{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:IE4W2A4LU5MMEPXH5CJV3ZTDTH","short_pith_number":"pith:IE4W2A4L","canonical_record":{"source":{"id":"1109.1995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-09T13:05:28Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"dc9d8d32a63ff56cc4f5810591f45072a65e0ca64d47685cc76c0cee9ea020d6","abstract_canon_sha256":"0f96ef91f49ace277fe3b39c37b649533fbc25f2a36bb0d0872c40f91576f65b"},"schema_version":"1.0"},"canonical_sha256":"41396d038ba758c23ee7e8935de66399c0f64532859e7f60082f228f70b233ef","source":{"kind":"arxiv","id":"1109.1995","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1995","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1995v2","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1995","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"pith_short_12","alias_value":"IE4W2A4LU5MM","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IE4W2A4LU5MMEPXH","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IE4W2A4L","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:IE4W2A4LU5MMEPXH5CJV3ZTDTH","target":"record","payload":{"canonical_record":{"source":{"id":"1109.1995","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-09T13:05:28Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"dc9d8d32a63ff56cc4f5810591f45072a65e0ca64d47685cc76c0cee9ea020d6","abstract_canon_sha256":"0f96ef91f49ace277fe3b39c37b649533fbc25f2a36bb0d0872c40f91576f65b"},"schema_version":"1.0"},"canonical_sha256":"41396d038ba758c23ee7e8935de66399c0f64532859e7f60082f228f70b233ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:39:05.389598Z","signature_b64":"rgEoMZCZFZEHESgLa9l9TK0q/IcfshU+f9KB8W4mo6cS7MtxMhipl4OdaeaWAzkoShh9WrTIyUGe6AsZAZk2BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41396d038ba758c23ee7e8935de66399c0f64532859e7f60082f228f70b233ef","last_reissued_at":"2026-05-18T03:39:05.389114Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:39:05.389114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.1995","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bSwOnys0ReCZ222JeKjF0Pr9uBhuK51Lvj0osOR9OjCQjl4uYj4wSjbJZdyOVbVb0KAQLXkMDIqgSwlOBfFiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:48:05.432291Z"},"content_sha256":"e5bb9eb444f8b4cf40fa2c65921a768e67fd2197888b0c0d56fede18e7102dbb","schema_version":"1.0","event_id":"sha256:e5bb9eb444f8b4cf40fa2c65921a768e67fd2197888b0c0d56fede18e7102dbb"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:IE4W2A4LU5MMEPXH5CJV3ZTDTH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Counting function of the embedded eigenvalues for some manifold with cusps, and magnetic Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Abderemane Morame (LMJL), Francoise Truc (IF)","submitted_at":"2011-09-09T13:05:28Z","abstract_excerpt":"We consider a non compact, complete manifold {\\bf{M}} of finite area with cuspidal ends. The generic cusp is isomorphic to ${\\bf{X}}\\times ]1,+\\infty [$ with metric $ds^2=(h+dy^2)/y^{2\\delta}.$ {\\bf{X}} is a compact manifold with nonzero first Betti number equipped with the metric $h.$ For a one-form $A$ on {\\bf{M}} such that in each cusp $A$ is a non exact one-form on the boundary at infinity, we prove that the magnetic Laplacian $-\\Delta_A=(id+A)^\\star (id+A)$ satisfies the Weyl asymptotic formula with sharp remainder. We deduce an upper bound for the counting function of the embedded eigenv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1995","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:39:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oyU4o6oAGGDxdRrV2maaPiH5y5C87PPt175b7UL9LXrgxo4ZTBg+sviao7jphERVwYWe8xbDfEE4n4MLbcTLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T04:48:05.432659Z"},"content_sha256":"3011151f5d2e0969ff68a36e45aa760a4c2b1a057b4e1863e6abef06629b0de5","schema_version":"1.0","event_id":"sha256:3011151f5d2e0969ff68a36e45aa760a4c2b1a057b4e1863e6abef06629b0de5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IE4W2A4LU5MMEPXH5CJV3ZTDTH/bundle.json","state_url":"https://pith.science/pith/IE4W2A4LU5MMEPXH5CJV3ZTDTH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