{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QLZLPQHR4UTDC4CYLQY2DLFAI5","short_pith_number":"pith:QLZLPQHR","canonical_record":{"source":{"id":"1510.01049","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-05T07:03:41Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"1a5f38c2f010dd61c5b93c39d305dc6a32acac3635f41cab1f632edc77d0b6d4","abstract_canon_sha256":"84a356b7823d32bac6406185f1c79c3bccc14fa6fc3220292de02a65e3c68b5e"},"schema_version":"1.0"},"canonical_sha256":"82f2b7c0f1e5263170585c31a1aca0476585bfba220108d3070451b4a9740df7","source":{"kind":"arxiv","id":"1510.01049","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01049","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01049v1","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01049","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"pith_short_12","alias_value":"QLZLPQHR4UTD","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QLZLPQHR4UTDC4CY","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QLZLPQHR","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QLZLPQHR4UTDC4CYLQY2DLFAI5","target":"record","payload":{"canonical_record":{"source":{"id":"1510.01049","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-05T07:03:41Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"1a5f38c2f010dd61c5b93c39d305dc6a32acac3635f41cab1f632edc77d0b6d4","abstract_canon_sha256":"84a356b7823d32bac6406185f1c79c3bccc14fa6fc3220292de02a65e3c68b5e"},"schema_version":"1.0"},"canonical_sha256":"82f2b7c0f1e5263170585c31a1aca0476585bfba220108d3070451b4a9740df7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:04.907522Z","signature_b64":"QnIToV1tHndjegtWXeW3frZKJQhh8ESGb83qt3y3v18mIDGctZbK4vcBU3taW3zlWHn5WPFxgwaxuDdo8SZUBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82f2b7c0f1e5263170585c31a1aca0476585bfba220108d3070451b4a9740df7","last_reissued_at":"2026-05-18T01:31:04.906914Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:04.906914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.01049","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":"2026-05-18T01:31:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rxmEQhyWMtI2owav53/AybTtElRNFRUydp5JR0M6KiqnFkcCP8CBpvQaygBGZMTtFl6K4HNFVSP8MIwjRnHwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:11:13.649415Z"},"content_sha256":"fc9f866c19b11c75280863978ac0dc75d2de60284bf642c87c54e1ed8f0318ad","schema_version":"1.0","event_id":"sha256:fc9f866c19b11c75280863978ac0dc75d2de60284bf642c87c54e1ed8f0318ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QLZLPQHR4UTDC4CYLQY2DLFAI5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Groups in NTP2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.LO","authors_text":"Alf Onshuus, Nadja Hempel (ICJ)","submitted_at":"2015-10-05T07:03:41Z","abstract_excerpt":"We prove the existence of abelian, solvable and nilpotent definable envelopes for groups definable in models of an NTP2 theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01049","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":"2026-05-18T01:31:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vN57ZaHrnA7TeW7sCB3HM4654s6vl2fcotGYgY75QmX+pn6v4FN3SNmXwcu7KqEWUSvPVJMOPMRqgYF0bTbHCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T02:11:13.650024Z"},"content_sha256":"64fc1cadddd15236ec7084d6a6de5fcdbb277b6e70617f50a65c8a86449c8472","schema_version":"1.0","event_id":"sha256:64fc1cadddd15236ec7084d6a6de5fcdbb277b6e70617f50a65c8a86449c8472"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QLZLPQHR4UTDC4CYLQY2DLFAI5/bundle.json","state_url":"https://pith.science/pith/QLZLPQHR4UTDC4CYLQY2DLFAI5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QLZLPQHR4UTDC4CYLQY2DLFAI5/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":"2026-05-27T02:11:13Z","links":{"resolver":"https://pith.science/pith/QLZLPQHR4UTDC4CYLQY2DLFAI5","bundle":"https://pith.science/pith/QLZLPQHR4UTDC4CYLQY2DLFAI5/bundle.json","state":"https://pith.science/pith/QLZLPQHR4UTDC4CYLQY2DLFAI5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QLZLPQHR4UTDC4CYLQY2DLFAI5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QLZLPQHR4UTDC4CYLQY2DLFAI5","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":"84a356b7823d32bac6406185f1c79c3bccc14fa6fc3220292de02a65e3c68b5e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-05T07:03:41Z","title_canon_sha256":"1a5f38c2f010dd61c5b93c39d305dc6a32acac3635f41cab1f632edc77d0b6d4"},"schema_version":"1.0","source":{"id":"1510.01049","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.01049","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"arxiv_version","alias_value":"1510.01049v1","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01049","created_at":"2026-05-18T01:31:04Z"},{"alias_kind":"pith_short_12","alias_value":"QLZLPQHR4UTD","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"QLZLPQHR4UTDC4CY","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"QLZLPQHR","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:64fc1cadddd15236ec7084d6a6de5fcdbb277b6e70617f50a65c8a86449c8472","target":"graph","created_at":"2026-05-18T01:31:04Z","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 prove the existence of abelian, solvable and nilpotent definable envelopes for groups definable in models of an NTP2 theory.","authors_text":"Alf Onshuus, Nadja Hempel (ICJ)","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-05T07:03:41Z","title":"Groups in NTP2"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01049","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:fc9f866c19b11c75280863978ac0dc75d2de60284bf642c87c54e1ed8f0318ad","target":"record","created_at":"2026-05-18T01:31:04Z","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":"84a356b7823d32bac6406185f1c79c3bccc14fa6fc3220292de02a65e3c68b5e","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-05T07:03:41Z","title_canon_sha256":"1a5f38c2f010dd61c5b93c39d305dc6a32acac3635f41cab1f632edc77d0b6d4"},"schema_version":"1.0","source":{"id":"1510.01049","kind":"arxiv","version":1}},"canonical_sha256":"82f2b7c0f1e5263170585c31a1aca0476585bfba220108d3070451b4a9740df7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"82f2b7c0f1e5263170585c31a1aca0476585bfba220108d3070451b4a9740df7","first_computed_at":"2026-05-18T01:31:04.906914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:04.906914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QnIToV1tHndjegtWXeW3frZKJQhh8ESGb83qt3y3v18mIDGctZbK4vcBU3taW3zlWHn5WPFxgwaxuDdo8SZUBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:04.907522Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.01049","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc9f866c19b11c75280863978ac0dc75d2de60284bf642c87c54e1ed8f0318ad","sha256:64fc1cadddd15236ec7084d6a6de5fcdbb277b6e70617f50a65c8a86449c8472"],"state_sha256":"f1c8a4c29131ab150e7aa89ce31cc4a6849c16055af2d927a07d66e99a735855"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eHKeNKuHZOVursbZKY3kALbYM2HGaoK6m6bFx++qqAuCRJFd5OZWSmHE4LTsys/MBp8kZhWjPpcnlfNVic6eAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T02:11:13.653579Z","bundle_sha256":"ae216b5ef61f422286d006f058e179ba290db3665dc3e3704dd2f90a608d0f48"}}