{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:E3XLOXDN4ITSDBGCQCN7CKFE2L","short_pith_number":"pith:E3XLOXDN","canonical_record":{"source":{"id":"1512.04137","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-13T23:31:03Z","cross_cats_sorted":[],"title_canon_sha256":"c8986f5fca74e20088f3fda5c4f78efb4c4634fe85f576bbed7a56c6543967bd","abstract_canon_sha256":"c671f59fa6528ffd1cf2d082fb012b1be3e437954dde7336f3173046c50e8bef"},"schema_version":"1.0"},"canonical_sha256":"26eeb75c6de2272184c2809bf128a4d2c472fff293489c91a84609e3c0f0acdd","source":{"kind":"arxiv","id":"1512.04137","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04137","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04137v3","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04137","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"E3XLOXDN4ITS","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E3XLOXDN4ITSDBGC","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E3XLOXDN","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:E3XLOXDN4ITSDBGCQCN7CKFE2L","target":"record","payload":{"canonical_record":{"source":{"id":"1512.04137","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-13T23:31:03Z","cross_cats_sorted":[],"title_canon_sha256":"c8986f5fca74e20088f3fda5c4f78efb4c4634fe85f576bbed7a56c6543967bd","abstract_canon_sha256":"c671f59fa6528ffd1cf2d082fb012b1be3e437954dde7336f3173046c50e8bef"},"schema_version":"1.0"},"canonical_sha256":"26eeb75c6de2272184c2809bf128a4d2c472fff293489c91a84609e3c0f0acdd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:56.655018Z","signature_b64":"1pmpF/d93SWTi0aHIfbpsPZxccHJW/nI6Qw+Me7gwDK0OoDynsbeiguSxhSnfzuYV/SEy/qG0AekRjUJcLUcCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"26eeb75c6de2272184c2809bf128a4d2c472fff293489c91a84609e3c0f0acdd","last_reissued_at":"2026-05-18T01:02:56.654360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:56.654360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.04137","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"it8pmAEOLubBzeWfFNXTpjykzbzDlPQ7sBy58GuxPPr4yQaz84551rXexjDA+FeVApm1gmvPSXNQsoxKhIaRDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:47:02.981730Z"},"content_sha256":"8553cd82a72f2fb5afe95bffa1af3bd93b2b95071895bc21b016150d4a934daa","schema_version":"1.0","event_id":"sha256:8553cd82a72f2fb5afe95bffa1af3bd93b2b95071895bc21b016150d4a934daa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:E3XLOXDN4ITSDBGCQCN7CKFE2L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$\\Omega$-results for the hyperbolic lattice point problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Dimitrios Chatzakos","submitted_at":"2015-12-13T23:31:03Z","abstract_excerpt":"For $\\Gamma$ a cocompact or cofinite Fuchsian group, we study the lattice point problem on the Riemann surface $\\Gamma\\backslash\\mathbb{H}$. The main asymptotic for the counting of the orbit $\\Gamma z$ inside a circle of radius $r$ centered at $z$ grows like $c e^r$. Phillips and Rudnick studied $\\Omega$-results for the error term and mean results in $r$ for the normalized error term. We investigate the normalized error term in the natural parameter $X=2 \\cosh r$ and prove $\\Omega_{\\pm}$-results for the orbit $\\Gamma w$ and circle centered at $z$, even for $z \\neq w$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04137","kind":"arxiv","version":3},"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":"2026-05-18T01:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"trQnqSKPSKttOyStTv2ibasY3deMYIbxOtgYgxxKvS1LXKE6ufYMqKGUiQA1ohERUgpkDUAZKUBgE4nfNwtRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T23:47:02.982079Z"},"content_sha256":"84af3b13c0d919b53696b887aedb6467b06960dd64a09e3f86e95db50b383ecc","schema_version":"1.0","event_id":"sha256:84af3b13c0d919b53696b887aedb6467b06960dd64a09e3f86e95db50b383ecc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E3XLOXDN4ITSDBGCQCN7CKFE2L/bundle.json","state_url":"https://pith.science/pith/E3XLOXDN4ITSDBGCQCN7CKFE2L