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Let $\\Delta$ be the positive Laplacian associated to $g$, and $P = \\Delta + V$, where $V$ is a potential function obeying certain conditions. We analyze the asymptotics of the spectral measure $dE(\\lambda) = (\\lambda/\\pi i) \\big(R(\\lambda+i0) - R(\\lambda - i0) \\big)$ of $P_+^{1/2}$, where $R(\\lambda) = (P - \\lambda^2)^{-1}$, as $\\lambda \\to 0$, in a mann"},"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":"1009.3084","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-09-16T03:24:27Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"4aa23281318b27ba61e3f7acfcf635ac7bd5aac609568b243ccd240b44b39af0","abstract_canon_sha256":"b37eefacf1d9a6ad3423b218ecac36f896e204d9e90bc98bfd7b14813a5f9339"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:36.480658Z","signature_b64":"sM9rbLfP7rpVfTI6u+lLbXkQTENgfjC79xUjnaPHO2/nVIwl15K6jc875tIaOlox0LXZJAIYcmoK7T/NvZe/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13948f2b6b1275404c22af7fe76d1863ac56fe8d31342d0545b19b06a72d6aa4","last_reissued_at":"2026-05-18T03:56:36.479913Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:36.479913Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resolvent at low energy III: the spectral measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Adam Sikora, Andrew Hassell, Colin Guillarmou","submitted_at":"2010-09-16T03:24:27Z","abstract_excerpt":"Let $M^\\circ$ be a complete noncompact manifold and $g$ an asymptotically conic Riemaniann metric on $M^\\circ$, in the sense that $M^\\circ$ compactifies to a manifold with boundary $M$ in such a way that $g$ becomes a scattering metric on $M$. Let $\\Delta$ be the positive Laplacian associated to $g$, and $P = \\Delta + V$, where $V$ is a potential function obeying certain conditions. We analyze the asymptotics of the spectral measure $dE(\\lambda) = (\\lambda/\\pi i) \\big(R(\\lambda+i0) - R(\\lambda - i0) \\big)$ of $P_+^{1/2}$, where $R(\\lambda) = (P - \\lambda^2)^{-1}$, as $\\lambda \\to 0$, in a mann"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.3084","kind":"arxiv","version":2},"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":"1009.3084","created_at":"2026-05-18T03:56:36.480026+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.3084v2","created_at":"2026-05-18T03:56:36.480026+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.3084","created_at":"2026-05-18T03:56:36.480026+00:00"},{"alias_kind":"pith_short_12","alias_value":"COKI6K3LCJ2U","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_16","alias_value":"COKI6K3LCJ2UATBC","created_at":"2026-05-18T12:26:06.534383+00:00"},{"alias_kind":"pith_short_8","alias_value":"COKI6K3L","created_at":"2026-05-18T12:26:06.534383+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/COKI6K3LCJ2UATBCV576O3IYMO","json":"https://pith.science/pith/COKI6K3LCJ2UATBCV576O3IYMO.json","graph_json":"https://pith.science/api/pith-number/COKI6K3LCJ2UATBCV576O3IYMO/graph.json","events_json":"https://pith.science/api/pith-number/COKI6K3LCJ2UATBCV576O3IYMO/events.json","paper":"https://pith.science/paper/COKI6K3L"},"agent_actions":{"view_html":"https://pith.science/pith/COKI6K3LCJ2UATBCV576O3IYMO","download_json":"https://pith.science/pith/COKI6K3LCJ2UATBCV576O3IYMO.json","view_paper":"https://pith.science/paper/COKI6K3L","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.3084&json=true","fetch_graph":"https://pith.science/api/pith-number/COKI6K3LCJ2UATBCV576O3IYMO/graph.json","fetch_events":"https://pith.science/api/pith-number/COKI6K3LCJ2UATBCV576O3IYMO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/COKI6K3LCJ2UATBCV576O3IYMO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/COKI6K3LCJ2UATBCV576O3IYMO/action/storage_attestation","attest_author":"https://pith.science/pith/COKI6K3LCJ2UATBCV576O3IYMO/action/author_attestation","sign_citation":"https://pith.science/pith/COKI6K3LCJ2UATBCV576O3IYMO/action/citation_signature","submit_replication":"https://pith.science/pith/COKI6K3LCJ2UATBCV576O3IYMO/action/replication_record"}},"created_at":"2026-05-18T03:56:36.480026+00:00","updated_at":"2026-05-18T03:56:36.480026+00:00"}