{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:NP7DZP7CHIHUF77LX47DPYPH4J","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":"dd0197487ab7f2c5736f05d1615c66de0220eee95b3be2027eed54fddf2f4e70","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2003-12-18T13:20:44Z","title_canon_sha256":"70fe9f6c2a7e5200335bfa1660136b8e33804189bffc30c43501302b2a7cd30f"},"schema_version":"1.0","source":{"id":"math/0312357","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0312357","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"arxiv_version","alias_value":"math/0312357v2","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0312357","created_at":"2026-05-18T03:59:12Z"},{"alias_kind":"pith_short_12","alias_value":"NP7DZP7CHIHU","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"NP7DZP7CHIHUF77L","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"NP7DZP7C","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:4ab98729bbe77f6c9fe87c3b71555a4306fa4c2b7736d004a1b200ca2d1ebf22","target":"graph","created_at":"2026-05-18T03:59:12Z","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 derive explicit formulas for the Arakelov-Green function and the Faltings delta-invariant of a Riemann surface. A numerical example illustrates how these formulas can be used to calculate Arakelov invariants of curves.","authors_text":"Robin de Jong","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"math.NT","submitted_at":"2003-12-18T13:20:44Z","title":"Arakelov invariants of Riemann surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0312357","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:b7334aabee9553adc5a0879ae4bb76908e4b0c7ee78f506cfef287689c2df640","target":"record","created_at":"2026-05-18T03:59:12Z","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":"dd0197487ab7f2c5736f05d1615c66de0220eee95b3be2027eed54fddf2f4e70","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"math.NT","submitted_at":"2003-12-18T13:20:44Z","title_canon_sha256":"70fe9f6c2a7e5200335bfa1660136b8e33804189bffc30c43501302b2a7cd30f"},"schema_version":"1.0","source":{"id":"math/0312357","kind":"arxiv","version":2}},"canonical_sha256":"6bfe3cbfe23a0f42ffebbf3e37e1e7e2524628917798da63473b5eee9de18307","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6bfe3cbfe23a0f42ffebbf3e37e1e7e2524628917798da63473b5eee9de18307","first_computed_at":"2026-05-18T03:59:12.590338Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:59:12.590338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7RkEzVvhnU5j/tKZCEuaYAdMHKZOR9ht6gulZJ0mjd3oplb/TBkoAi8lFEBMwCjkfvsBzwDzOnWj278XVb7qDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:59:12.590869Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0312357","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7334aabee9553adc5a0879ae4bb76908e4b0c7ee78f506cfef287689c2df640","sha256:4ab98729bbe77f6c9fe87c3b71555a4306fa4c2b7736d004a1b200ca2d1ebf22"],"state_sha256":"8dc750f3cf4e017e121e774729b382e396946fa1ce998070839699fd8c3b561e"}