{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:OAF5O6QU4L3YL6VHMBW5AIHRFJ","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":"9e42e10301ce1fd7fe27c91059a0e7d1ad2b24bfab003eb72058859cf6536126","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-11T09:18:05Z","title_canon_sha256":"d5da5daac65ee28189b3297b007d9df09b65fea9aa669f7a3b2440661966ca01"},"schema_version":"1.0","source":{"id":"0906.2056","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.2056","created_at":"2026-05-18T03:15:58Z"},{"alias_kind":"arxiv_version","alias_value":"0906.2056v2","created_at":"2026-05-18T03:15:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.2056","created_at":"2026-05-18T03:15:58Z"},{"alias_kind":"pith_short_12","alias_value":"OAF5O6QU4L3Y","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"OAF5O6QU4L3YL6VH","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"OAF5O6QU","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:31f359d177f2b97617b011a96bb4513008924e4eeec02b68f7af63981cbd17da","target":"graph","created_at":"2026-05-18T03:15:58Z","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":"We study the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces with respect to morphisms of a particular kind. We obtain upper bounds for the arithmetic self-intersection number of the dualizing sheaf on minimal regular models of the modular curves associated with congruence subgroups $\\Gamma_0(N)$ with square free level, as well as for the modular curves X(N) and the Fermat curves with prime exponent.","authors_text":"Ulf Kuehn","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-11T09:18:05Z","title":"On the arithmetic self-intersection number of the dualizing sheaf on arithmetic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.2056","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:d18781d94b00370197b909d1fdfb56140e3ca22faba3b2d0953a4aad3b21332f","target":"record","created_at":"2026-05-18T03:15:58Z","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":"9e42e10301ce1fd7fe27c91059a0e7d1ad2b24bfab003eb72058859cf6536126","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2009-06-11T09:18:05Z","title_canon_sha256":"d5da5daac65ee28189b3297b007d9df09b65fea9aa669f7a3b2440661966ca01"},"schema_version":"1.0","source":{"id":"0906.2056","kind":"arxiv","version":2}},"canonical_sha256":"700bd77a14e2f785faa7606dd020f12a6f2517093ccefb31d74e88e9587d36c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"700bd77a14e2f785faa7606dd020f12a6f2517093ccefb31d74e88e9587d36c3","first_computed_at":"2026-05-18T03:15:58.039655Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:15:58.039655Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X6IizwWmIfGbNq/4OBHnr2v3c3UU5WUpZUlhsAZd61M2uH0mBdEUXKGUfOFO0Luirw/bXCVBjTyPGsftqsjSDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:15:58.040399Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.2056","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d18781d94b00370197b909d1fdfb56140e3ca22faba3b2d0953a4aad3b21332f","sha256:31f359d177f2b97617b011a96bb4513008924e4eeec02b68f7af63981cbd17da"],"state_sha256":"2e1d06b23a90dd456e780f0e72947fd466f99d8529b408a7031f2bea7a81b82a"}