global nonexistence of solutions for the viscoelastic wave equation of Kirchhoff type with high energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.5916","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:f15f90a9d3119737e93ee36d354ab2a88b3e085bc6afaf830bb2a3938e5e9e98","target":"record","created_at":"2026-05-18T03:56:22Z","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":"469f5b4aaf468a9fa003b70fdce3e6d2233698ebc81ed1ad733f09b7e41a62a4","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.AP","submitted_at":"2011-09-27T14:49:34Z","title_canon_sha256":"e466e9847fe656f658429d4d02753e5059d8d343ad0dd55c09e067a3a966760d"},"schema_version":"1.0","source":{"id":"1109.5916","kind":"arxiv","version":1}},"canonical_sha256":"eb3acc792a7279e13347762142fb7d1d983504a7f89e7f4ff54f374e38b0049f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb3acc792a7279e13347762142fb7d1d983504a7f89e7f4ff54f374e38b0049f","first_computed_at":"2026-05-18T03:56:22.483869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:22.483869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y7mqsYKEshKf3a/hjzl9u0e3/LSAVpkeGOV6dn+EXXJ4vYRf9j1Nu5XZOGGYnZS5veAXhnGovJPH3Y/hnDn4Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:22.484570Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.5916","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f15f90a9d3119737e93ee36d354ab2a88b3e085bc6afaf830bb2a3938e5e9e98","sha256:7b760aafdda161f81f4951758bb104e44c3bc6196a5bdc88578bb5b1d1757864"],"state_sha256":"91249e3b0e2ebc5a28269d2d7d64d4eec5a0a0aa28f04dca063eea0598fc9614"}