{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:7TUE6VFH4WMGMIANSFQXYRWUWK","short_pith_number":"pith:7TUE6VFH","canonical_record":{"source":{"id":"1303.7471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-29T19:47:44Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"2cce561b6e8c2f2eda9dd3fe0b7e45be7516a602e9df3ba7192936f53319a97e","abstract_canon_sha256":"29591565bc1f75f20233686122fca7488faab3ae9e719dc707f6eef74c1381c0"},"schema_version":"1.0"},"canonical_sha256":"fce84f54a7e59866200d91617c46d4b29053b37db6a725b16768894b7cf6f80d","source":{"kind":"arxiv","id":"1303.7471","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.7471","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"arxiv_version","alias_value":"1303.7471v2","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7471","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"pith_short_12","alias_value":"7TUE6VFH4WMG","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7TUE6VFH4WMGMIAN","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7TUE6VFH","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:7TUE6VFH4WMGMIANSFQXYRWUWK","target":"record","payload":{"canonical_record":{"source":{"id":"1303.7471","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-29T19:47:44Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"2cce561b6e8c2f2eda9dd3fe0b7e45be7516a602e9df3ba7192936f53319a97e","abstract_canon_sha256":"29591565bc1f75f20233686122fca7488faab3ae9e719dc707f6eef74c1381c0"},"schema_version":"1.0"},"canonical_sha256":"fce84f54a7e59866200d91617c46d4b29053b37db6a725b16768894b7cf6f80d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:44.389255Z","signature_b64":"STz22SszmWCt2cXkqI3NEiGEgtm63HTN22vyJPdUd1yA5pcBUPrUI+XX/RuqVkpaOTN26LtklM5kPABrEIYCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fce84f54a7e59866200d91617c46d4b29053b37db6a725b16768894b7cf6f80d","last_reissued_at":"2026-05-18T03:27:44.388823Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:44.388823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.7471","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":"2026-05-18T03:27:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0in5WeXYkA+hqFc3bqDYabPiupY0goQn7Oki+GfQ/6FsN1gZTQ1Gl4dDPYXTNqFGf+pbVsCL0d5qTwi6ACFeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:32:18.367417Z"},"content_sha256":"4aed36f6014b00e14707572e95159bd6fab507100dea1c5d2cfc71e1cc69460e","schema_version":"1.0","event_id":"sha256:4aed36f6014b00e14707572e95159bd6fab507100dea1c5d2cfc71e1cc69460e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:7TUE6VFH4WMGMIANSFQXYRWUWK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.SP","authors_text":"Colin Guillarmou, David Borthwick","submitted_at":"2013-03-29T19:47:44Z","abstract_excerpt":"On geometrically finite hyperbolic manifolds $\\Gamma\\backslash H^{d}$, including those with non-maximal rank cusps, we give upper bounds on the number $N(R)$ of resonances of the Laplacian in disks of size $R$ as $R\\to \\infty$. In particular, if the parabolic subgroups of $\\Gamma$ satisfy a certain Diophantine condition, the bound is $N(R)= O(R^d (\\log R)^{d+1})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7471","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":"2026-05-18T03:27:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PKHJpBuxQMAcHoAB7x97T1ws1Iq1Rprjuei0DncpxUQ//+l7w34JL6bd1WSYNvsNqWixFhbkQ585SjIYAvx4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:32:18.367768Z"},"content_sha256":"424bc9aa839bd75ab284116ab1e45b049f5fe71e8f2c80a4ac1d1554a58f381d","schema_version":"1.0","event_id":"sha256:424bc9aa839bd75ab284116ab1e45b049f5fe71e8f2c80a4ac1d1554a58f381d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7TUE6VFH4WMGMIANSFQXYRWUWK/bundle.json","state_url":"https://pith.science/pith/7TUE6VFH4WMGMIANSFQXYRWUWK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7TUE6VFH4WMGMIANSFQXYRWUWK/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":"2026-05-28T03:32:18Z","links":{"resolver":"https://pith.science/pith/7TUE6VFH4WMGMIANSFQXYRWUWK","bundle":"https://pith.science/pith/7TUE6VFH4WMGMIANSFQXYRWUWK/bundle.json","state":"https://pith.science/pith/7TUE6VFH4WMGMIANSFQXYRWUWK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7TUE6VFH4WMGMIANSFQXYRWUWK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:7TUE6VFH4WMGMIANSFQXYRWUWK","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":"29591565bc1f75f20233686122fca7488faab3ae9e719dc707f6eef74c1381c0","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-29T19:47:44Z","title_canon_sha256":"2cce561b6e8c2f2eda9dd3fe0b7e45be7516a602e9df3ba7192936f53319a97e"},"schema_version":"1.0","source":{"id":"1303.7471","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.7471","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"arxiv_version","alias_value":"1303.7471v2","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7471","created_at":"2026-05-18T03:27:44Z"},{"alias_kind":"pith_short_12","alias_value":"7TUE6VFH4WMG","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"7TUE6VFH4WMGMIAN","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"7TUE6VFH","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:424bc9aa839bd75ab284116ab1e45b049f5fe71e8f2c80a4ac1d1554a58f381d","target":"graph","created_at":"2026-05-18T03:27:44Z","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":"On geometrically finite hyperbolic manifolds $\\Gamma\\backslash H^{d}$, including those with non-maximal rank cusps, we give upper bounds on the number $N(R)$ of resonances of the Laplacian in disks of size $R$ as $R\\to \\infty$. In particular, if the parabolic subgroups of $\\Gamma$ satisfy a certain Diophantine condition, the bound is $N(R)= O(R^d (\\log R)^{d+1})$.","authors_text":"Colin Guillarmou, David Borthwick","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-29T19:47:44Z","title":"Upper bounds for the number of resonances on geometrically finite hyperbolic manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7471","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":"sha256:4aed36f6014b00e14707572e95159bd6fab507100dea1c5d2cfc71e1cc69460e","target":"record","created_at":"2026-05-18T03:27:44Z","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":"29591565bc1f75f20233686122fca7488faab3ae9e719dc707f6eef74c1381c0","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2013-03-29T19:47:44Z","title_canon_sha256":"2cce561b6e8c2f2eda9dd3fe0b7e45be7516a602e9df3ba7192936f53319a97e"},"schema_version":"1.0","source":{"id":"1303.7471","kind":"arxiv","version":2}},"canonical_sha256":"fce84f54a7e59866200d91617c46d4b29053b37db6a725b16768894b7cf6f80d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fce84f54a7e59866200d91617c46d4b29053b37db6a725b16768894b7cf6f80d","first_computed_at":"2026-05-18T03:27:44.388823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:44.388823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"STz22SszmWCt2cXkqI3NEiGEgtm63HTN22vyJPdUd1yA5pcBUPrUI+XX/RuqVkpaOTN26LtklM5kPABrEIYCDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:44.389255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.7471","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4aed36f6014b00e14707572e95159bd6fab507100dea1c5d2cfc71e1cc69460e","sha256:424bc9aa839bd75ab284116ab1e45b049f5fe71e8f2c80a4ac1d1554a58f381d"],"state_sha256":"045db34423d91ac870dcf03d9a515b981677205f2d225e0781462e46726eb8b5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xirttJn8fv90KNDZLKc/orCVIiIYhE267FkL3KdbC8TbKbKchgurVeuG1T9f/Vd5oaBNMIcT6xkz8BeNo6dLDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:32:18.369844Z","bundle_sha256":"d418519a5e17309deeb787cf00dfd873f57cc21bd320babb5932edc226dd88a2"}}