{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:GJZVCT2LWDQ7SAQQZDY7HLWAJE","short_pith_number":"pith:GJZVCT2L","canonical_record":{"source":{"id":"2004.04651","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-09T16:37:58Z","cross_cats_sorted":[],"title_canon_sha256":"ab7ab9876be076f2b055ec498771205eea32a4d1ebafc5eeca683317286b8514","abstract_canon_sha256":"9094808904158135104460c9e05b2e297bec47d9240d72bc94ad661a06914e42"},"schema_version":"1.0"},"canonical_sha256":"3273514f4bb0e1f90210c8f1f3aec049327e3263f92f56249a1e4828879d97c3","source":{"kind":"arxiv","id":"2004.04651","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.04651","created_at":"2026-07-05T01:01:24Z"},{"alias_kind":"arxiv_version","alias_value":"2004.04651v2","created_at":"2026-07-05T01:01:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.04651","created_at":"2026-07-05T01:01:24Z"},{"alias_kind":"pith_short_12","alias_value":"GJZVCT2LWDQ7","created_at":"2026-07-05T01:01:24Z"},{"alias_kind":"pith_short_16","alias_value":"GJZVCT2LWDQ7SAQQ","created_at":"2026-07-05T01:01:24Z"},{"alias_kind":"pith_short_8","alias_value":"GJZVCT2L","created_at":"2026-07-05T01:01:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:GJZVCT2LWDQ7SAQQZDY7HLWAJE","target":"record","payload":{"canonical_record":{"source":{"id":"2004.04651","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-09T16:37:58Z","cross_cats_sorted":[],"title_canon_sha256":"ab7ab9876be076f2b055ec498771205eea32a4d1ebafc5eeca683317286b8514","abstract_canon_sha256":"9094808904158135104460c9e05b2e297bec47d9240d72bc94ad661a06914e42"},"schema_version":"1.0"},"canonical_sha256":"3273514f4bb0e1f90210c8f1f3aec049327e3263f92f56249a1e4828879d97c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T01:01:24.465907Z","signature_b64":"pSALc4C2OeuOnRgFRPzcZ6vqWhbBwKOEAbObnkcSb/FKXqC2ufz4DinnJab5oq+8Alz+MghICH8wpXr95LCADQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3273514f4bb0e1f90210c8f1f3aec049327e3263f92f56249a1e4828879d97c3","last_reissued_at":"2026-07-05T01:01:24.465447Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T01:01:24.465447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.04651","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T01:01:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tU12CaG3B5TXxt/8SlZIZdbEdjMUEklVAaTMcz65addKDXRc+G7yIelubGqta+49OzwY91FUoAdjQ1kK3d+MBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T00:42:38.337496Z"},"content_sha256":"a23cdad13e837cf024c1114d44b4c6e19c8018923d81485b67add1ffbaa823e0","schema_version":"1.0","event_id":"sha256:a23cdad13e837cf024c1114d44b4c6e19c8018923d81485b67add1ffbaa823e0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:GJZVCT2LWDQ7SAQQZDY7HLWAJE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Malle's Conjecture for $G \\times A$, with $G = S_3, S_4, S_5$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Frank Thorne, Jiuya Wang, Riad Masri, Wei-Lun Tsai","submitted_at":"2020-04-09T16:37:58Z","abstract_excerpt":"We prove Malle's conjecture for $G \\times A$, with $G=S_3, S_4, S_5$ and $A$ an abelian group. This builds upon work of the fourth author, who proved this result with restrictions on the primes dividing $A$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.04651","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.04651/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T01:01:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tBTCA5E5vWMBtp67KruU1oeAE2Krd1vsUkZRRFaAqoJ1kXuMJRcw7bCzJbTJYcIIawNcNp3JN0HcI7/93MZICQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T00:42:38.338336Z"},"content_sha256":"6ef1f352f9053744bef0477e76e3383031e0b9f05bf7a632c29f3fcc01c055ca","schema_version":"1.0","event_id":"sha256:6ef1f352f9053744bef0477e76e3383031e0b9f05bf7a632c29f3fcc01c055ca"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GJZVCT2LWDQ7SAQQZDY7HLWAJE/bundle.json","state_url":"https://pith.science/pith/GJZVCT2LWDQ7SAQQZDY7HLWAJE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GJZVCT2LWDQ7SAQQZDY7HLWAJE/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":"2026-08-11T00:42:38Z","links":{"resolver":"https://pith.science/pith/GJZVCT2LWDQ7SAQQZDY7HLWAJE","bundle":"https://pith.science/pith/GJZVCT2LWDQ7SAQQZDY7HLWAJE/bundle.json","state":"https://pith.science/pith/GJZVCT2LWDQ7SAQQZDY7HLWAJE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GJZVCT2LWDQ7SAQQZDY7HLWAJE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:GJZVCT2LWDQ7SAQQZDY7HLWAJE","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":"9094808904158135104460c9e05b2e297bec47d9240d72bc94ad661a06914e42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-09T16:37:58Z","title_canon_sha256":"ab7ab9876be076f2b055ec498771205eea32a4d1ebafc5eeca683317286b8514"},"schema_version":"1.0","source":{"id":"2004.04651","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.04651","created_at":"2026-07-05T01:01:24Z"},{"alias_kind":"arxiv_version","alias_value":"2004.04651v2","created_at":"2026-07-05T01:01:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.04651","created_at":"2026-07-05T01:01:24Z"},{"alias_kind":"pith_short_12","alias_value":"GJZVCT2LWDQ7","created_at":"2026-07-05T01:01:24Z"},{"alias_kind":"pith_short_16","alias_value":"GJZVCT2LWDQ7SAQQ","created_at":"2026-07-05T01:01:24Z"},{"alias_kind":"pith_short_8","alias_value":"GJZVCT2L","created_at":"2026-07-05T01:01:24Z"}],"graph_snapshots":[{"event_id":"sha256:6ef1f352f9053744bef0477e76e3383031e0b9f05bf7a632c29f3fcc01c055ca","target":"graph","created_at":"2026-07-05T01:01:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2004.04651/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove Malle's conjecture for $G \\times A$, with $G=S_3, S_4, S_5$ and $A$ an abelian group. This builds upon work of the fourth author, who proved this result with restrictions on the primes dividing $A$.","authors_text":"Frank Thorne, Jiuya Wang, Riad Masri, Wei-Lun Tsai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-09T16:37:58Z","title":"Malle's Conjecture for $G \\times A$, with $G = S_3, S_4, S_5$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.04651","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:a23cdad13e837cf024c1114d44b4c6e19c8018923d81485b67add1ffbaa823e0","target":"record","created_at":"2026-07-05T01:01:24Z","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":"9094808904158135104460c9e05b2e297bec47d9240d72bc94ad661a06914e42","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2020-04-09T16:37:58Z","title_canon_sha256":"ab7ab9876be076f2b055ec498771205eea32a4d1ebafc5eeca683317286b8514"},"schema_version":"1.0","source":{"id":"2004.04651","kind":"arxiv","version":2}},"canonical_sha256":"3273514f4bb0e1f90210c8f1f3aec049327e3263f92f56249a1e4828879d97c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3273514f4bb0e1f90210c8f1f3aec049327e3263f92f56249a1e4828879d97c3","first_computed_at":"2026-07-05T01:01:24.465447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:01:24.465447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pSALc4C2OeuOnRgFRPzcZ6vqWhbBwKOEAbObnkcSb/FKXqC2ufz4DinnJab5oq+8Alz+MghICH8wpXr95LCADQ==","signature_status":"signed_v1","signed_at":"2026-07-05T01:01:24.465907Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.04651","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a23cdad13e837cf024c1114d44b4c6e19c8018923d81485b67add1ffbaa823e0","sha256:6ef1f352f9053744bef0477e76e3383031e0b9f05bf7a632c29f3fcc01c055ca"],"state_sha256":"5a815773fbc89e4129772a848ed49f92762c80c454e2ac778c184ff415370aa4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qicwVMapqNE6jpVO5b4UXlBu2jmHQWp2Rv5OPPeLi1nzwbEctrmrTgEef6GjpxD5yqK+FYhRCgHAGjQNX+7TCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T00:42:38.344362Z","bundle_sha256":"ed33cd9d3ce8e96495619b21146ced660eaf73d5d564737d05292f3b64da40a7"}}