{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:BVHZZF7YZG2AECI7PLZQLJAVVL","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":"36a719910e100b9f9ce87095397d9621d4e0f11bd0192995a2424a60831caa36","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-26T09:01:36Z","title_canon_sha256":"2469b833d40cc2b607fd37f836fedb1c78f6a20ce5fb1c745d3c80a26a502553"},"schema_version":"1.0","source":{"id":"1605.08196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.08196","created_at":"2026-05-18T01:13:36Z"},{"alias_kind":"arxiv_version","alias_value":"1605.08196v1","created_at":"2026-05-18T01:13:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.08196","created_at":"2026-05-18T01:13:36Z"},{"alias_kind":"pith_short_12","alias_value":"BVHZZF7YZG2A","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"BVHZZF7YZG2AECI7","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"BVHZZF7Y","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:ca0864cdb637e17cb465424be56ae5a962682e3108f416d4318df64de043cfda","target":"graph","created_at":"2026-05-18T01:13:36Z","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 approach to identify the normal subgroups determined by ideals in free group rings with the help of the derived functors of non-additive functors is explored. A similar approach, i.e., via derived functors, for computing limits of functors from the category of free presentations to the category of abelian groups, arising from commutator structure of free groups, is also discussed.","authors_text":"Inder Bir S. Passi, Roman Mikhailov","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-26T09:01:36Z","title":"Free Group Rings and Derived Functors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.08196","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:a4159ffc3ed7b962b0b086e6b91dcc3164ed39ba94e2821127454437d29ebf6f","target":"record","created_at":"2026-05-18T01:13:36Z","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":"36a719910e100b9f9ce87095397d9621d4e0f11bd0192995a2424a60831caa36","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-05-26T09:01:36Z","title_canon_sha256":"2469b833d40cc2b607fd37f836fedb1c78f6a20ce5fb1c745d3c80a26a502553"},"schema_version":"1.0","source":{"id":"1605.08196","kind":"arxiv","version":1}},"canonical_sha256":"0d4f9c97f8c9b402091f7af305a415aaf6c7a06651d729b2121972f840d565a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0d4f9c97f8c9b402091f7af305a415aaf6c7a06651d729b2121972f840d565a2","first_computed_at":"2026-05-18T01:13:36.750704Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:36.750704Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QXMMtn9wCLdAOfyLJsoFHXrdeLc+uHiYslon+jho0IHIV2s8zEds5uuG0B2NK6ip7KhkQWOYI7ArUhXbDpJJBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:36.751374Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.08196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a4159ffc3ed7b962b0b086e6b91dcc3164ed39ba94e2821127454437d29ebf6f","sha256:ca0864cdb637e17cb465424be56ae5a962682e3108f416d4318df64de043cfda"],"state_sha256":"54b29eab075065a538b62b831a01df1582f493a462e3da3a7012937babadd8a1"}