{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:B3THARAVBAVQQUSO7JCFKFG5S3","short_pith_number":"pith:B3THARAV","canonical_record":{"source":{"id":"hep-th/0410189","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-10-18T23:07:29Z","cross_cats_sorted":[],"title_canon_sha256":"9c32abd584134c852df2f69a59d2261e83a9beb09a8c497f32c6affe95dc5bb8","abstract_canon_sha256":"3279c018df47a6b7688b1fe354fd9fc54e891b0aacf6ee45cbc6c5c93d52428f"},"schema_version":"1.0"},"canonical_sha256":"0ee6704415082b08524efa445514dd96f096087dfafc3410cf94af4ede42149a","source":{"kind":"arxiv","id":"hep-th/0410189","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0410189","created_at":"2026-05-18T01:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0410189v1","created_at":"2026-05-18T01:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0410189","created_at":"2026-05-18T01:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"B3THARAVBAVQ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"B3THARAVBAVQQUSO","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"B3THARAV","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:B3THARAVBAVQQUSO7JCFKFG5S3","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0410189","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-10-18T23:07:29Z","cross_cats_sorted":[],"title_canon_sha256":"9c32abd584134c852df2f69a59d2261e83a9beb09a8c497f32c6affe95dc5bb8","abstract_canon_sha256":"3279c018df47a6b7688b1fe354fd9fc54e891b0aacf6ee45cbc6c5c93d52428f"},"schema_version":"1.0"},"canonical_sha256":"0ee6704415082b08524efa445514dd96f096087dfafc3410cf94af4ede42149a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:46.045005Z","signature_b64":"AxNlwX3FDekkCCg+vsurWbMBftOjoK2wjS9zfkJexKdkWG5Ur2dui9jihJIIvoWRF/T4Dcm7GmWe0TcBdiKuAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ee6704415082b08524efa445514dd96f096087dfafc3410cf94af4ede42149a","last_reissued_at":"2026-05-18T01:38:46.044417Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:46.044417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0410189","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":"2026-05-18T01:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7iJVHJ14L/eXFDDBg4iwPj9349op1j//uRa8u79HA8AH6SJSslo0gBqIG/sVJHHN/SDWNjecF4b182CxkqkYDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:20:27.097364Z"},"content_sha256":"6ba1b5a9e6580810fc525ea99c57f14a5d495f874c88bfd4c753ceb58411c826","schema_version":"1.0","event_id":"sha256:6ba1b5a9e6580810fc525ea99c57f14a5d495f874c88bfd4c753ceb58411c826"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:B3THARAVBAVQQUSO7JCFKFG5S3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Kac-Moody Modularity","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Monika Lynker, Rolf Schimmrigk","submitted_at":"2004-10-18T23:07:29Z","abstract_excerpt":"It is shown how the arithmetic structure of algebraic curves encoded in the Hasse-Weil L-function can be related to affine Kac-Moody algebras. This result is useful in relating the arithmetic geometry of Calabi-Yau varieties to the underlying exactly solvable theory. In the case of the genus three Fermat curve we identify the Hasse-Weil L-function with the Mellin transform of the twist of a number theoretic modular form derived from the string function of a non-twisted affine Lie algebra. The twist character is associated to the number field of quantum dimensions of the conformal field theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0410189","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":""},"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":"2026-05-18T01:38:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ikVYJ96HxfdNuM/OHbrKCnaj8sUXQoF4cgD6zEjoQ/gwFUCwBuaXVixZ1x7hTGnYLtWbjWxgfwFXK1aZqb0qCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T12:20:27.097852Z"},"content_sha256":"a8a157ada25620fa843ac95e6162f7c12faeaa4e251339e3100f844495b6b1f4","schema_version":"1.0","event_id":"sha256:a8a157ada25620fa843ac95e6162f7c12faeaa4e251339e3100f844495b6b1f4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B3THARAVBAVQQUSO7JCFKFG5S3/bundle.json","state_url":"https://pith.science