{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:MCCTZ4CLM2C7KF5QIY7ADM25QT","short_pith_number":"pith:MCCTZ4CL","schema_version":"1.0","canonical_sha256":"60853cf04b6685f517b0463e01b35d84c7919cd6f41bcd5855b8020de74d63fa","source":{"kind":"arxiv","id":"0906.0293","version":4},"attestation_state":"computed","paper":{"title":"Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luchezar Stoyanov, Vesselin Petkov","submitted_at":"2009-06-01T14:23:31Z","abstract_excerpt":"Let $s_0 < 0$ be the abscissa of absolute convergence of the dynamical zeta function $Z(s)$ for several disjoint strictly convex compact obstacles $K_i \\subset \\R^N, i = 1,..., \\kappa_0,\\: \\ka_0 \\geq 3,$ and let $R_{\\chi}(z) = \\chi (-\\Delta_D - z^2)^{-1}\\chi,\\: \\chi \\in C_0^{\\infty}(\\R^N),$ be the cut-off resolvent of the Dirichlet Laplacian $-\\Delta_D$ in $\\Omega = \\bar{\\R^N \\setminus \\cup_{i = 1}^{k_0} K_i}$. We prove that there exists $\\sigma_1 < s_0$ such that $Z(s)$ is analytic for $\\Re (s) \\geq \\sigma_1$ and the cut-off resolvent $R_{\\chi}(z)$ has an analytic continuation for $\\Im (z) < "},"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":"0906.0293","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2009-06-01T14:23:31Z","cross_cats_sorted":[],"title_canon_sha256":"dfd3e40be8dc887318ddd8bd37ae11660d7a2813db820b2e34bd440b6f3175a5","abstract_canon_sha256":"536e374ea7a0ecb01bb9aa6b921a3734e04cb4c971b94aa85714037d91d77c43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:34.109703Z","signature_b64":"rOrVeTWOotrpzdagA75i5GuYT4wkwN5nfM0e4QuuEoZ5dOuvIlVsZ5XjoMVwMSd9IQfx7Ghxqh9o0mM3WdkNCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"60853cf04b6685f517b0463e01b35d84c7919cd6f41bcd5855b8020de74d63fa","last_reissued_at":"2026-05-18T04:37:34.109010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:34.109010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic continuation of the resolvent of the Laplacian and the dynamical zeta function","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luchezar Stoyanov, Vesselin Petkov","submitted_at":"2009-06-01T14:23:31Z","abstract_excerpt":"Let $s_0 < 0$ be the abscissa of absolute convergence of the dynamical zeta function $Z(s)$ for several disjoint strictly convex compact obstacles $K_i \\subset \\R^N, i = 1,..., \\kappa_0,\\: \\ka_0 \\geq 3,$ and let $R_{\\chi}(z) = \\chi (-\\Delta_D - z^2)^{-1}\\chi,\\: \\chi \\in C_0^{\\infty}(\\R^N),$ be the cut-off resolvent of the Dirichlet Laplacian $-\\Delta_D$ in $\\Omega = \\bar{\\R^N \\setminus \\cup_{i = 1}^{k_0} K_i}$. We prove that there exists $\\sigma_1 < s_0$ such that $Z(s)$ is analytic for $\\Re (s) \\geq \\sigma_1$ and the cut-off resolvent $R_{\\chi}(z)$ has an analytic continuation for $\\Im (z) < "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.0293","kind":"arxiv","version":4},"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":"0906.0293","created_at":"2026-05-18T04:37:34.109113+00:00"},{"alias_kind":"arxiv_version","alias_value":"0906.0293v4","created_at":"2026-05-18T04:37:34.109113+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.0293","created_at":"2026-05-18T04:37:34.109113+00:00"},{"alias_kind":"pith_short_12","alias_value":"MCCTZ4CLM2C7","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"MCCTZ4CLM2C7KF5Q","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"MCCTZ4CL","created_at":"2026-05-18T12:26:00.592388+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/MCCTZ4CLM2C7KF5QIY7ADM25QT","json":"https://pith.science/pith/MCCTZ4CLM2C7KF5QIY7ADM25QT.json","graph_json":"https://pith.science/api/pith-number/MCCTZ4CLM2C7KF5QIY7ADM25QT/graph.json","events_json":"https://pith.science/api/pith-number/MCCTZ4CLM2C7KF5QIY7ADM25QT/events.json","paper":"https://pith.science/paper/MCCTZ4CL"},"agent_actions":{"view_html":"https://pith.science/pith/MCCTZ4CLM2C7KF5QIY7ADM25QT","download_json":"https://pith.science/pith/MCCTZ4CLM2C7KF5QIY7ADM25QT.json","view_paper":"https://pith.science/paper/MCCTZ4CL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0906.0293&json=true","fetch_graph":"https://pith.science/api/pith-number/MCCTZ4CLM2C7KF5QIY7ADM25QT/graph.json","fetch_events":"https://pith.science/api/pith-number/MCCTZ4CLM2C7KF5QIY7ADM25QT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MCCTZ4CLM2C7KF5QIY7ADM25QT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MCCTZ4CLM2C7KF5QIY7ADM25QT/action/storage_attestation","attest_author":"https://pith.science/pith/MCCTZ4CLM2C7KF5QIY7ADM25QT/action/author_attestation","sign_citation":"https://pith.science/pith/MCCTZ4CLM2C7KF5QIY7ADM25QT/action/citation_signature","submit_replication":"https://pith.science/pith/MCCTZ4CLM2C7KF5QIY7ADM25QT/action/replication_record"}},"created_at":"2026-05-18T04:37:34.109113+00:00","updated_at":"2026-05-18T04:37:34.109113+00:00"}