{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:E626H7SGL4OK4XALZXPGEBXCPD","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":"aed587736c3bc5460aeaa462e2f82af3ae32f7dfb4be733dfe69716a911d802f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-19T13:22:57Z","title_canon_sha256":"04180b7492a4f8ad28234ed04683c6b73b5a274162c18baacd90deeb2af1654c"},"schema_version":"1.0","source":{"id":"1811.07667","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.07667","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"arxiv_version","alias_value":"1811.07667v1","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.07667","created_at":"2026-05-18T00:00:23Z"},{"alias_kind":"pith_short_12","alias_value":"E626H7SGL4OK","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"E626H7SGL4OK4XAL","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"E626H7SG","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:feff07d6ae62efaa18a26d9ddc666c1416cc85f0df731d5884ddb88278dccb35","target":"graph","created_at":"2026-05-18T00:00:23Z","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 contraction semigroup $S(t)={\\rm e}^{t\\mathbb{A}}$ generated by the abstract linear dissipative evolution equation $$ \\ddot u + A u + f(A) \\dot u=0 $$ is analyzed, where $A$ is a strictly positive selfadjoint operator and $f$ is an arbitrary nonnegative continuous function on the spectrum of $A$. A full description of the spectrum of the infinitesimal generator $\\mathbb{A}$ of $S(t)$ is provided. Necessary and sufficient conditions for the stability, the semiuniform stability and the exponential stability of the semigroup are found, depending on the behavior of $f$ and the spectral propert","authors_text":"Filippo Dell'Oro, Vittorino Pata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-19T13:22:57Z","title":"Second order linear evolution equations with general dissipation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.07667","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":"sha256:2754022c962379d6da4e894573bc1441acde96e69d1ea9d2221cd92620b61912","target":"record","created_at":"2026-05-18T00:00:23Z","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":"aed587736c3bc5460aeaa462e2f82af3ae32f7dfb4be733dfe69716a911d802f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-11-19T13:22:57Z","title_canon_sha256":"04180b7492a4f8ad28234ed04683c6b73b5a274162c18baacd90deeb2af1654c"},"schema_version":"1.0","source":{"id":"1811.07667","kind":"arxiv","version":1}},"canonical_sha256":"27b5e3fe465f1cae5c0bcdde6206e278f8e5155bd551c63e01956fc0de11cdb3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27b5e3fe465f1cae5c0bcdde6206e278f8e5155bd551c63e01956fc0de11cdb3","first_computed_at":"2026-05-18T00:00:23.820072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:23.820072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Nhzydbx4zThUG2hmsswexbmIUAb9PKJfyXd2pf7LTdoeWaFaUyr/aM8E7s5wZsV8Ao+MPXgd7UwD4pdIwc7OBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:23.820682Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.07667","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2754022c962379d6da4e894573bc1441acde96e69d1ea9d2221cd92620b61912","sha256:feff07d6ae62efaa18a26d9ddc666c1416cc85f0df731d5884ddb88278dccb35"],"state_sha256":"390c8e9994439196beb245f11e1de7a761c9abfc27ba0be0cd13ab8fc107586b"}