{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:RLT75ET6LS27UTS44L5WFEB7C3","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":"2a06880ddf08a3edbe4c33c3547d7147e548bb507662a4ebccbaa57c9e6ee0b7","cross_cats_sorted":["hep-th","math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-13T15:18:47Z","title_canon_sha256":"fb59e5844e4542a942b7fddc58f452f52fc78f193d36b927e9bd8e5c7255a54e"},"schema_version":"1.0","source":{"id":"1012.2754","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1012.2754","created_at":"2026-05-18T04:22:11Z"},{"alias_kind":"arxiv_version","alias_value":"1012.2754v3","created_at":"2026-05-18T04:22:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1012.2754","created_at":"2026-05-18T04:22:11Z"},{"alias_kind":"pith_short_12","alias_value":"RLT75ET6LS27","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_16","alias_value":"RLT75ET6LS27UTS4","created_at":"2026-05-18T12:26:13Z"},{"alias_kind":"pith_short_8","alias_value":"RLT75ET6","created_at":"2026-05-18T12:26:13Z"}],"graph_snapshots":[{"event_id":"sha256:9c91433a294bd573987675348372566fe3f049637890a1e956523c7e12832946","target":"graph","created_at":"2026-05-18T04:22:11Z","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":"There is an intriguing connection between the dynamics of the horocycle flow in the modular surface $SL_{2}(\\pmb{Z}) \\backslash SL_{2}(\\pmb{R})$ and the Riemann hypothesis. It appears in the error term for the asymptotic of the horocycle average of a modular function of rapid decay. We study whether similar results occur for a broader class of modular functions, including functions of polynomial growth, and of exponential growth at the cusp. Hints on their long horocycle average are derived by translating the horocycle flow dynamical problem in string theory language. Results are then proved b","authors_text":"Matteo A. Cardella","cross_cats":["hep-th","math-ph","math.DS","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-13T15:18:47Z","title":"Error Estimates in Horocycle Averages Asymptotics: Challenges from String Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.2754","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":"sha256:1d808a6e2a71ea9e56485e0a7dd33be9ac4bf8d8ef703d9ef889dde65f870f23","target":"record","created_at":"2026-05-18T04:22:11Z","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":"2a06880ddf08a3edbe4c33c3547d7147e548bb507662a4ebccbaa57c9e6ee0b7","cross_cats_sorted":["hep-th","math-ph","math.DS","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-12-13T15:18:47Z","title_canon_sha256":"fb59e5844e4542a942b7fddc58f452f52fc78f193d36b927e9bd8e5c7255a54e"},"schema_version":"1.0","source":{"id":"1012.2754","kind":"arxiv","version":3}},"canonical_sha256":"8ae7fe927e5cb5fa4e5ce2fb62903f16f6bce37be448842dea590065fbd90601","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ae7fe927e5cb5fa4e5ce2fb62903f16f6bce37be448842dea590065fbd90601","first_computed_at":"2026-05-18T04:22:11.153777Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:22:11.153777Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oeRmpUjy/db+GLI/6s+B1GfkSJvj3MfjQpNm6xLhP3HCAc+b7sHDG+KuOXnaG62NCRs1TjAwO3yOfFFyrNe8CA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:22:11.154186Z","signed_message":"canonical_sha256_bytes"},"source_id":"1012.2754","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d808a6e2a71ea9e56485e0a7dd33be9ac4bf8d8ef703d9ef889dde65f870f23","sha256:9c91433a294bd573987675348372566fe3f049637890a1e956523c7e12832946"],"state_sha256":"e97246aa31f1aa0e86b8ba7bedf12119cd4b20185b2a5b12373dea1d31f5521d"}