{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6AGXYUBKHZBCL3Q2J6NEYCCBER","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":"f0623a71750258104f4eed7160069e4b6219aa2306d733581891f27ae1d9e52e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-10T19:34:45Z","title_canon_sha256":"94b438e610ed8fa4c72f68b5fdca2700b65eb69340f1359552a4c12f0f393493"},"schema_version":"1.0","source":{"id":"1306.2294","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.2294","created_at":"2026-05-18T03:21:21Z"},{"alias_kind":"arxiv_version","alias_value":"1306.2294v1","created_at":"2026-05-18T03:21:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.2294","created_at":"2026-05-18T03:21:21Z"},{"alias_kind":"pith_short_12","alias_value":"6AGXYUBKHZBC","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6AGXYUBKHZBCL3Q2","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6AGXYUBK","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:a0ac0be5a9c08b26f6f1be075f2f3c7923910a8e1c96f55a81ffa71b2519579e","target":"graph","created_at":"2026-05-18T03:21:21Z","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":"Dissipative wave equations with critical quintic nonlinearity and damping term involving the fractional Laplacian are considered. The additional regularity of energy solutions is established by constructing the new Lyapunov-type functional and based on this, the global well-posedness and dissipativity of the energy solutions as well as the existence of a smooth global and exponential attractors of finite Hausdorff and fractal dimension is verified.","authors_text":"Anton Savostianov, Sergey Zelik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-10T19:34:45Z","title":"Smooth attractors for the quintic wave equations with fractional damping"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.2294","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:e824a5452cc163074625520bedcfec556bfccc9594f952f934e233a05ea48d88","target":"record","created_at":"2026-05-18T03:21:21Z","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":"f0623a71750258104f4eed7160069e4b6219aa2306d733581891f27ae1d9e52e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-06-10T19:34:45Z","title_canon_sha256":"94b438e610ed8fa4c72f68b5fdca2700b65eb69340f1359552a4c12f0f393493"},"schema_version":"1.0","source":{"id":"1306.2294","kind":"arxiv","version":1}},"canonical_sha256":"f00d7c502a3e4225ee1a4f9a4c0841246921da5037bf8615a80289d806afc5b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f00d7c502a3e4225ee1a4f9a4c0841246921da5037bf8615a80289d806afc5b3","first_computed_at":"2026-05-18T03:21:21.887984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:21.887984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aTfku2/0AGEPucal77LAe+fle13cq42+E6w6VK5zDzTu3qPj9SIAR9PEiQleLToQNpCYdIUpuDX9XAGmzLNkBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:21.888676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.2294","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e824a5452cc163074625520bedcfec556bfccc9594f952f934e233a05ea48d88","sha256:a0ac0be5a9c08b26f6f1be075f2f3c7923910a8e1c96f55a81ffa71b2519579e"],"state_sha256":"3f14511ed44ca7497cb71f77f43d3cf1ad1e58ca2b533ee4de638d2a9f126eb1"}