IE4W2A4LU5MMEPXH5CJV3ZTDTH/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-03T04:48:05Z","links":{"resolver":"https://pith.science/pith/IE4W2A4LU5MMEPXH5CJV3ZTDTH","bundle":"https://pith.science/pith/IE4W2A4LU5MMEPXH5CJV3ZTDTH/bundle.json","state":"https://pith.science/pith/IE4W2A4LU5MMEPXH5CJV3ZTDTH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IE4W2A4LU5MMEPXH5CJV3ZTDTH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IE4W2A4LU5MMEPXH5CJV3ZTDTH","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":"0f96ef91f49ace277fe3b39c37b649533fbc25f2a36bb0d0872c40f91576f65b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-09T13:05:28Z","title_canon_sha256":"dc9d8d32a63ff56cc4f5810591f45072a65e0ca64d47685cc76c0cee9ea020d6"},"schema_version":"1.0","source":{"id":"1109.1995","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.1995","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"arxiv_version","alias_value":"1109.1995v2","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.1995","created_at":"2026-05-18T03:39:05Z"},{"alias_kind":"pith_short_12","alias_value":"IE4W2A4LU5MM","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IE4W2A4LU5MMEPXH","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IE4W2A4L","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:3011151f5d2e0969ff68a36e45aa760a4c2b1a057b4e1863e6abef06629b0de5","target":"graph","created_at":"2026-05-18T03:39:05Z","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":"We consider a non compact, complete manifold {\\bf{M}} of finite area with cuspidal ends. The generic cusp is isomorphic to ${\\bf{X}}\\times ]1,+\\infty [$ with metric $ds^2=(h+dy^2)/y^{2\\delta}.$ {\\bf{X}} is a compact manifold with nonzero first Betti number equipped with the metric $h.$ For a one-form $A$ on {\\bf{M}} such that in each cusp $A$ is a non exact one-form on the boundary at infinity, we prove that the magnetic Laplacian $-\\Delta_A=(id+A)^\\star (id+A)$ satisfies the Weyl asymptotic formula with sharp remainder. We deduce an upper bound for the counting function of the embedded eigenv","authors_text":"Abderemane Morame (LMJL), Francoise Truc (IF)","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-09T13:05:28Z","title":"Counting function of the embedded eigenvalues for some manifold with cusps, and magnetic Laplacian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.1995","kind":"arxiv","version":2},"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:e5bb9eb444f8b4cf40fa2c65921a768e67fd2197888b0c0d56fede18e7102dbb","target":"record","created_at":"2026-05-18T03:39:05Z","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":"0f96ef91f49ace277fe3b39c37b649533fbc25f2a36bb0d0872c40f91576f65b","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2011-09-09T13:05:28Z","title_canon_sha256":"dc9d8d32a63ff56cc4f5810591f45072a65e0ca64d47685cc76c0cee9ea020d6"},"schema_version":"1.0","source":{"id":"1109.1995","kind":"arxiv","version":2}},"canonical_sha256":"41396d038ba758c23ee7e8935de66399c0f64532859e7f60082f228f70b233ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41396d038ba758c23ee7e8935de66399c0f64532859e7f60082f228f70b233ef","first_computed_at":"2026-05-18T03:39:05.389114Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:05.389114Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rgEoMZCZFZEHESgLa9l9TK0q/IcfshU+f9KB8W4mo6cS7MtxMhipl4OdaeaWAzkoShh9WrTIyUGe6AsZAZk2BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:05.389598Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.1995","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e5bb9eb444f8b4cf40fa2c65921a768e67fd2197888b0c0d56fede18e7102dbb","sha256:3011151f5d2e0969ff68a36e45aa760a4c2b1a057b4e1863e6abef06629b0de5"],"state_sha256":"1df282b9c97ee40501b567f331ef95857fbf534f72c1330fe8ec8ec9a3dd1772"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"flShJqX8Fd214oE4QfDQa10kyilZbp/LRbzrvcTitupLCyM6RsIpYOmGCFcIpaFIBff8B3xbrhFc/Qek7GEWCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T04:48:05.434594Z","bundle_sha256":"62b5b7b8b194685c8ec305f40d0e26a19f89ddeba1ff33e20869b733d2ec6a88"}}