{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:4BXFI7L3UMY4XYXFBALEC6KRHF","short_pith_number":"pith:4BXFI7L3","schema_version":"1.0","canonical_sha256":"e06e547d7ba331cbe2e50816417951395b4b78b4a18113d40e25e9e298df0220","source":{"kind":"arxiv","id":"1209.1733","version":1},"attestation_state":"computed","paper":{"title":"Local energy decay for the wave equation with nonlinear time dependent damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"A. Bchatnia, M. Daoulatli","submitted_at":"2012-09-08T17:13:04Z","abstract_excerpt":"This paper addresses a wave equation on a exterior domain in R^{d}(d odd) with nonlinear time dependent dissipation. Under a microlocal geometric condition we prove that the decay rates of the local energy functional are obtained by solving a nonlinear non-autonomous differential equation."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1209.1733","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-09-08T17:13:04Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"c461259ab213bbe57e551b1a0bf4cb147a064fa5e6c71cfd903dd0d85b203d41","abstract_canon_sha256":"f1fe6fa9a1acabf41de3cfe662d4e9f2cdd366ce196b46d4e4fdb565a08d0a42"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:54.500706Z","signature_b64":"TZd4/xFhjncGBVaZGmfM3nkTgsXiBYOryCzJMuClzh9fO2sirEteKqHnlladrat/oN3/Bu4xjKQjbQ7xF/6XCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e06e547d7ba331cbe2e50816417951395b4b78b4a18113d40e25e9e298df0220","last_reissued_at":"2026-05-18T03:45:54.499786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:54.499786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local energy decay for the wave equation with nonlinear time dependent damping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.OC","authors_text":"A. Bchatnia, M. Daoulatli","submitted_at":"2012-09-08T17:13:04Z","abstract_excerpt":"This paper addresses a wave equation on a exterior domain in R^{d}(d odd) with nonlinear time dependent dissipation. Under a microlocal geometric condition we prove that the decay rates of the local energy functional are obtained by solving a nonlinear non-autonomous differential equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.1733","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1209.1733","created_at":"2026-05-18T03:45:54.499904+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.1733v1","created_at":"2026-05-18T03:45:54.499904+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.1733","created_at":"2026-05-18T03:45:54.499904+00:00"},{"alias_kind":"pith_short_12","alias_value":"4BXFI7L3UMY4","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_16","alias_value":"4BXFI7L3UMY4XYXF","created_at":"2026-05-18T12:26:53.410803+00:00"},{"alias_kind":"pith_short_8","alias_value":"4BXFI7L3","created_at":"2026-05-18T12:26:53.410803+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4BXFI7L3UMY4XYXFBALEC6KRHF","json":"https://pith.science/pith/4BXFI7L3UMY4XYXFBALEC6KRHF.json","graph_json":"https://pith.science/api/pith-number/4BXFI7L3UMY4XYXFBALEC6KRHF/graph.json","events_json":"https://pith.science/api/pith-number/4BXFI7L3UMY4XYXFBALEC6KRHF/events.json","paper":"https://pith.science/paper/4BXFI7L3"},"agent_actions":{"view_html":"https://pith.science/pith/4BXFI7L3UMY4XYXFBALEC6KRHF","download_json":"https://pith.science/pith/4BXFI7L3UMY4XYXFBALEC6KRHF.json","view_paper":"https://pith.science/paper/4BXFI7L3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.1733&json=true","fetch_graph":"https://pith.science/api/pith-number/4BXFI7L3UMY4XYXFBALEC6KRHF/graph.json","fetch_events":"https://pith.science/api/pith-number/4BXFI7L3UMY4XYXFBALEC6KRHF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4BXFI7L3UMY4XYXFBALEC6KRHF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4BXFI7L3UMY4XYXFBALEC6KRHF/action/storage_attestation","attest_author":"https://pith.science/pith/4BXFI7L3UMY4XYXFBALEC6KRHF/action/author_attestation","sign_citation":"https://pith.science/pith/4BXFI7L3UMY4XYXFBALEC6KRHF/action/citation_signature","submit_replication":"https://pith.science/pith/4BXFI7L3UMY4XYXFBALEC6KRHF/action/replication_record"}},"created_at":"2026-05-18T03:45:54.499904+00:00","updated_at":"2026-05-18T03:45:54.499904+00:00"}