{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:VSJB5LPPTUM2QETEG5HUBQKYEN","short_pith_number":"pith:VSJB5LPP","canonical_record":{"source":{"id":"0712.1391","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2007-12-10T03:58:37Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"4f165cf91df2f54e210d0e450fc68ea12434d196d0fb6a2383c1d846f35be190","abstract_canon_sha256":"cbb07e6e9de3c20115cff791988b33bbebafcf5ce2c457c1286768cd409296f6"},"schema_version":"1.0"},"canonical_sha256":"ac921eadef9d19a81264374f40c158237f26184af360f9541125d07232320fed","source":{"kind":"arxiv","id":"0712.1391","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1391","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1391v2","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1391","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"pith_short_12","alias_value":"VSJB5LPPTUM2","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"VSJB5LPPTUM2QETE","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"VSJB5LPP","created_at":"2026-07-05T00:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:VSJB5LPPTUM2QETEG5HUBQKYEN","target":"record","payload":{"canonical_record":{"source":{"id":"0712.1391","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2007-12-10T03:58:37Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"4f165cf91df2f54e210d0e450fc68ea12434d196d0fb6a2383c1d846f35be190","abstract_canon_sha256":"cbb07e6e9de3c20115cff791988b33bbebafcf5ce2c457c1286768cd409296f6"},"schema_version":"1.0"},"canonical_sha256":"ac921eadef9d19a81264374f40c158237f26184af360f9541125d07232320fed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:26:50.250481Z","signature_b64":"RUZ06jOlI2fmE4EksniUnwDgS0OemPnO+RPIq4FtdYiZ6cNxP0AFzGJX1XAjz3suX7JigtK7mJWjl0QeJYhnDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac921eadef9d19a81264374f40c158237f26184af360f9541125d07232320fed","last_reissued_at":"2026-07-05T00:26:50.250102Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:26:50.250102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0712.1391","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":"2026-07-05T00:26:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I0sTe6Z1zo4L4ru/51pWvoVZGG5ZJWqH20NrdM+KBlv80GZNZZdzm/WM4zhVE7vGj5TiL25I6H9OJnumr17WCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T16:31:13.274868Z"},"content_sha256":"51e896c9a8083ea57d5980dec09d35096d5233d6bc41bd668b883845e976edb1","schema_version":"1.0","event_id":"sha256:51e896c9a8083ea57d5980dec09d35096d5233d6bc41bd668b883845e976edb1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:VSJB5LPPTUM2QETEG5HUBQKYEN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Hyperbolic Lattice Point Count in Infinite Volume with Applications to Sieves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.NT","authors_text":"Alex V. Kontorovich","submitted_at":"2007-12-10T03:58:37Z","abstract_excerpt":"We develop novel techniques using abstract operator theory to obtain asymptotic formulae for lattice counting problems on infinite-volume hyperbolic manifolds, with error terms which are uniform as the lattice moves through \"congruence\" subgroups.\n  We give the following application to the theory of affine linear sieves. In the spirit of Fermat, consider the problem of primes in the sum of two squares, f(c,d)=c^2+d^2, but restrict (c,d) to the orbit O = (0,1).Gamma, where Gamma is an infinite-index non-elementary finitely-generated subgroup of SL(2,Z). Assume that the Reimann surface Gamma\\H^2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1391","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0712.1391/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:26:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PpG0HYA7bB6PQqMr/0u97usg0v7EHjTTtt8g4LPF4FoAOKZrSGZo22phEI5KlHD6KRYhCR/6aFOXg1wuA8agCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T16:31:13.275437Z"},"content_sha256":"4aeffb9d35be62ffaaa381b199fe74bb3ee351e888a903b6f6d7c627bff34e3b","schema_version":"1.0","event_id":"sha256:4aeffb9d35be62ffaaa381b199fe74bb3ee351e888a903b6f6d7c627bff34e3b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VSJB5LPPTUM2QETEG5HUBQKYEN/bundle.json","state_url":"https://pith.science/pith/VSJB5LPPTUM2QETEG5HUBQKYEN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VSJB5LPPTUM2QETEG5HUBQKYEN/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":"2026-08-15T16:31:13Z","links":{"resolver":"https://pith.science/pith/VSJB5LPPTUM2QETEG5HUBQKYEN","bundle":"https://pith.science/pith/VSJB5LPPTUM2QETEG5HUBQKYEN/bundle.json","state":"https://pith.science/pith/VSJB5LPPTUM2QETEG5HUBQKYEN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VSJB5LPPTUM2QETEG5HUBQKYEN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:VSJB5LPPTUM2QETEG5HUBQKYEN","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":"cbb07e6e9de3c20115cff791988b33bbebafcf5ce2c457c1286768cd409296f6","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2007-12-10T03:58:37Z","title_canon_sha256":"4f165cf91df2f54e210d0e450fc68ea12434d196d0fb6a2383c1d846f35be190"},"schema_version":"1.0","source":{"id":"0712.1391","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0712.1391","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"arxiv_version","alias_value":"0712.1391v2","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0712.1391","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"pith_short_12","alias_value":"VSJB5LPPTUM2","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"VSJB5LPPTUM2QETE","created_at":"2026-07-05T00:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"VSJB5LPP","created_at":"2026-07-05T00:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:4aeffb9d35be62ffaaa381b199fe74bb3ee351e888a903b6f6d7c627bff34e3b","target":"graph","created_at":"2026-07-05T00:26:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0712.1391/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop novel techniques using abstract operator theory to obtain asymptotic formulae for lattice counting problems on infinite-volume hyperbolic manifolds, with error terms which are uniform as the lattice moves through \"congruence\" subgroups.\n  We give the following application to the theory of affine linear sieves. In the spirit of Fermat, consider the problem of primes in the sum of two squares, f(c,d)=c^2+d^2, but restrict (c,d) to the orbit O = (0,1).Gamma, where Gamma is an infinite-index non-elementary finitely-generated subgroup of SL(2,Z). Assume that the Reimann surface Gamma\\H^2","authors_text":"Alex V. Kontorovich","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2007-12-10T03:58:37Z","title":"The Hyperbolic Lattice Point Count in Infinite Volume with Applications to Sieves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1391","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":"sha256:51e896c9a8083ea57d5980dec09d35096d5233d6bc41bd668b883845e976edb1","target":"record","created_at":"2026-07-05T00:26:50Z","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":"cbb07e6e9de3c20115cff791988b33bbebafcf5ce2c457c1286768cd409296f6","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2007-12-10T03:58:37Z","title_canon_sha256":"4f165cf91df2f54e210d0e450fc68ea12434d196d0fb6a2383c1d846f35be190"},"schema_version":"1.0","source":{"id":"0712.1391","kind":"arxiv","version":2}},"canonical_sha256":"ac921eadef9d19a81264374f40c158237f26184af360f9541125d07232320fed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac921eadef9d19a81264374f40c158237f26184af360f9541125d07232320fed","first_computed_at":"2026-07-05T00:26:50.250102Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:26:50.250102Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RUZ06jOlI2fmE4EksniUnwDgS0OemPnO+RPIq4FtdYiZ6cNxP0AFzGJX1XAjz3suX7JigtK7mJWjl0QeJYhnDw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:26:50.250481Z","signed_message":"canonical_sha256_bytes"},"source_id":"0712.1391","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:51e896c9a8083ea57d5980dec09d35096d5233d6bc41bd668b883845e976edb1","sha256:4aeffb9d35be62ffaaa381b199fe74bb3ee351e888a903b6f6d7c627bff34e3b"],"state_sha256":"c9e1105a0f53da43b06719c75081890689e406a84de007f007633ae5108911dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dPymrkuaywNF9ZAw1TYJpH9kfsyaNK/oBhi4J2Xc0llRaZ54j7YfBcxv9Xq/Ftiowu1AqhtwgQnbq1bVF9EeBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T16:31:13.279353Z","bundle_sha256":"67b0dca7cc8275af9dbf4c277d375ec0e868b02e94dfa0606f59f3c59225d0fb"}}