{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:LGRXYWRSMJL32L6T6RMASY3HDQ","short_pith_number":"pith:LGRXYWRS","canonical_record":{"source":{"id":"2506.17753","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-21T16:17:50Z","cross_cats_sorted":[],"title_canon_sha256":"17a525f477c958206cbee83e3f78cbbc0f16ffbd663a8ff22b7760f21d866663","abstract_canon_sha256":"e9135a800cec25a49b1a9240e2c4aa55d1ec84716e6cebae6a8263c81889f461"},"schema_version":"1.0"},"canonical_sha256":"59a37c5a326257bd2fd3f4580963671c32d6000b7b1a634cd7b10f34d004550d","source":{"kind":"arxiv","id":"2506.17753","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.17753","created_at":"2026-07-05T11:25:22Z"},{"alias_kind":"arxiv_version","alias_value":"2506.17753v1","created_at":"2026-07-05T11:25:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.17753","created_at":"2026-07-05T11:25:22Z"},{"alias_kind":"pith_short_12","alias_value":"LGRXYWRSMJL3","created_at":"2026-07-05T11:25:22Z"},{"alias_kind":"pith_short_16","alias_value":"LGRXYWRSMJL32L6T","created_at":"2026-07-05T11:25:22Z"},{"alias_kind":"pith_short_8","alias_value":"LGRXYWRS","created_at":"2026-07-05T11:25:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:LGRXYWRSMJL32L6T6RMASY3HDQ","target":"record","payload":{"canonical_record":{"source":{"id":"2506.17753","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-21T16:17:50Z","cross_cats_sorted":[],"title_canon_sha256":"17a525f477c958206cbee83e3f78cbbc0f16ffbd663a8ff22b7760f21d866663","abstract_canon_sha256":"e9135a800cec25a49b1a9240e2c4aa55d1ec84716e6cebae6a8263c81889f461"},"schema_version":"1.0"},"canonical_sha256":"59a37c5a326257bd2fd3f4580963671c32d6000b7b1a634cd7b10f34d004550d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:25:22.783616Z","signature_b64":"UaK7g5iSK0tRw5GesFj0PG6eb1rUXr01QcPN2lmF2/cHf91G8f/Mgt90NOaJ4q8f81biuajGW4kIWFQ5ity2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"59a37c5a326257bd2fd3f4580963671c32d6000b7b1a634cd7b10f34d004550d","last_reissued_at":"2026-07-05T11:25:22.783246Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:25:22.783246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.17753","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:25:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W4lC/jxNiwJhnuGhvrAKt0QMRVcunvBCt2u6uUK50UoFaG62PtY/xkz5jELhmiMK6OzfJdRhIH9B3xSB4oCOBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T11:54:29.629027Z"},"content_sha256":"a58a1107c0c24953f1a6eb6d53888eb34fe31b9a50f27fcafcaef662714492b0","schema_version":"1.0","event_id":"sha256:a58a1107c0c24953f1a6eb6d53888eb34fe31b9a50f27fcafcaef662714492b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:LGRXYWRSMJL32L6T6RMASY3HDQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The hyperbolic lattice counting problem in large dimensions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Christos Katsivelos","submitted_at":"2025-06-21T16:17:50Z","abstract_excerpt":"For $n\\geq 3$ and $\\Gamma$ a cocompact lattice acting on the hyperbolic space $\\mathbb{H}^n$, we investigate the average behaviour of the error term in the circle problem. First, we explore the local average of the error term over compact sets of $\\Gamma\\backslash\\mathbb{H}^n$. Our upper bound depends on the quantum variance and the spectral exponential sums appearing in the study of the Prime geodesic theorem. We also prove $\\Omega$-results for the mean value and the second moment of the error term."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17753","kind":"arxiv","version":1},"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/2506.17753/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":"2026-07-05T11:25:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JjfxO0kEfFC5pNsH0gpnRLfzi1YhyO4S1DP86lNlROObgBEXaxtSuBBti6QSmJ78t9kT27ZMW/qJMiMeHwBeCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T11:54:29.629591Z"},"content_sha256":"b756d6065c840015cc2f447b93a340748a917b5df61aca773c7bc5f526463d3c","schema_version":"1.0","event_id":"sha256:b756d6065c840015cc2f447b93a340748a917b5df61aca773c7bc5f526463d3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LGRXYWRSMJL32L6T6RMASY3HDQ/bundle.json","state_url":"https://pith.science/pith/