{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:UCO6UN5JONQGBCUJEPNHAEQGOY","short_pith_number":"pith:UCO6UN5J","canonical_record":{"source":{"id":"1301.1568","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-08T15:41:05Z","cross_cats_sorted":[],"title_canon_sha256":"034a14cb9cef6ec8f3abd3cfd9c92020e150b1e78c1c6db9e44348050f37441e","abstract_canon_sha256":"3f23129d9889602272096801cb73815cc40ca8a9562c650923a27fd78a7a0f2e"},"schema_version":"1.0"},"canonical_sha256":"a09dea37a97360608a8923da7012067602f1bd4e44957a1590bea2a78785c84a","source":{"kind":"arxiv","id":"1301.1568","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1568","created_at":"2026-05-18T00:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1568v3","created_at":"2026-05-18T00:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1568","created_at":"2026-05-18T00:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"UCO6UN5JONQG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UCO6UN5JONQGBCUJ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UCO6UN5J","created_at":"2026-05-18T12:28:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:UCO6UN5JONQGBCUJEPNHAEQGOY","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1568","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-08T15:41:05Z","cross_cats_sorted":[],"title_canon_sha256":"034a14cb9cef6ec8f3abd3cfd9c92020e150b1e78c1c6db9e44348050f37441e","abstract_canon_sha256":"3f23129d9889602272096801cb73815cc40ca8a9562c650923a27fd78a7a0f2e"},"schema_version":"1.0"},"canonical_sha256":"a09dea37a97360608a8923da7012067602f1bd4e44957a1590bea2a78785c84a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:54.127241Z","signature_b64":"Eoh50ybk9NqYaegZvTKvQtihO7GvbniecMF1dKWLmheLmrsvNUBvtYgbLAb2RpCLH+lHPDCs+W+km2L2NdQ3Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a09dea37a97360608a8923da7012067602f1bd4e44957a1590bea2a78785c84a","last_reissued_at":"2026-05-18T00:41:54.126510Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:54.126510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1568","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IG6lBl9TdZhLGK5vsO7qZXKGqZazfnO/3InmodFOItgIi09ZqtTdET9ODZEczje6iNtNrPEomEnU1H04uRUGDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:13:19.760824Z"},"content_sha256":"ebbb149a3a2e5fd01d6d0d012ae3b71eda33705e658a987e95cf77ab2dcea111","schema_version":"1.0","event_id":"sha256:ebbb149a3a2e5fd01d6d0d012ae3b71eda33705e658a987e95cf77ab2dcea111"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:UCO6UN5JONQGBCUJEPNHAEQGOY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conjugation in Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ant\\'onio Malheiro, Janusz Konieczny, Jo\\~ao Ara\\'ujo","submitted_at":"2013-01-08T15:41:05Z","abstract_excerpt":"The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing definitions, characterize the conjugacy in various semigroups of transformations on a set, and count the number of conjugacy classes in these semigroups when"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1568","kind":"arxiv","version":3},"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":"2026-05-18T00:41:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XsGQkKRSds/V69h5YRw0V0kLezjgSNQsDlL8a6epB5gAOarlQD40Ojamg0WFojfV/pVsxscf+WtoFjqAEUOCAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T03:13:19.761509Z"},"content_sha256":"a5da0656f525dd5cb9c5d466ec7536af042a3106e167e7eb61bd62233ba2ab3c","schema_version":"1.0","event_id":"sha256:a5da0656f525dd5cb9c5d466ec7536af042a3106e167e7eb61bd62233ba2ab3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UCO6UN5JONQGBCUJEPNHAEQGOY/bundle.json","state_url":"https://pith.science/pith/UCO6UN5JONQGBCUJEPNHAEQGOY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UCO6UN5JONQGBCUJEPNHAEQGOY/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":"2026-06-12T03:13:19Z","links":{"resolver":"https://pith.science/pith/UCO6UN5JONQGBCUJEPNHAEQGOY","bundle":"https://pith.science/pith/UCO6UN5JONQGBCUJEPNHAEQGOY/bundle.json","state":"https://pith.science/pith/UCO6UN5JONQGBCUJEPNHAEQGOY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UCO6UN5JONQGBCUJEPNHAEQGOY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UCO6UN5JONQGBCUJEPNHAEQGOY","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":"3f23129d9889602272096801cb73815cc40ca8a9562c650923a27fd78a7a0f2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-08T15:41:05Z","title_canon_sha256":"034a14cb9cef6ec8f3abd3cfd9c92020e150b1e78c1c6db9e44348050f37441e"},"schema_version":"1.0","source":{"id":"1301.1568","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1568","created_at":"2026-05-18T00:41:54Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1568v3","created_at":"2026-05-18T00:41:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1568","created_at":"2026-05-18T00:41:54Z"},{"alias_kind":"pith_short_12","alias_value":"UCO6UN5JONQG","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UCO6UN5JONQGBCUJ","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UCO6UN5J","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:a5da0656f525dd5cb9c5d466ec7536af042a3106e167e7eb61bd62233ba2ab3c","target":"graph","created_at":"2026-05-18T00:41:54Z","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":"The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been several attempts to extend the notion of conjugacy to semigroups. In this paper, we present a new definition of conjugacy that can be applied to an arbitrary semigroup and it does not reduce to the universal relation in semigroups with a zero. We compare the new notion of conjugacy with existing definitions, characterize the conjugacy in various semigroups of transformations on a set, and count the number of conjugacy classes in these semigroups when","authors_text":"Ant\\'onio Malheiro, Janusz Konieczny, Jo\\~ao Ara\\'ujo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-08T15:41:05Z","title":"Conjugation in Semigroups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1568","kind":"arxiv","version":3},"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:ebbb149a3a2e5fd01d6d0d012ae3b71eda33705e658a987e95cf77ab2dcea111","target":"record","created_at":"2026-05-18T00:41:54Z","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":"3f23129d9889602272096801cb73815cc40ca8a9562c650923a27fd78a7a0f2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-08T15:41:05Z","title_canon_sha256":"034a14cb9cef6ec8f3abd3cfd9c92020e150b1e78c1c6db9e44348050f37441e"},"schema_version":"1.0","source":{"id":"1301.1568","kind":"arxiv","version":3}},"canonical_sha256":"a09dea37a97360608a8923da7012067602f1bd4e44957a1590bea2a78785c84a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a09dea37a97360608a8923da7012067602f1bd4e44957a1590bea2a78785c84a","first_computed_at":"2026-05-18T00:41:54.126510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:54.126510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Eoh50ybk9NqYaegZvTKvQtihO7GvbniecMF1dKWLmheLmrsvNUBvtYgbLAb2RpCLH+lHPDCs+W+km2L2NdQ3Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:54.127241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1568","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ebbb149a3a2e5fd01d6d0d012ae3b71eda33705e658a987e95cf77ab2dcea111","sha256:a5da0656f525dd5cb9c5d466ec7536af042a3106e167e7eb61bd62233ba2ab3c"],"state_sha256":"cafc797eedcdfa84d9157d9947479ca3afb2bee4f1e8378f1243b7a951e245de"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U/XaUakbB97r0IDPG8bj2+BlOIAop8LBe8zYShP1/t13J1rSxf8SV7bXy+YNV43I9RpP0H8M1hDbxr4KGtJnAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T03:13:19.766143Z","bundle_sha256":"039d6cefa5d3909e16caaa259abfd96e5e4a71d585caaa9bbdc631079ff828d7"}}