{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:XWI7SA464CXEUTBM2WSCJ2SCPK","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":"79f42658efa912be13278d6582fca33bd3d16173758b204a59a64f3c130d3543","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-05T12:48:12Z","title_canon_sha256":"05c7e2d8594ebd5bfd4b5f7ce7e304c00799b163d2ac342fedd1d01b3dd9d9cd"},"schema_version":"1.0","source":{"id":"1807.01968","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.01968","created_at":"2026-05-17T23:57:46Z"},{"alias_kind":"arxiv_version","alias_value":"1807.01968v3","created_at":"2026-05-17T23:57:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.01968","created_at":"2026-05-17T23:57:46Z"},{"alias_kind":"pith_short_12","alias_value":"XWI7SA464CXE","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"XWI7SA464CXEUTBM","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"XWI7SA46","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:327f81dbf30198a3d224392f938a56ecffee495a0ac07a43ff0b87841bed2bca","target":"graph","created_at":"2026-05-17T23:57:46Z","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 study the long time behavior for a semilinear wave equation with space-dependent and nonlinear damping term. After rewriting the equation as a first order system, we define a class of approximate solutions that employ tipical tools of hyperbolic systems of conservation laws, such as the Riemann problem. By recasting the problem as a discrete-time nonhomogeneous system, which is related to a probabilistic interpretation of the solution, we provide a strategy to study its long-time behavior uniformly with respect to the mesh size parameter $\\Delta x=1/N\\to 0$. The proof makes us","authors_text":"Debora Amadori, Edda Dal Santo, Fatima Al-Zahr\\`a Aqel","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-05T12:48:12Z","title":"Decay of approximate solutions for the damped semilinear wave equation on a bounded 1d domain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.01968","kind":"arxiv","version":3},"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":"sha256:68fd2db22fa3290f1de8ad764caa255ae62a5c85d81b04e560427a49e4e8b6c6","target":"record","created_at":"2026-05-17T23:57:46Z","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":"79f42658efa912be13278d6582fca33bd3d16173758b204a59a64f3c130d3543","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-07-05T12:48:12Z","title_canon_sha256":"05c7e2d8594ebd5bfd4b5f7ce7e304c00799b163d2ac342fedd1d01b3dd9d9cd"},"schema_version":"1.0","source":{"id":"1807.01968","kind":"arxiv","version":3}},"canonical_sha256":"bd91f9039ee0ae4a4c2cd5a424ea427aa399012b8cdf6f85583aebf913fe712f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd91f9039ee0ae4a4c2cd5a424ea427aa399012b8cdf6f85583aebf913fe712f","first_computed_at":"2026-05-17T23:57:46.750507Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:46.750507Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ltSYaCmH7pYsbmIx/4QUIOthOUKM8pLz/mPQRotI7/n3bv3q/aJUCz/zAYPx0EJsOy2bg6BU4cJP3apRFIJGBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:46.751045Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.01968","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:68fd2db22fa3290f1de8ad764caa255ae62a5c85d81b04e560427a49e4e8b6c6","sha256:327f81dbf30198a3d224392f938a56ecffee495a0ac07a43ff0b87841bed2bca"],"state_sha256":"f06c6ca6a9b0fc251a2b2f115b0fdb7ad9deb36aa7790c06185a0d77a12b6d4d"}