{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:NTV32ICBEO5M4TDKQLMKYCVKXL","short_pith_number":"pith:NTV32ICB","schema_version":"1.0","canonical_sha256":"6cebbd204123bace4c6a82d8ac0aaabaff29b64334e63a820f1bf2b535260d50","source":{"kind":"arxiv","id":"1102.4280","version":3},"attestation_state":"computed","paper":{"title":"Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yavar Kian","submitted_at":"2011-02-21T17:00:08Z","abstract_excerpt":"Consider the mixed problem with Dirichelet condition associated to the wave equation $\\partial_t^2u-\\Div_{x}(a(t,x)\\nabla_{x}u)=0$, where the scalar metric $a(t,x)$ is $T$-periodic in $t$ and uniformly equal to 1 outside a compact set in $x$, on a $T$-periodic domain. Let $\\mathcal U(t, 0)$ be the associated propagator. Assuming that the perturbations are non-trapping, we prove the meromorphic continuation of the cut-off resolvent of the Floquet operator $\\mathcal U(T, 0)$ and establish sufficient conditions for local energy decay."},"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":"1102.4280","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-02-21T17:00:08Z","cross_cats_sorted":[],"title_canon_sha256":"8817de1ff3787700a5be02493dcbd30072880bfaaa0527ec4ff26a2101112a5f","abstract_canon_sha256":"af0652b48c7e88042f2feca2206ceec7d1402e635cf2091d502c8cf5abe5511d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:07.103540Z","signature_b64":"4hggT3RL8UlqGYh/RDKTEf3PTy8Lb1l1DjGXzoJPS5vZ+Eq/zSmauNXd6ePUTO2dZ5SjXh3fjaJmU7KoOfVPAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6cebbd204123bace4c6a82d8ac0aaabaff29b64334e63a820f1bf2b535260d50","last_reissued_at":"2026-05-18T04:03:07.102786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:07.102786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local energy decay for the wave equation with a time-periodic non-trapping metric and moving obstacle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yavar Kian","submitted_at":"2011-02-21T17:00:08Z","abstract_excerpt":"Consider the mixed problem with Dirichelet condition associated to the wave equation $\\partial_t^2u-\\Div_{x}(a(t,x)\\nabla_{x}u)=0$, where the scalar metric $a(t,x)$ is $T$-periodic in $t$ and uniformly equal to 1 outside a compact set in $x$, on a $T$-periodic domain. Let $\\mathcal U(t, 0)$ be the associated propagator. Assuming that the perturbations are non-trapping, we prove the meromorphic continuation of the cut-off resolvent of the Floquet operator $\\mathcal U(T, 0)$ and establish sufficient conditions for local energy decay."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4280","kind":"arxiv","version":3},"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":"1102.4280","created_at":"2026-05-18T04:03:07.102898+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.4280v3","created_at":"2026-05-18T04:03:07.102898+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4280","created_at":"2026-05-18T04:03:07.102898+00:00"},{"alias_kind":"pith_short_12","alias_value":"NTV32ICBEO5M","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_16","alias_value":"NTV32ICBEO5M4TDK","created_at":"2026-05-18T12:26:37.096874+00:00"},{"alias_kind":"pith_short_8","alias_value":"NTV32ICB","created_at":"2026-05-18T12:26:37.096874+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/NTV32ICBEO5M4TDKQLMKYCVKXL","json":"https://pith.science/pith/NTV32ICBEO5M4TDKQLMKYCVKXL.json","graph_json":"https://pith.science/api/pith-number/NTV32ICBEO5M4TDKQLMKYCVKXL/graph.json","events_json":"https://pith.science/api/pith-number/NTV32ICBEO5M4TDKQLMKYCVKXL/events.json","paper":"https://pith.science/paper/NTV32ICB"},"agent_actions":{"view_html":"https://pith.science/pith/NTV32ICBEO5M4TDKQLMKYCVKXL","download_json":"https://pith.science/pith/NTV32ICBEO5M4TDKQLMKYCVKXL.json","view_paper":"https://pith.science/paper/NTV32ICB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.4280&json=true","fetch_graph":"https://pith.science/api/pith-number/NTV32ICBEO5M4TDKQLMKYCVKXL/graph.json","fetch_events":"https://pith.science/api/pith-number/NTV32ICBEO5M4TDKQLMKYCVKXL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NTV32ICBEO5M4TDKQLMKYCVKXL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NTV32ICBEO5M4TDKQLMKYCVKXL/action/storage_attestation","attest_author":"https://pith.science/pith/NTV32ICBEO5M4TDKQLMKYCVKXL/action/author_attestation","sign_citation":"https://pith.science/pith/NTV32ICBEO5M4TDKQLMKYCVKXL/action/citation_signature","submit_replication":"https://pith.science/pith/NTV32ICBEO5M4TDKQLMKYCVKXL/action/replication_record"}},"created_at":"2026-05-18T04:03:07.102898+00:00","updated_at":"2026-05-18T04:03:07.102898+00:00"}