{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:XE3CKIISSP7N57C6BQ3THC6RWX","short_pith_number":"pith:XE3CKIIS","canonical_record":{"source":{"id":"1510.05291","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-18T18:21:03Z","cross_cats_sorted":[],"title_canon_sha256":"fea713a56c3c1f82e882e37b317018395101bdb3cf20d0ec347fa57bba2d7c96","abstract_canon_sha256":"703bd0ecdf76d0a22b440e3b7e72879dabfe960f66f6ed3807af117b912b1af8"},"schema_version":"1.0"},"canonical_sha256":"b93625211293fedefc5e0c37338bd1b5d3efdff173ade62cf03c00a3c11cff94","source":{"kind":"arxiv","id":"1510.05291","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05291","created_at":"2026-05-18T01:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05291v1","created_at":"2026-05-18T01:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05291","created_at":"2026-05-18T01:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"XE3CKIISSP7N","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XE3CKIISSP7N57C6","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XE3CKIIS","created_at":"2026-05-18T12:29:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:XE3CKIISSP7N57C6BQ3THC6RWX","target":"record","payload":{"canonical_record":{"source":{"id":"1510.05291","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-18T18:21:03Z","cross_cats_sorted":[],"title_canon_sha256":"fea713a56c3c1f82e882e37b317018395101bdb3cf20d0ec347fa57bba2d7c96","abstract_canon_sha256":"703bd0ecdf76d0a22b440e3b7e72879dabfe960f66f6ed3807af117b912b1af8"},"schema_version":"1.0"},"canonical_sha256":"b93625211293fedefc5e0c37338bd1b5d3efdff173ade62cf03c00a3c11cff94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:52.655909Z","signature_b64":"dAXRw60bxIbUf8mXoE+8gehzcxioqjIE4USjz/Y4govflfyu2rrrK0nGA4QRTwu8zjmrfUyYw6Hx25UFxmZhBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b93625211293fedefc5e0c37338bd1b5d3efdff173ade62cf03c00a3c11cff94","last_reissued_at":"2026-05-18T01:29:52.655290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:52.655290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.05291","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":"2026-05-18T01:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U6fn//mh2j4R52BVz6ycnbnR4/qOSTMCPThgq7S8ZDZehLlG/O0HD6a97LgGIfBqWlkBl9Up5iB3a5hNzpvmDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:36:11.708379Z"},"content_sha256":"c32e591538cad87ae5dc74d55969c168fd938eaa5ce6bc828e1efa6afa11b3aa","schema_version":"1.0","event_id":"sha256:c32e591538cad87ae5dc74d55969c168fd938eaa5ce6bc828e1efa6afa11b3aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:XE3CKIISSP7N57C6BQ3THC6RWX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Special Semigroups Derived From an Arbitrary Semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Attila Nagy","submitted_at":"2015-10-18T18:21:03Z","abstract_excerpt":"Let $S$ be a semigroup, $\\Lambda$ a non-empty set and $P$ a mapping of $\\Lambda$ into $S$. The set $S\\times \\Lambda$ together with the operation $\\circ _P$ defined by $(s, \\lambda)\\circ _P(t, \\mu )=(sP(\\lambda)t, \\mu )$ form a semigroup which is denoted by $(S, \\Lambda , \\circ _P)$. Using this construction, we prove a common connection between the semigroups $S$, $S/\\theta$ and $S/\\theta ^*=(S/\\theta)/(\\theta ^*/\\theta)$, where $\\theta$ and $\\theta ^*/\\theta$ are the kernels of the right regular representations of $S$ and $S/\\theta$, respectively. We also prove an embedding theorem for the sem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05291","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":"2026-05-18T01:29:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dvYCszNnW1mrKmbiqIyvXY2bvTrXHCslcVo/ew+uDEAYBO+uYLP673VvEpd1DNvKTJFmbZxmUV1X9exU2PYHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T04:36:11.708926Z"},"content_sha256":"0d7bea5895a84cd2dc0fbd0e4cffb80e0a8af69fb1caf7cc30a651bd75b48569","schema_version":"1.0","event_id":"sha256:0d7bea5895a84cd2dc0fbd0e4cffb80e0a8af69fb1caf7cc30a651bd75b48569"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX/bundle.json","state_url":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