/pith/B3THARAVBAVQQUSO7JCFKFG5S3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B3THARAVBAVQQUSO7JCFKFG5S3/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":"2026-05-26T12:20:27Z","links":{"resolver":"https://pith.science/pith/B3THARAVBAVQQUSO7JCFKFG5S3","bundle":"https://pith.science/pith/B3THARAVBAVQQUSO7JCFKFG5S3/bundle.json","state":"https://pith.science/pith/B3THARAVBAVQQUSO7JCFKFG5S3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B3THARAVBAVQQUSO7JCFKFG5S3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:B3THARAVBAVQQUSO7JCFKFG5S3","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":"3279c018df47a6b7688b1fe354fd9fc54e891b0aacf6ee45cbc6c5c93d52428f","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2004-10-18T23:07:29Z","title_canon_sha256":"9c32abd584134c852df2f69a59d2261e83a9beb09a8c497f32c6affe95dc5bb8"},"schema_version":"1.0","source":{"id":"hep-th/0410189","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0410189","created_at":"2026-05-18T01:38:46Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0410189v1","created_at":"2026-05-18T01:38:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0410189","created_at":"2026-05-18T01:38:46Z"},{"alias_kind":"pith_short_12","alias_value":"B3THARAVBAVQ","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"B3THARAVBAVQQUSO","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"B3THARAV","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:a8a157ada25620fa843ac95e6162f7c12faeaa4e251339e3100f844495b6b1f4","target":"graph","created_at":"2026-05-18T01:38:46Z","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":"It is shown how the arithmetic structure of algebraic curves encoded in the Hasse-Weil L-function can be related to affine Kac-Moody algebras. This result is useful in relating the arithmetic geometry of Calabi-Yau varieties to the underlying exactly solvable theory. In the case of the genus three Fermat curve we identify the Hasse-Weil L-function with the Mellin transform of the twist of a number theoretic modular form derived from the string function of a non-twisted affine Lie algebra. The twist character is associated to the number field of quantum dimensions of the conformal field theory.","authors_text":"Monika Lynker, Rolf Schimmrigk","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2004-10-18T23:07:29Z","title":"Geometric Kac-Moody Modularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0410189","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":"sha256:6ba1b5a9e6580810fc525ea99c57f14a5d495f874c88bfd4c753ceb58411c826","target":"record","created_at":"2026-05-18T01:38:46Z","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":"3279c018df47a6b7688b1fe354fd9fc54e891b0aacf6ee45cbc6c5c93d52428f","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2004-10-18T23:07:29Z","title_canon_sha256":"9c32abd584134c852df2f69a59d2261e83a9beb09a8c497f32c6affe95dc5bb8"},"schema_version":"1.0","source":{"id":"hep-th/0410189","kind":"arxiv","version":1}},"canonical_sha256":"0ee6704415082b08524efa445514dd96f096087dfafc3410cf94af4ede42149a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ee6704415082b08524efa445514dd96f096087dfafc3410cf94af4ede42149a","first_computed_at":"2026-05-18T01:38:46.044417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:46.044417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AxNlwX3FDekkCCg+vsurWbMBftOjoK2wjS9zfkJexKdkWG5Ur2dui9jihJIIvoWRF/T4Dcm7GmWe0TcBdiKuAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:46.045005Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0410189","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ba1b5a9e6580810fc525ea99c57f14a5d495f874c88bfd4c753ceb58411c826","sha256:a8a157ada25620fa843ac95e6162f7c12faeaa4e251339e3100f844495b6b1f4"],"state_sha256":"3e688ce1d1ca47b5a02cbb07e41774c976e46e6247144a16e6dc8e6b6e68a48c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RozIAGICrYIl/j49MOGHOmHHXJH+/3w3bL8H6Ze4V2ksdWAtLtL5wyGOb8qwmH1xU5TuPz0uztpqrhNtS0TOBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T12:20:27.100661Z","bundle_sha256":"84fc047f732f2634234fd83486e41deacbd0add2512c6b3638a02640e3ef9b58"}}