{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:MKI3NAP6XUDS3DAASGMVRH7IKQ","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":"c04dc3f186ad09863b5ed1c47229610cea833b3c2d17aea69eff6ae392b8195b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-04T16:28:39Z","title_canon_sha256":"c7758f2afaca8b22b0274f020574ffd8446f74042320540afc36fed5e7267f51"},"schema_version":"1.0","source":{"id":"1408.0737","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.0737","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1408.0737v3","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.0737","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"MKI3NAP6XUDS","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"MKI3NAP6XUDS3DAA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"MKI3NAP6","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:d1a7ae170787ac0cf1a1dc0364e64b659d190513d83df213d33351a296cc0169","target":"graph","created_at":"2026-05-18T02:17:01Z","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 a wave model with non-effective mass and dissipation terms and provide asymptotic descriptions of its representation of solutions. In particular we conclude sharp estimates for a corresponding energy and estimates of dispersive type.","authors_text":"Jens Wirth, Wanderley Nunes do Nascimento","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-04T16:28:39Z","title":"Wave equations with mass and dissipation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.0737","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":"sha256:18b59df3f9499039aa7a1d8852510e757dfe13cd84326a8729d436b04afa705f","target":"record","created_at":"2026-05-18T02:17:01Z","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":"c04dc3f186ad09863b5ed1c47229610cea833b3c2d17aea69eff6ae392b8195b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-08-04T16:28:39Z","title_canon_sha256":"c7758f2afaca8b22b0274f020574ffd8446f74042320540afc36fed5e7267f51"},"schema_version":"1.0","source":{"id":"1408.0737","kind":"arxiv","version":3}},"canonical_sha256":"6291b681febd072d8c009199589fe85426bb9630c4798e9cc32c56f7fa2a90fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6291b681febd072d8c009199589fe85426bb9630c4798e9cc32c56f7fa2a90fe","first_computed_at":"2026-05-18T02:17:01.229100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:01.229100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xbWGsG6tChUQVOHomrGsUMtrNBFR2+gtuG9eiqb1ZA87O8n/G6p8/pLwB6HDd/GVOxCZXzFSnIgpBl6oY21vCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:01.229791Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.0737","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18b59df3f9499039aa7a1d8852510e757dfe13cd84326a8729d436b04afa705f","sha256:d1a7ae170787ac0cf1a1dc0364e64b659d190513d83df213d33351a296cc0169"],"state_sha256":"4e7daf264c0b2f0b0fb7bc12f831a8c9ba13c649864ca586867a1ad4650ed907"}