XE3CKIISSP7N57C6BQ3THC6RWX/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":"2026-06-07T04:36:11Z","links":{"resolver":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX","bundle":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX/bundle.json","state":"https://pith.science/pith/XE3CKIISSP7N57C6BQ3THC6RWX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XE3CKIISSP7N57C6BQ3THC6RWX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:XE3CKIISSP7N57C6BQ3THC6RWX","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":"703bd0ecdf76d0a22b440e3b7e72879dabfe960f66f6ed3807af117b912b1af8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-18T18:21:03Z","title_canon_sha256":"fea713a56c3c1f82e882e37b317018395101bdb3cf20d0ec347fa57bba2d7c96"},"schema_version":"1.0","source":{"id":"1510.05291","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05291","created_at":"2026-05-18T01:29:52Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05291v1","created_at":"2026-05-18T01:29:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05291","created_at":"2026-05-18T01:29:52Z"},{"alias_kind":"pith_short_12","alias_value":"XE3CKIISSP7N","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_16","alias_value":"XE3CKIISSP7N57C6","created_at":"2026-05-18T12:29:50Z"},{"alias_kind":"pith_short_8","alias_value":"XE3CKIIS","created_at":"2026-05-18T12:29:50Z"}],"graph_snapshots":[{"event_id":"sha256:0d7bea5895a84cd2dc0fbd0e4cffb80e0a8af69fb1caf7cc30a651bd75b48569","target":"graph","created_at":"2026-05-18T01:29:52Z","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":"Let $S$ be a semigroup, $\\Lambda$ a non-empty set and $P$ a mapping of $\\Lambda$ into $S$. The set $S\\times \\Lambda$ together with the operation $\\circ _P$ defined by $(s, \\lambda)\\circ _P(t, \\mu )=(sP(\\lambda)t, \\mu )$ form a semigroup which is denoted by $(S, \\Lambda , \\circ _P)$. Using this construction, we prove a common connection between the semigroups $S$, $S/\\theta$ and $S/\\theta ^*=(S/\\theta)/(\\theta ^*/\\theta)$, where $\\theta$ and $\\theta ^*/\\theta$ are the kernels of the right regular representations of $S$ and $S/\\theta$, respectively. We also prove an embedding theorem for the sem","authors_text":"Attila Nagy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-18T18:21:03Z","title":"On Special Semigroups Derived From an Arbitrary Semigroup"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05291","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:c32e591538cad87ae5dc74d55969c168fd938eaa5ce6bc828e1efa6afa11b3aa","target":"record","created_at":"2026-05-18T01:29:52Z","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":"703bd0ecdf76d0a22b440e3b7e72879dabfe960f66f6ed3807af117b912b1af8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-10-18T18:21:03Z","title_canon_sha256":"fea713a56c3c1f82e882e37b317018395101bdb3cf20d0ec347fa57bba2d7c96"},"schema_version":"1.0","source":{"id":"1510.05291","kind":"arxiv","version":1}},"canonical_sha256":"b93625211293fedefc5e0c37338bd1b5d3efdff173ade62cf03c00a3c11cff94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b93625211293fedefc5e0c37338bd1b5d3efdff173ade62cf03c00a3c11cff94","first_computed_at":"2026-05-18T01:29:52.655290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:52.655290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dAXRw60bxIbUf8mXoE+8gehzcxioqjIE4USjz/Y4govflfyu2rrrK0nGA4QRTwu8zjmrfUyYw6Hx25UFxmZhBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:52.655909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05291","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c32e591538cad87ae5dc74d55969c168fd938eaa5ce6bc828e1efa6afa11b3aa","sha256:0d7bea5895a84cd2dc0fbd0e4cffb80e0a8af69fb1caf7cc30a651bd75b48569"],"state_sha256":"eafb156f2c18ea5e35f28e2e0b613d236efda2033a966bbb4c8daa4a97b1904c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DjtQq+7ICoD+ybOAGnTysVPZOogYTR8XiXh1GT5BXYK0WWDuU5qnMgqfu/oHi3uqBwadpCE6W2emYe1fOg4NBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T04:36:11.711920Z","bundle_sha256":"067f8682dd71fbee3974ea78dd07c993e2078d3c2428776c6b8b9227badf26e0"}}