{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ANA2HZ77YT5YQHBQOROIZQMJSP","short_pith_number":"pith:ANA2HZ77","schema_version":"1.0","canonical_sha256":"0341a3e7ffc4fb881c30745c8cc18993f282660ca5f27a7eb232f6ab7441d6de","source":{"kind":"arxiv","id":"1706.07869","version":5},"attestation_state":"computed","paper":{"title":"On resonances generated by conic diffraction","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Jared Wunsch, Luc Hillairet","submitted_at":"2017-06-23T21:20:50Z","abstract_excerpt":"We describe the resonances closest to the real axis generated by diffraction of waves among cone points on a manifold with Euclidean ends. These resonances lie asymptotically evenly spaced along a curve of the form $$\\frac{\\Im \\lambda}{\\log \\left |\\Re\n  \\lambda\\right |}= -\\nu;$$ here $\\nu=(n-1)/2 L_0$ where $n$ is the dimension and $L_0$ is the length of the longest geodesic connecting two cone points. Moreover there are asymptotically no resonances below this curve and above the curve $$ \\frac{\\Im \\lambda}{\\log \\left |\\Re\n  \\lambda\\right |}= -\\Lambda $$ for a fixed $\\Lambda>\\nu.$"},"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":"1706.07869","kind":"arxiv","version":5},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2017-06-23T21:20:50Z","cross_cats_sorted":["math-ph","math.MP","math.SP"],"title_canon_sha256":"1f21fc51fc0616b4a78ef719d2fbf9d527be67cbb0bf27bf7e9423788464ba02","abstract_canon_sha256":"4bb5b39a5297117093a92f59ef7a992ce7ce093d2ba3b731ed29243b2ece8a94"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:14:13.769128Z","signature_b64":"RO9krR8OkyBuDUSrK3vdXLmj9tj8+dYUibn6xgBSo8doZ9jUYDw5ehbPENagVuiLRBat1w1cP633VHXkTVE7AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0341a3e7ffc4fb881c30745c8cc18993f282660ca5f27a7eb232f6ab7441d6de","last_reissued_at":"2026-07-05T01:14:13.768745Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:14:13.768745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On resonances generated by conic diffraction","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP"],"primary_cat":"math.AP","authors_text":"Jared Wunsch, Luc Hillairet","submitted_at":"2017-06-23T21:20:50Z","abstract_excerpt":"We describe the resonances closest to the real axis generated by diffraction of waves among cone points on a manifold with Euclidean ends. These resonances lie asymptotically evenly spaced along a curve of the form $$\\frac{\\Im \\lambda}{\\log \\left |\\Re\n  \\lambda\\right |}= -\\nu;$$ here $\\nu=(n-1)/2 L_0$ where $n$ is the dimension and $L_0$ is the length of the longest geodesic connecting two cone points. Moreover there are asymptotically no resonances below this curve and above the curve $$ \\frac{\\Im \\lambda}{\\log \\left |\\Re\n  \\lambda\\right |}= -\\Lambda $$ for a fixed $\\Lambda>\\nu.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07869","kind":"arxiv","version":5},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1706.07869/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1706.07869","created_at":"2026-07-05T01:14:13.768805+00:00"},{"alias_kind":"arxiv_version","alias_value":"1706.07869v5","created_at":"2026-07-05T01:14:13.768805+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07869","created_at":"2026-07-05T01:14:13.768805+00:00"},{"alias_kind":"pith_short_12","alias_value":"ANA2HZ77YT5Y","created_at":"2026-07-05T01:14:13.768805+00:00"},{"alias_kind":"pith_short_16","alias_value":"ANA2HZ77YT5YQHBQ","created_at":"2026-07-05T01:14:13.768805+00:00"},{"alias_kind":"pith_short_8","alias_value":"ANA2HZ77","created_at":"2026-07-05T01:14:13.768805+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.06949","citing_title":"Riemann moduli spaces are quantum ergodic","ref_index":9,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ANA2HZ77YT5YQHBQOROIZQMJSP","json":"https://pith.science/pith/ANA2HZ77YT5YQHBQOROIZQMJSP.json","graph_json":"https://pith.science/api/pith-number/ANA2HZ77YT5YQHBQOROIZQMJSP/graph.json","events_json":"https://pith.science/api/pith-number/ANA2HZ77YT5YQHBQOROIZQMJSP/events.json","paper":"https://pith.science/paper/ANA2HZ77"},"agent_actions":{"view_html":"https://pith.science/pith/ANA2HZ77YT5YQHBQOROIZQMJSP","download_json":"https://pith.science/pith/ANA2HZ77YT5YQHBQOROIZQMJSP.json","view_paper":"https://pith.science/paper/ANA2HZ77","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1706.07869&json=true","fetch_graph":"https://pith.science/api/pith-number/ANA2HZ77YT5YQHBQOROIZQMJSP/graph.json","fetch_events":"https://pith.science/api/pith-number/ANA2HZ77YT5YQHBQOROIZQMJSP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ANA2HZ77YT5YQHBQOROIZQMJSP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ANA2HZ77YT5YQHBQOROIZQMJSP/action/storage_attestation","attest_author":"https://pith.science/pith/ANA2HZ77YT5YQHBQOROIZQMJSP/action/author_attestation","sign_citation":"https://pith.science/pith/ANA2HZ77YT5YQHBQOROIZQMJSP/action/citation_signature","submit_replication":"https://pith.science/pith/ANA2HZ77YT5YQHBQOROIZQMJSP/action/replication_record"}},"created_at":"2026-07-05T01:14:13.768805+00:00","updated_at":"2026-07-05T01:14:13.768805+00:00"}