LGRXYWRSMJL32L6T6RMASY3HDQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LGRXYWRSMJL32L6T6RMASY3HDQ/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":"2026-08-21T11:54:29Z","links":{"resolver":"https://pith.science/pith/LGRXYWRSMJL32L6T6RMASY3HDQ","bundle":"https://pith.science/pith/LGRXYWRSMJL32L6T6RMASY3HDQ/bundle.json","state":"https://pith.science/pith/LGRXYWRSMJL32L6T6RMASY3HDQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LGRXYWRSMJL32L6T6RMASY3HDQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:LGRXYWRSMJL32L6T6RMASY3HDQ","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":"e9135a800cec25a49b1a9240e2c4aa55d1ec84716e6cebae6a8263c81889f461","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-21T16:17:50Z","title_canon_sha256":"17a525f477c958206cbee83e3f78cbbc0f16ffbd663a8ff22b7760f21d866663"},"schema_version":"1.0","source":{"id":"2506.17753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.17753","created_at":"2026-07-05T11:25:22Z"},{"alias_kind":"arxiv_version","alias_value":"2506.17753v1","created_at":"2026-07-05T11:25:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.17753","created_at":"2026-07-05T11:25:22Z"},{"alias_kind":"pith_short_12","alias_value":"LGRXYWRSMJL3","created_at":"2026-07-05T11:25:22Z"},{"alias_kind":"pith_short_16","alias_value":"LGRXYWRSMJL32L6T","created_at":"2026-07-05T11:25:22Z"},{"alias_kind":"pith_short_8","alias_value":"LGRXYWRS","created_at":"2026-07-05T11:25:22Z"}],"graph_snapshots":[{"event_id":"sha256:b756d6065c840015cc2f447b93a340748a917b5df61aca773c7bc5f526463d3c","target":"graph","created_at":"2026-07-05T11:25:22Z","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/2506.17753/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For $n\\geq 3$ and $\\Gamma$ a cocompact lattice acting on the hyperbolic space $\\mathbb{H}^n$, we investigate the average behaviour of the error term in the circle problem. First, we explore the local average of the error term over compact sets of $\\Gamma\\backslash\\mathbb{H}^n$. Our upper bound depends on the quantum variance and the spectral exponential sums appearing in the study of the Prime geodesic theorem. We also prove $\\Omega$-results for the mean value and the second moment of the error term.","authors_text":"Christos Katsivelos","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-21T16:17:50Z","title":"The hyperbolic lattice counting problem in large dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17753","kind":"arxiv","version":1},"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:a58a1107c0c24953f1a6eb6d53888eb34fe31b9a50f27fcafcaef662714492b0","target":"record","created_at":"2026-07-05T11:25:22Z","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":"e9135a800cec25a49b1a9240e2c4aa55d1ec84716e6cebae6a8263c81889f461","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NT","submitted_at":"2025-06-21T16:17:50Z","title_canon_sha256":"17a525f477c958206cbee83e3f78cbbc0f16ffbd663a8ff22b7760f21d866663"},"schema_version":"1.0","source":{"id":"2506.17753","kind":"arxiv","version":1}},"canonical_sha256":"59a37c5a326257bd2fd3f4580963671c32d6000b7b1a634cd7b10f34d004550d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"59a37c5a326257bd2fd3f4580963671c32d6000b7b1a634cd7b10f34d004550d","first_computed_at":"2026-07-05T11:25:22.783246Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:25:22.783246Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UaK7g5iSK0tRw5GesFj0PG6eb1rUXr01QcPN2lmF2/cHf91G8f/Mgt90NOaJ4q8f81biuajGW4kIWFQ5ity2Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:25:22.783616Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.17753","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a58a1107c0c24953f1a6eb6d53888eb34fe31b9a50f27fcafcaef662714492b0","sha256:b756d6065c840015cc2f447b93a340748a917b5df61aca773c7bc5f526463d3c"],"state_sha256":"9c11f602f63bb60ecf4daa6ef02a4de3e7db539558348baa1093eadf615ecc5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2bc36nBdHMFU8Ow2erhWC6iw7NUsllpXDBEJkN63/wcyyAyoT5Y6A2Z5Sr/PUVhSsLZdwkOk0zeQJ6EdNtLJCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T11:54:29.633320Z","bundle_sha256":"3040f3e7ae54f0dc98b4fdf62e5d51436845790cb1a113c77a70d23a79e2774d"}}