{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:BLOZWQBHVV7ZIHBWBDNTPPJHCM","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":"d06dc22b67d0a6dd482d09927fbd213efee74dd5538c3309d0cee09b4533cde7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-19T07:16:10Z","title_canon_sha256":"b6826e82b06953e2966a42294d4aeebfc31bdba8b5f0b4f0224da5d0146a1f31"},"schema_version":"1.0","source":{"id":"1103.3760","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3760","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3760v1","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3760","created_at":"2026-05-18T04:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"BLOZWQBHVV7Z","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"BLOZWQBHVV7ZIHBW","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"BLOZWQBH","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:a3f3777eb6e7af7fd8d6f1e867aa217247ebb6a5dbc137f3a32e3ff7beb16a8b","target":"graph","created_at":"2026-05-18T04:26:22Z","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 spectral properties associated to Schrodinger operator with potential that is an exponential decaying function. As applications we prove local energy decay for solutions to the perturbed wave equation and lack of resonances for the NLS.","authors_text":"Mirko Tarulli, Vladimir Georgiev","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-19T07:16:10Z","title":"Local energy decay for wave equation in the absence of resonance at zero energy in 3D"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3760","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:d15f0a360dcb36aebfb2be6ba7758aa72c5cd236db06d143cf3ca5052c73180a","target":"record","created_at":"2026-05-18T04:26:22Z","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":"d06dc22b67d0a6dd482d09927fbd213efee74dd5538c3309d0cee09b4533cde7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-03-19T07:16:10Z","title_canon_sha256":"b6826e82b06953e2966a42294d4aeebfc31bdba8b5f0b4f0224da5d0146a1f31"},"schema_version":"1.0","source":{"id":"1103.3760","kind":"arxiv","version":1}},"canonical_sha256":"0add9b4027ad7f941c3608db37bd2713275a35cdb9b126afdc759b1d797b498f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0add9b4027ad7f941c3608db37bd2713275a35cdb9b126afdc759b1d797b498f","first_computed_at":"2026-05-18T04:26:22.378575Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:22.378575Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wRUfGbI4hJ2QuAd7AxxoLtyNeX72p4DAsMZW+WhFo9il1gDizw1ZvoHQsWQiMDCe8LhcD71rC8Q4u2cuCEtgDw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:22.379121Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3760","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d15f0a360dcb36aebfb2be6ba7758aa72c5cd236db06d143cf3ca5052c73180a","sha256:a3f3777eb6e7af7fd8d6f1e867aa217247ebb6a5dbc137f3a32e3ff7beb16a8b"],"state_sha256":"94f294d988210bcddb8066c68e2e879d35042f03a4761e5eae0d99c852aa1b6f"}