{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:C3JS77F5UVCNLAFWM5N6MY24N4","short_pith_number":"pith:C3JS77F5","canonical_record":{"source":{"id":"1812.04425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-11T14:27:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"387a880cc524973cebfc27e3028fdfbd5042aaf23ad0e2103e0b2fb0d177fd5c","abstract_canon_sha256":"8932a187c9cf1350422121769b1c0cf26f18d54c4ddcff498e4a2614ac842806"},"schema_version":"1.0"},"canonical_sha256":"16d32ffcbda544d580b6675be6635c6f095b714dc6b60cfe878d7ef917245fcc","source":{"kind":"arxiv","id":"1812.04425","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04425","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04425v1","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04425","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"C3JS77F5UVCN","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C3JS77F5UVCNLAFW","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C3JS77F5","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:C3JS77F5UVCNLAFWM5N6MY24N4","target":"record","payload":{"canonical_record":{"source":{"id":"1812.04425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-11T14:27:49Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"387a880cc524973cebfc27e3028fdfbd5042aaf23ad0e2103e0b2fb0d177fd5c","abstract_canon_sha256":"8932a187c9cf1350422121769b1c0cf26f18d54c4ddcff498e4a2614ac842806"},"schema_version":"1.0"},"canonical_sha256":"16d32ffcbda544d580b6675be6635c6f095b714dc6b60cfe878d7ef917245fcc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:32.186067Z","signature_b64":"rxJIAKSKqmoH9hdLXYQNb8zK+kkx/9lo2p4fOXh0yeoAgwXNMW81zKxo17aBP9tRsfZKd1uZJxVQtWmZK5BeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16d32ffcbda544d580b6675be6635c6f095b714dc6b60cfe878d7ef917245fcc","last_reissued_at":"2026-05-17T23:58:32.185262Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:32.185262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.04425","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":"2026-05-17T23:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SSKinIYuwSwaVBKIKe6SGwa8VNJyWGcFEnrBeTMB5LTdHXgLINaKM7a0mIg6lM8BTGwzWQj8Dn4dwSnPBaZ+AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:14:22.149076Z"},"content_sha256":"fb31ed096de6b9bdfe8b11dacf72b7bdee03005b88ae0d7219363624c4cb8322","schema_version":"1.0","event_id":"sha256:fb31ed096de6b9bdfe8b11dacf72b7bdee03005b88ae0d7219363624c4cb8322"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:C3JS77F5UVCNLAFWM5N6MY24N4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rings of modular forms and a splitting of $TMF_0(7)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AT","authors_text":"Lennart Meier, Viktoriya Ozornova","submitted_at":"2018-12-11T14:27:49Z","abstract_excerpt":"Among topological modular forms with level structure, $TMF_0(7)$ at the prime $3$ is the first example that had not been understood yet. We provide a splitting of $TMF_0(7)$ at the prime 3 as $TMF$-module into two shifted copies of $TMF$ and two shifted copies of $TMF_1(2)$. This gives evidence to a much more general splitting conjecture. Along the way, we develop several new results on the algebraic side. For example, we show the normality of rings of modular forms of level $n$ and introduce cubical versions of moduli stacks of elliptic curves with level structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04425","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":"2026-05-17T23:58:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5D2cVSdcdvCmWKBcfMPoFc3Gh3hCBxOgwMzhpsES6hZ+OTVV6Uesbh6in/im4/Tvv/EYLUdGlXZ6iWwBgCXMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:14:22.149741Z"},"content_sha256":"7b93ce03b12bd59e418a024db3b3b6876cb1025bb7e3751791fc58e8928b0059","schema_version":"1.0","event_id":"sha256:7b93ce03b12bd59e418a024db3b3b6876cb1025bb7e3751791fc58e8928b0059"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3JS77F5UVCNLAFWM5N6MY24N4/bundle.json","state_url":"https://pith.science/pith/C3JS77F5UVCNLAFWM5N6MY24N4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3JS77F5UVCNLAFWM5N6MY24N4/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":"2026-06-04T06:14:22Z","links":{"resolver":"https://pith.science/pith/C3JS77F5UVCNLAFWM5N6MY24N4","bundle":"https://pith.science/pith/C3JS77F5UVCNLAFWM5N6MY24N4/bundle.json","state":"https://pith.science/pith/C3JS77F5UVCNLAFWM5N6MY24N4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3JS77F5UVCNLAFWM5N6MY24N4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:C3JS77F5UVCNLAFWM5N6MY24N4","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":"8932a187c9cf1350422121769b1c0cf26f18d54c4ddcff498e4a2614ac842806","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-11T14:27:49Z","title_canon_sha256":"387a880cc524973cebfc27e3028fdfbd5042aaf23ad0e2103e0b2fb0d177fd5c"},"schema_version":"1.0","source":{"id":"1812.04425","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.04425","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"arxiv_version","alias_value":"1812.04425v1","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.04425","created_at":"2026-05-17T23:58:32Z"},{"alias_kind":"pith_short_12","alias_value":"C3JS77F5UVCN","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"C3JS77F5UVCNLAFW","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"C3JS77F5","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:7b93ce03b12bd59e418a024db3b3b6876cb1025bb7e3751791fc58e8928b0059","target":"graph","created_at":"2026-05-17T23:58:32Z","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":"Among topological modular forms with level structure, $TMF_0(7)$ at the prime $3$ is the first example that had not been understood yet. We provide a splitting of $TMF_0(7)$ at the prime 3 as $TMF$-module into two shifted copies of $TMF$ and two shifted copies of $TMF_1(2)$. This gives evidence to a much more general splitting conjecture. Along the way, we develop several new results on the algebraic side. For example, we show the normality of rings of modular forms of level $n$ and introduce cubical versions of moduli stacks of elliptic curves with level structure.","authors_text":"Lennart Meier, Viktoriya Ozornova","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-11T14:27:49Z","title":"Rings of modular forms and a splitting of $TMF_0(7)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.04425","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:fb31ed096de6b9bdfe8b11dacf72b7bdee03005b88ae0d7219363624c4cb8322","target":"record","created_at":"2026-05-17T23:58:32Z","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":"8932a187c9cf1350422121769b1c0cf26f18d54c4ddcff498e4a2614ac842806","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2018-12-11T14:27:49Z","title_canon_sha256":"387a880cc524973cebfc27e3028fdfbd5042aaf23ad0e2103e0b2fb0d177fd5c"},"schema_version":"1.0","source":{"id":"1812.04425","kind":"arxiv","version":1}},"canonical_sha256":"16d32ffcbda544d580b6675be6635c6f095b714dc6b60cfe878d7ef917245fcc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16d32ffcbda544d580b6675be6635c6f095b714dc6b60cfe878d7ef917245fcc","first_computed_at":"2026-05-17T23:58:32.185262Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:32.185262Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rxJIAKSKqmoH9hdLXYQNb8zK+kkx/9lo2p4fOXh0yeoAgwXNMW81zKxo17aBP9tRsfZKd1uZJxVQtWmZK5BeCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:32.186067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.04425","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb31ed096de6b9bdfe8b11dacf72b7bdee03005b88ae0d7219363624c4cb8322","sha256:7b93ce03b12bd59e418a024db3b3b6876cb1025bb7e3751791fc58e8928b0059"],"state_sha256":"5d24468d36eb1de34ba2f0599962e2561b1188f9bfb55ed627559b0ae6b66043"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oL1CDSvcrXoBvIn+OW7zJ16r1hzzlhEDBxvHIY+O6UuVM50p8GtGD7IaXNRIet93824tC2MWxfETB4PmHwaPDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:14:22.153189Z","bundle_sha256":"2fe94ab7239b7daad9a81a7563a4a6c47c13ab7c41ee41f1c40dfda113b952f2"}}