{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:IASS3QHUXEJKST4NOJNNUK3W2L","short_pith_number":"pith:IASS3QHU","canonical_record":{"source":{"id":"1809.07434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-20T00:03:23Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"6e850fa2440040e5b77c867a0e54af6f38f480d2028cec0eb6b4940ececaef1f","abstract_canon_sha256":"bd6ef0422e7341de08b190710f8a60701161ce26fbf58db4aa49e7447a686d89"},"schema_version":"1.0"},"canonical_sha256":"40252dc0f4b912a94f8d725ada2b76d2eadd6181203380d27145762099060c72","source":{"kind":"arxiv","id":"1809.07434","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07434","created_at":"2026-05-18T00:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07434v1","created_at":"2026-05-18T00:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07434","created_at":"2026-05-18T00:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"IASS3QHUXEJK","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IASS3QHUXEJKST4N","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IASS3QHU","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:IASS3QHUXEJKST4NOJNNUK3W2L","target":"record","payload":{"canonical_record":{"source":{"id":"1809.07434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-20T00:03:23Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"6e850fa2440040e5b77c867a0e54af6f38f480d2028cec0eb6b4940ececaef1f","abstract_canon_sha256":"bd6ef0422e7341de08b190710f8a60701161ce26fbf58db4aa49e7447a686d89"},"schema_version":"1.0"},"canonical_sha256":"40252dc0f4b912a94f8d725ada2b76d2eadd6181203380d27145762099060c72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:16.339709Z","signature_b64":"uwnIsv5/K1Frb6fDVU7zmtXedrDPg8pCezBvs4OPAaY3pwY4m5WiX2AcMAlpIQDZhKKDVeSwNhP+ATaduQ09CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40252dc0f4b912a94f8d725ada2b76d2eadd6181203380d27145762099060c72","last_reissued_at":"2026-05-18T00:05:16.339083Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:16.339083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.07434","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":"2026-05-18T00:05:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E3izxrxa6pedOlPnkju9meHjtT152kjw8xx+lg/Iv1oYzGs/slPW5spnmgOf7Ctw385fnTRWMDKuHj1wSoyCBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:07:36.877205Z"},"content_sha256":"4287d60809958c4a92beb709577db8c1ee9cdf5ceafea3166c365f0c67c927d7","schema_version":"1.0","event_id":"sha256:4287d60809958c4a92beb709577db8c1ee9cdf5ceafea3166c365f0c67c927d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:IASS3QHUXEJKST4NOJNNUK3W2L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Hurwitz Theory of Elliptic Orbifolds, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.AG","authors_text":"Philip Engel","submitted_at":"2018-09-20T00:03:23Z","abstract_excerpt":"An elliptic orbifold is the quotient of an elliptic curve by a finite group. In 2001, Eskin and Okounkov proved that generating functions for the number of branched covers of an elliptic curve with specified ramification are quasimodular forms for $SL_2(\\mathbb{Z}).$ In 2006, they generalized this theorem to the enumeration of branched covers of the quotient of an elliptic curve by $\\pm 1$, proving quasi-modularity for $\\Gamma_1(2)$. In 2017, the author generalized their work to the quotient of an elliptic curve by $\\langle \\zeta_N\\rangle$ for $N=3, 4, 6$, proving quasimodularity for $\\Gamma_1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07434","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":"2026-05-18T00:05:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UsNFrH/dwm3MNZ7CUaQxlC/w4lNRclt3OMIgzjkJBTgJxSuMHftwXJKkMXYpY9hfBqS4XcqgrCAYpy12Jy0GAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T03:07:36.877869Z"},"content_sha256":"450c121bfd279f15e229c781ec7e9334c5e04df5ffca553650b6134aadc74490","schema_version":"1.0","event_id":"sha256:450c121bfd279f15e229c781ec7e9334c5e04df5ffca553650b6134aadc74490"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IASS3QHUXEJKST4NOJNNUK3W2L/bundle.json","state_url":"https://pith.science