{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GYEJEJDFRNKPZVA6JJYBGNBLCA","short_pith_number":"pith:GYEJEJDF","canonical_record":{"source":{"id":"1806.07614","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-20T08:57:10Z","cross_cats_sorted":[],"title_canon_sha256":"860a6193bba296751543d6dd050601df75e940bb09c376cce4cade2a0b6dd473","abstract_canon_sha256":"636dfaefed0675da45262068ee199371b7f0745ee9638940e2c56aae78032a9d"},"schema_version":"1.0"},"canonical_sha256":"36089224658b54fcd41e4a7013342b103a1a3044dd0f8772dc12f3ae2c57f461","source":{"kind":"arxiv","id":"1806.07614","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07614","created_at":"2026-05-18T00:12:47Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07614v1","created_at":"2026-05-18T00:12:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07614","created_at":"2026-05-18T00:12:47Z"},{"alias_kind":"pith_short_12","alias_value":"GYEJEJDFRNKP","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GYEJEJDFRNKPZVA6","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GYEJEJDF","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GYEJEJDFRNKPZVA6JJYBGNBLCA","target":"record","payload":{"canonical_record":{"source":{"id":"1806.07614","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-20T08:57:10Z","cross_cats_sorted":[],"title_canon_sha256":"860a6193bba296751543d6dd050601df75e940bb09c376cce4cade2a0b6dd473","abstract_canon_sha256":"636dfaefed0675da45262068ee199371b7f0745ee9638940e2c56aae78032a9d"},"schema_version":"1.0"},"canonical_sha256":"36089224658b54fcd41e4a7013342b103a1a3044dd0f8772dc12f3ae2c57f461","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:47.200454Z","signature_b64":"LTo3fRsQbohnz9RYpzWCGLlGdwK8KEdjcZycAxJ2VBF0vu5qX9iZ7dS90BR9oI4ZvEeEvkwZiMw05stZMiJwAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36089224658b54fcd41e4a7013342b103a1a3044dd0f8772dc12f3ae2c57f461","last_reissued_at":"2026-05-18T00:12:47.199811Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:47.199811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.07614","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":"2026-05-18T00:12:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9CkGQQ4GuhhNxmNCZSRx9eoc1aW5YQd8vO7O1JaigWIulx+VgnO0a13+nCkNZn7sxVBXEidBpv+so9ndiam+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:08:25.111973Z"},"content_sha256":"9636818bf93769b27a88b68a4c3ca14065dd11c5edf73aa00bc5592653d103f7","schema_version":"1.0","event_id":"sha256:9636818bf93769b27a88b68a4c3ca14065dd11c5edf73aa00bc5592653d103f7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GYEJEJDFRNKPZVA6JJYBGNBLCA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two-sided wreath product done right","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Michal Botur, Tomasz Kowalski","submitted_at":"2018-06-20T08:57:10Z","abstract_excerpt":"We investigate a semigroup construction related to the two-sided wreath product. It encompasses a range of known constructions and gives a slightly finer version of the decomposition in the Krohn-Rhodes Theorem, in which the three-element flip-flop is replaced by the two-element semilattice. We develop foundations of the theory of our construction, showing in the process that it naturally combines ideas from semigroup theory (wreath products), category theory (Grothendieck construction), and ordered structures (residuated lattices)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07614","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":"2026-05-18T00:12:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VL407LquP5eXba0Ov65R0imQ2zASCHPal9DQ+IHA0VqKxZlRo++djha21ckTlusLkQrEZga6kzKhs71Y8lKvAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T04:08:25.112329Z"},"content_sha256":"5630025a4fb8e492c45913d5462f1024d6c04a408c38bd32617dad9eaea74ec5","schema_version":"1.0","event_id":"sha256:5630025a4fb8e492c45913d5462f1024d6c04a408c38bd32617dad9eaea74ec5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GYEJEJDFRNKPZVA6JJYBGNBLCA/bundle.json","state_url":"https://pith.science/pith/GYEJEJDFRNKPZVA6JJYBGNBLCA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GYEJEJDFRNKPZVA6JJYBGNBLCA/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":"2026-06-04T04:08:25Z","links":{"resolver":"https://pith.science/pith/GYEJEJDFRNKPZVA6JJYBGNBLCA","bundle":"https://pith.science/pith/GYEJEJDFRNKPZVA6JJYBGNBLCA/bundle.json","state":"https://pith.science/pith/GYEJEJDFRNKPZVA6JJYBGNBLCA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GYEJEJDFRNKPZVA6JJYBGNBLCA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GYEJEJDFRNKPZVA6JJYBGNBLCA","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":"636dfaefed0675da45262068ee199371b7f0745ee9638940e2c56aae78032a9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-20T08:57:10Z","title_canon_sha256":"860a6193bba296751543d6dd050601df75e940bb09c376cce4cade2a0b6dd473"},"schema_version":"1.0","source":{"id":"1806.07614","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07614","created_at":"2026-05-18T00:12:47Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07614v1","created_at":"2026-05-18T00:12:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07614","created_at":"2026-05-18T00:12:47Z"},{"alias_kind":"pith_short_12","alias_value":"GYEJEJDFRNKP","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GYEJEJDFRNKPZVA6","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GYEJEJDF","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:5630025a4fb8e492c45913d5462f1024d6c04a408c38bd32617dad9eaea74ec5","target":"graph","created_at":"2026-05-18T00:12:47Z","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 investigate a semigroup construction related to the two-sided wreath product. It encompasses a range of known constructions and gives a slightly finer version of the decomposition in the Krohn-Rhodes Theorem, in which the three-element flip-flop is replaced by the two-element semilattice. We develop foundations of the theory of our construction, showing in the process that it naturally combines ideas from semigroup theory (wreath products), category theory (Grothendieck construction), and ordered structures (residuated lattices).","authors_text":"Michal Botur, Tomasz Kowalski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-20T08:57:10Z","title":"Two-sided wreath product done right"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07614","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":"sha256:9636818bf93769b27a88b68a4c3ca14065dd11c5edf73aa00bc5592653d103f7","target":"record","created_at":"2026-05-18T00:12:47Z","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":"636dfaefed0675da45262068ee199371b7f0745ee9638940e2c56aae78032a9d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2018-06-20T08:57:10Z","title_canon_sha256":"860a6193bba296751543d6dd050601df75e940bb09c376cce4cade2a0b6dd473"},"schema_version":"1.0","source":{"id":"1806.07614","kind":"arxiv","version":1}},"canonical_sha256":"36089224658b54fcd41e4a7013342b103a1a3044dd0f8772dc12f3ae2c57f461","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36089224658b54fcd41e4a7013342b103a1a3044dd0f8772dc12f3ae2c57f461","first_computed_at":"2026-05-18T00:12:47.199811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:47.199811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LTo3fRsQbohnz9RYpzWCGLlGdwK8KEdjcZycAxJ2VBF0vu5qX9iZ7dS90BR9oI4ZvEeEvkwZiMw05stZMiJwAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:47.200454Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07614","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9636818bf93769b27a88b68a4c3ca14065dd11c5edf73aa00bc5592653d103f7","sha256:5630025a4fb8e492c45913d5462f1024d6c04a408c38bd32617dad9eaea74ec5"],"state_sha256":"509a65cc0d6797fb7cda9ff0123e371912f193161f085adf98589b9137cbbe83"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tyAvFgM9b9h/Cmyq63JQY66vTGSaeI0UO1dYVgCZoxRSHPS4qWK88kQAm2B6NRtKLxJjPxbZHAQ5iG8ULek3DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T04:08:25.114476Z","bundle_sha256":"e52199ee0983ca8cc6247ea99c9085bf8c8eca67cdefc3ee58fde6b5b2351739"}}