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E3XLOXDN4ITSDBGCQCN7CKFE2L/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":"2026-06-21T23:47:02Z","links":{"resolver":"https://pith.science/pith/E3XLOXDN4ITSDBGCQCN7CKFE2L","bundle":"https://pith.science/pith/E3XLOXDN4ITSDBGCQCN7CKFE2L/bundle.json","state":"https://pith.science/pith/E3XLOXDN4ITSDBGCQCN7CKFE2L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E3XLOXDN4ITSDBGCQCN7CKFE2L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:E3XLOXDN4ITSDBGCQCN7CKFE2L","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":"c671f59fa6528ffd1cf2d082fb012b1be3e437954dde7336f3173046c50e8bef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-13T23:31:03Z","title_canon_sha256":"c8986f5fca74e20088f3fda5c4f78efb4c4634fe85f576bbed7a56c6543967bd"},"schema_version":"1.0","source":{"id":"1512.04137","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04137","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04137v3","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04137","created_at":"2026-05-18T01:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"E3XLOXDN4ITS","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"E3XLOXDN4ITSDBGC","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"E3XLOXDN","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:84af3b13c0d919b53696b887aedb6467b06960dd64a09e3f86e95db50b383ecc","target":"graph","created_at":"2026-05-18T01:02:56Z","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":"For $\\Gamma$ a cocompact or cofinite Fuchsian group, we study the lattice point problem on the Riemann surface $\\Gamma\\backslash\\mathbb{H}$. The main asymptotic for the counting of the orbit $\\Gamma z$ inside a circle of radius $r$ centered at $z$ grows like $c e^r$. Phillips and Rudnick studied $\\Omega$-results for the error term and mean results in $r$ for the normalized error term. We investigate the normalized error term in the natural parameter $X=2 \\cosh r$ and prove $\\Omega_{\\pm}$-results for the orbit $\\Gamma w$ and circle centered at $z$, even for $z \\neq w$.","authors_text":"Dimitrios Chatzakos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-13T23:31:03Z","title":"$\\Omega$-results for the hyperbolic lattice point problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04137","kind":"arxiv","version":3},"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":"sha256:8553cd82a72f2fb5afe95bffa1af3bd93b2b95071895bc21b016150d4a934daa","target":"record","created_at":"2026-05-18T01:02:56Z","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":"c671f59fa6528ffd1cf2d082fb012b1be3e437954dde7336f3173046c50e8bef","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-12-13T23:31:03Z","title_canon_sha256":"c8986f5fca74e20088f3fda5c4f78efb4c4634fe85f576bbed7a56c6543967bd"},"schema_version":"1.0","source":{"id":"1512.04137","kind":"arxiv","version":3}},"canonical_sha256":"26eeb75c6de2272184c2809bf128a4d2c472fff293489c91a84609e3c0f0acdd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26eeb75c6de2272184c2809bf128a4d2c472fff293489c91a84609e3c0f0acdd","first_computed_at":"2026-05-18T01:02:56.654360Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:02:56.654360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1pmpF/d93SWTi0aHIfbpsPZxccHJW/nI6Qw+Me7gwDK0OoDynsbeiguSxhSnfzuYV/SEy/qG0AekRjUJcLUcCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:02:56.655018Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04137","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8553cd82a72f2fb5afe95bffa1af3bd93b2b95071895bc21b016150d4a934daa","sha256:84af3b13c0d919b53696b887aedb6467b06960dd64a09e3f86e95db50b383ecc"],"state_sha256":"b583a95856048db0ea0eb4ee9ba16898db7566f1a11cf5237155e8db5f2de34d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+MTuogEEHbS30FomDjmihVX7LBGY/IP2eUshpL/Um8OayTxxdquahbj4wBq2+gJY/b9DiY5nCkM3NbILSxwVAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T23:47:02.984027Z","bundle_sha256":"14ad808a02f787c0975f0bb5cc6e87839b5cee8435d06ac8be187a8802579b98"}}