{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:3JOUIQSITLG47PLI3PFILPVV2K","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":"8abcfc23182aeaa0fdcdf30cf8c38fecefe2bfb99b996fabcefc0c3f45f73b54","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-13T16:28:18Z","title_canon_sha256":"b0e520f3687a150d43e5cbfc4fe27227721939a4b1b073658c3ee743dfdd7ba1"},"schema_version":"1.0","source":{"id":"1107.2589","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.2589","created_at":"2026-05-18T04:18:22Z"},{"alias_kind":"arxiv_version","alias_value":"1107.2589v1","created_at":"2026-05-18T04:18:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.2589","created_at":"2026-05-18T04:18:22Z"},{"alias_kind":"pith_short_12","alias_value":"3JOUIQSITLG4","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"3JOUIQSITLG47PLI","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"3JOUIQSI","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:5ef5076cac8a6a9a073d34fb4b2bbc8ec71b75f48148395cf738c5b07ba74996","target":"graph","created_at":"2026-05-18T04:18:22Z","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":"Under fairly general assumptions, we prove that every compact invariant set $\\mathcal I$ of the semiflow generated by the semilinear damped wave equation\nu_{tt}+\\alpha u_t+\\beta(x)u-\\Deltau = f(x,u),   (t,x)\\in[0,+\\infty[\\times\\Omega,\nu = 0,   (t,x)\\in[0,+\\infty[\\times\\partial\\Omega in $H^1_0(\\Omega)\\times L^2(\\Omega)\nhas finite Hausdorff and fractal dimension. Here $\\Omega$ is a regular, possibly unbounded, domain in $\\R^3$ and $f(x,u)$ is a nonlinearity of critical growth. The nonlinearity $f(x,u)$ needs not to satisfy any dissipativeness assumption and the invariant subset $\\mathcal I$ need","authors_text":"Martino Prizzi","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-13T16:28:18Z","title":"Dimension of attractors and invariant sets of damped wave equations in unbounded domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.2589","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:e7eba87c49e399d66dc6134a1a720a1cd2425470ca6e899b8e19d4f10c3e8bea","target":"record","created_at":"2026-05-18T04:18:22Z","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":"8abcfc23182aeaa0fdcdf30cf8c38fecefe2bfb99b996fabcefc0c3f45f73b54","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-07-13T16:28:18Z","title_canon_sha256":"b0e520f3687a150d43e5cbfc4fe27227721939a4b1b073658c3ee743dfdd7ba1"},"schema_version":"1.0","source":{"id":"1107.2589","kind":"arxiv","version":1}},"canonical_sha256":"da5d4442489acdcfbd68dbca85beb5d2ad6b2e60a3e268d7d4ba26c790667949","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"da5d4442489acdcfbd68dbca85beb5d2ad6b2e60a3e268d7d4ba26c790667949","first_computed_at":"2026-05-18T04:18:22.819555Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:18:22.819555Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uHZ0puv1N3sLmKL2RRl6mPKRhDXSv70LbXBIBqXVoI8H5sm1egm1iJRZEkp8WnZ4RM8gaPbyIUswYdbFTxOqAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:18:22.819957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.2589","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7eba87c49e399d66dc6134a1a720a1cd2425470ca6e899b8e19d4f10c3e8bea","sha256:5ef5076cac8a6a9a073d34fb4b2bbc8ec71b75f48148395cf738c5b07ba74996"],"state_sha256":"f04cc6b91a73934247b851ba17471982e6f9a83c1743fb38178dabf241c09edf"}