{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RP5BHTV4DSHNCC2DAZ3ASGHY2H","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":"d54b29fa13cebc0849dc7fa426ae4e23bd8bf73cfdc2b9bd6fb0b05e6477c6b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-05T07:02:34Z","title_canon_sha256":"d35d60df6109f567b157cb7cba0fec8af117474c9053cbbfa0849ceff2253ebc"},"schema_version":"1.0","source":{"id":"1308.0895","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0895","created_at":"2026-05-18T03:16:41Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0895v1","created_at":"2026-05-18T03:16:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0895","created_at":"2026-05-18T03:16:41Z"},{"alias_kind":"pith_short_12","alias_value":"RP5BHTV4DSHN","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RP5BHTV4DSHNCC2D","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RP5BHTV4","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:e81738795b51221ddddf4820ffe3871eabd8305895317d33cab3f910b2efc29f","target":"graph","created_at":"2026-05-18T03:16:41Z","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":"In this paper, we define a new structure analogous to group, called partial group. This structure concerns the partial stability by the composition inner law. We generalize the three isomorphism theorems for groups to partial groups.","authors_text":"Adlene Ayadi, Yahya N'Dao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-05T07:02:34Z","title":"Generalization of isomorphism theorems groups to Partial groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0895","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":"sha256:4ff2a464d644dd501e37db127f2258078c921c9b4868a583a2152a297257d7e1","target":"record","created_at":"2026-05-18T03:16:41Z","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":"d54b29fa13cebc0849dc7fa426ae4e23bd8bf73cfdc2b9bd6fb0b05e6477c6b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-05T07:02:34Z","title_canon_sha256":"d35d60df6109f567b157cb7cba0fec8af117474c9053cbbfa0849ceff2253ebc"},"schema_version":"1.0","source":{"id":"1308.0895","kind":"arxiv","version":1}},"canonical_sha256":"8bfa13cebc1c8ed10b4306760918f8d1fd2ef0308c3c9c70b64765aa2fcad4b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8bfa13cebc1c8ed10b4306760918f8d1fd2ef0308c3c9c70b64765aa2fcad4b0","first_computed_at":"2026-05-18T03:16:41.216682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:41.216682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f9mnn5EaGww3XFAihOIjEb0/EOVjWd2y6UgD70yRVuMlxcfp4U65NqFhtZqJtGjEi1QwQatjEELrDjqRSbXgAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:41.217340Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0895","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4ff2a464d644dd501e37db127f2258078c921c9b4868a583a2152a297257d7e1","sha256:e81738795b51221ddddf4820ffe3871eabd8305895317d33cab3f910b2efc29f"],"state_sha256":"2283c82d5a5abf0c23cf25075e80f594861be827f6057483a279af7723d97e38"}