/pith/IASS3QHUXEJKST4NOJNNUK3W2L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IASS3QHUXEJKST4NOJNNUK3W2L/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":"2026-06-08T03:07:36Z","links":{"resolver":"https://pith.science/pith/IASS3QHUXEJKST4NOJNNUK3W2L","bundle":"https://pith.science/pith/IASS3QHUXEJKST4NOJNNUK3W2L/bundle.json","state":"https://pith.science/pith/IASS3QHUXEJKST4NOJNNUK3W2L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IASS3QHUXEJKST4NOJNNUK3W2L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:IASS3QHUXEJKST4NOJNNUK3W2L","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":"bd6ef0422e7341de08b190710f8a60701161ce26fbf58db4aa49e7447a686d89","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-20T00:03:23Z","title_canon_sha256":"6e850fa2440040e5b77c867a0e54af6f38f480d2028cec0eb6b4940ececaef1f"},"schema_version":"1.0","source":{"id":"1809.07434","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.07434","created_at":"2026-05-18T00:05:16Z"},{"alias_kind":"arxiv_version","alias_value":"1809.07434v1","created_at":"2026-05-18T00:05:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.07434","created_at":"2026-05-18T00:05:16Z"},{"alias_kind":"pith_short_12","alias_value":"IASS3QHUXEJK","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"IASS3QHUXEJKST4N","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"IASS3QHU","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:450c121bfd279f15e229c781ec7e9334c5e04df5ffca553650b6134aadc74490","target":"graph","created_at":"2026-05-18T00:05:16Z","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":"An elliptic orbifold is the quotient of an elliptic curve by a finite group. In 2001, Eskin and Okounkov proved that generating functions for the number of branched covers of an elliptic curve with specified ramification are quasimodular forms for $SL_2(\\mathbb{Z}).$ In 2006, they generalized this theorem to the enumeration of branched covers of the quotient of an elliptic curve by $\\pm 1$, proving quasi-modularity for $\\Gamma_1(2)$. In 2017, the author generalized their work to the quotient of an elliptic curve by $\\langle \\zeta_N\\rangle$ for $N=3, 4, 6$, proving quasimodularity for $\\Gamma_1","authors_text":"Philip Engel","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-20T00:03:23Z","title":"Hurwitz Theory of Elliptic Orbifolds, II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.07434","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":"sha256:4287d60809958c4a92beb709577db8c1ee9cdf5ceafea3166c365f0c67c927d7","target":"record","created_at":"2026-05-18T00:05:16Z","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":"bd6ef0422e7341de08b190710f8a60701161ce26fbf58db4aa49e7447a686d89","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-09-20T00:03:23Z","title_canon_sha256":"6e850fa2440040e5b77c867a0e54af6f38f480d2028cec0eb6b4940ececaef1f"},"schema_version":"1.0","source":{"id":"1809.07434","kind":"arxiv","version":1}},"canonical_sha256":"40252dc0f4b912a94f8d725ada2b76d2eadd6181203380d27145762099060c72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40252dc0f4b912a94f8d725ada2b76d2eadd6181203380d27145762099060c72","first_computed_at":"2026-05-18T00:05:16.339083Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:16.339083Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uwnIsv5/K1Frb6fDVU7zmtXedrDPg8pCezBvs4OPAaY3pwY4m5WiX2AcMAlpIQDZhKKDVeSwNhP+ATaduQ09CA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:16.339709Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.07434","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4287d60809958c4a92beb709577db8c1ee9cdf5ceafea3166c365f0c67c927d7","sha256:450c121bfd279f15e229c781ec7e9334c5e04df5ffca553650b6134aadc74490"],"state_sha256":"6e4de4ed64ade100cb728f740b0fa1f6cbaa33f074b7b1a1d913c95cd9416e6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wullDpumXwr7XkvUFUWP3m6+pIGT4iW23t1zLmCdXUzo4iVgHQvWx9Bjj7EJPQ5ABOooqZWOXAxgbBKE1ozzDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T03:07:36.881530Z","bundle_sha256":"fcee7bf905590cd04c8850ca3c0a4810dbe135b3d72e03f06e23b09d61e43cc6"}}