{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7XJUDDIN42WDEJKAPEWS2JLNRE","short_pith_number":"pith:7XJUDDIN","canonical_record":{"source":{"id":"1512.09112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-30T20:41:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"6b66bdd9348141259b7d82d34eee4fbe2d82710ec45f2b31c576f7ab0a4a62c4","abstract_canon_sha256":"3959b4338b2d4178325200819a997e0ded55c931a3c8c93407193a63d1a2e70d"},"schema_version":"1.0"},"canonical_sha256":"fdd3418d0de6ac322540792d2d256d89206c94157effe5bcd8de97e0f4f6cc29","source":{"kind":"arxiv","id":"1512.09112","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09112","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09112v1","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09112","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"7XJUDDIN42WD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7XJUDDIN42WDEJKA","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7XJUDDIN","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7XJUDDIN42WDEJKAPEWS2JLNRE","target":"record","payload":{"canonical_record":{"source":{"id":"1512.09112","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-30T20:41:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"6b66bdd9348141259b7d82d34eee4fbe2d82710ec45f2b31c576f7ab0a4a62c4","abstract_canon_sha256":"3959b4338b2d4178325200819a997e0ded55c931a3c8c93407193a63d1a2e70d"},"schema_version":"1.0"},"canonical_sha256":"fdd3418d0de6ac322540792d2d256d89206c94157effe5bcd8de97e0f4f6cc29","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:33.985298Z","signature_b64":"+N3Elv3A6kcUXx9Lym9WIjoYeIOCr44BjAmVnP4tlC1jKXVwm34zevDEGKHMmU66ASyhEJ8MXx5rIxnw9Ca0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdd3418d0de6ac322540792d2d256d89206c94157effe5bcd8de97e0f4f6cc29","last_reissued_at":"2026-05-18T01:23:33.984639Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:33.984639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.09112","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":"2026-05-18T01:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dZLb/kKiPH0ITgV0NTbTUmbW4J4oF0Osgu0WyLHqY73SCkZyozwIpmHD9abCsQ0IwK+HU7RwdVaJTrNErDIXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:44:04.629724Z"},"content_sha256":"f4cdd1cc18b296fa257147c88c524193a6adf0256dc61eee4330610bd9677461","schema_version":"1.0","event_id":"sha256:f4cdd1cc18b296fa257147c88c524193a6adf0256dc61eee4330610bd9677461"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7XJUDDIN42WDEJKAPEWS2JLNRE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global Oort Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.GR","authors_text":"David Harbater, Robert Guralnick, Ted Chinburg","submitted_at":"2015-12-30T20:41:54Z","abstract_excerpt":"We study the Oort groups for a prime p, i.e. finite groups G such that every G-Galois branched cover of smooth curves over an algebraically closed field of characteristic p lifts to a G-cover of curves in characteristic 0. We prove that all Oort groups lie in a particular class of finite groups that we characterize, with equality of classes under a conjecture about local liftings. We prove this equality unconditionally if the order of G is not divisible by 2p^2. We also treat the local lifting problem and relate it to the global problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09112","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":"2026-05-18T01:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ofWHUNdefYINEwtiCTBDrImQLIkJ7lrCVcW2Nna76MPPZbBC1KsgvO619LeI2Z1kcE0fxkI3uy6Ydn2yaPFaAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T04:44:04.630385Z"},"content_sha256":"65449a434ec038b236ab58c652ef1439c27b32c58b8d6f30aa9dba7d3db37834","schema_version":"1.0","event_id":"sha256:65449a434ec038b236ab58c652ef1439c27b32c58b8d6f30aa9dba7d3db37834"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7XJUDDIN42WDEJKAPEWS2JLNRE/bundle.json","state_url":"https://pith.science/pith/7XJUDDIN42WDEJKAPEWS2JLNRE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7XJUDDIN42WDEJKAPEWS2JLNRE/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":"2026-05-26T04:44:04Z","links":{"resolver":"https://pith.science/pith/7XJUDDIN42WDEJKAPEWS2JLNRE","bundle":"https://pith.science/pith/7XJUDDIN42WDEJKAPEWS2JLNRE/bundle.json","state":"https://pith.science/pith/7XJUDDIN42WDEJKAPEWS2JLNRE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7XJUDDIN42WDEJKAPEWS2JLNRE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7XJUDDIN42WDEJKAPEWS2JLNRE","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":"3959b4338b2d4178325200819a997e0ded55c931a3c8c93407193a63d1a2e70d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-30T20:41:54Z","title_canon_sha256":"6b66bdd9348141259b7d82d34eee4fbe2d82710ec45f2b31c576f7ab0a4a62c4"},"schema_version":"1.0","source":{"id":"1512.09112","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.09112","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1512.09112v1","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.09112","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"7XJUDDIN42WD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7XJUDDIN42WDEJKA","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7XJUDDIN","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:65449a434ec038b236ab58c652ef1439c27b32c58b8d6f30aa9dba7d3db37834","target":"graph","created_at":"2026-05-18T01:23:33Z","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 study the Oort groups for a prime p, i.e. finite groups G such that every G-Galois branched cover of smooth curves over an algebraically closed field of characteristic p lifts to a G-cover of curves in characteristic 0. We prove that all Oort groups lie in a particular class of finite groups that we characterize, with equality of classes under a conjecture about local liftings. We prove this equality unconditionally if the order of G is not divisible by 2p^2. We also treat the local lifting problem and relate it to the global problem.","authors_text":"David Harbater, Robert Guralnick, Ted Chinburg","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-30T20:41:54Z","title":"Global Oort Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09112","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:f4cdd1cc18b296fa257147c88c524193a6adf0256dc61eee4330610bd9677461","target":"record","created_at":"2026-05-18T01:23:33Z","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":"3959b4338b2d4178325200819a997e0ded55c931a3c8c93407193a63d1a2e70d","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-12-30T20:41:54Z","title_canon_sha256":"6b66bdd9348141259b7d82d34eee4fbe2d82710ec45f2b31c576f7ab0a4a62c4"},"schema_version":"1.0","source":{"id":"1512.09112","kind":"arxiv","version":1}},"canonical_sha256":"fdd3418d0de6ac322540792d2d256d89206c94157effe5bcd8de97e0f4f6cc29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fdd3418d0de6ac322540792d2d256d89206c94157effe5bcd8de97e0f4f6cc29","first_computed_at":"2026-05-18T01:23:33.984639Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:33.984639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+N3Elv3A6kcUXx9Lym9WIjoYeIOCr44BjAmVnP4tlC1jKXVwm34zevDEGKHMmU66ASyhEJ8MXx5rIxnw9Ca0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:33.985298Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.09112","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f4cdd1cc18b296fa257147c88c524193a6adf0256dc61eee4330610bd9677461","sha256:65449a434ec038b236ab58c652ef1439c27b32c58b8d6f30aa9dba7d3db37834"],"state_sha256":"3d3fb2739366e0b6d2e0325fbcf11db24939fc1a83b7f983a9ec7c24e9892630"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fdgzq1Ldf6oPWrAm5mMkm1iKza7r5Lo2DI5aAqPY17ciliRZtwEwmCZswNROsO0VfN76v0OPJLIzn6r8qzEaBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T04:44:04.634287Z","bundle_sha256":"614ab71682ccf39c36f7c20afdc08c25a11f44eb575031994becbf8ebd7e2e3b"}}