{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Z3BG4LX4UZI3GQFNN3CNOZ3IW5","short_pith_number":"pith:Z3BG4LX4","canonical_record":{"source":{"id":"1309.3884","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-16T10:04:20Z","cross_cats_sorted":[],"title_canon_sha256":"7ff4fbe825a63f1168e5af45960c8fd1c88aa5307d44bebe1b192ef6f5d3b019","abstract_canon_sha256":"8a0d7e7e61669f0a4dcccd99f93e954631628c130de52b9543513757a63274ea"},"schema_version":"1.0"},"canonical_sha256":"cec26e2efca651b340ad6ec4d76768b76ed79a083e2df197892a669e805f3548","source":{"kind":"arxiv","id":"1309.3884","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3884","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3884v2","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3884","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"Z3BG4LX4UZI3","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z3BG4LX4UZI3GQFN","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z3BG4LX4","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Z3BG4LX4UZI3GQFNN3CNOZ3IW5","target":"record","payload":{"canonical_record":{"source":{"id":"1309.3884","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-16T10:04:20Z","cross_cats_sorted":[],"title_canon_sha256":"7ff4fbe825a63f1168e5af45960c8fd1c88aa5307d44bebe1b192ef6f5d3b019","abstract_canon_sha256":"8a0d7e7e61669f0a4dcccd99f93e954631628c130de52b9543513757a63274ea"},"schema_version":"1.0"},"canonical_sha256":"cec26e2efca651b340ad6ec4d76768b76ed79a083e2df197892a669e805f3548","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:31:36.165935Z","signature_b64":"wafT9c0yeVJFYFekNtEIu/bkWh5MKFSlnQ+M8gz1fxUAFR1MJJOJLRTBMLIVM/5qH7Q8jRKK4u/znmepO0zPBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cec26e2efca651b340ad6ec4d76768b76ed79a083e2df197892a669e805f3548","last_reissued_at":"2026-05-18T02:31:36.165248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:31:36.165248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.3884","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"04JkIL1gexRP4Ql8LUt/+v1Y7yTvy9lqWjvji+3HRQFwIkKlMcIZeUvrEDoXlzMo6kL2uJUMXg4AeFFl7889Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:04:58.977266Z"},"content_sha256":"187fcc39a16cae3e174693d8819b4b5b9cd150bc0456e20a03a08e726d233fae","schema_version":"1.0","event_id":"sha256:187fcc39a16cae3e174693d8819b4b5b9cd150bc0456e20a03a08e726d233fae"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Z3BG4LX4UZI3GQFNN3CNOZ3IW5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finitely Presented Monoids and Algebras defined by Permutation Relations of Abelian Type, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Eric Jespers, Ferran Cedo, Georg Klein","submitted_at":"2013-09-16T10:04:20Z","abstract_excerpt":"The class of finitely presented algebras A over a field K with a set of generators x_{1},...,x_{n} and defined by homogeneous relations of the form x_{i_1}x_{i_2}...x_{i_l}=x_{sigma(i_1)}x_{sigma(i_2)}...x_{sigma(i_l)}, where l geq 2 is a given integer and sigma runs through a subgroup H of Sym_n, is considered. It is shown that the underlying monoid S_{n,l}(H)= <x_1,x_2,...,x_n|x_{i_1}x_{i_2}...x_{i_l}=x_{sigma(i_1)}x_{sigma(i_2)}...x_{\\sigma (i_l)}, sigma in H, i_1,...,i_l in {1,...,n}> is cancellative if and only if H is semiregular and abelian. In this case S_{n,l}(H) is a submonoid of its"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3884","kind":"arxiv","version":2},"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":"2026-05-18T02:31:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4XjBpx219Po4k75ghABRZkWOf1YON1mQqBEqz/cGu8QaYIYjGNs3kjTXxADiC7Cuv9IAIhhlBG6gbstDcG8QDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T09:04:58.977813Z"},"content_sha256":"1b248d2a71e1b6c2da1bad1d205392061f90d801dd5e63ad6c823c5662d02ef2","schema_version":"1.0","event_id":"sha256:1b248d2a71e1b6c2da1bad1d205392061f90d801dd5e63ad6c823c5662d02ef2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3BG4LX4UZI3GQFNN3CNOZ3IW5/bundle.json","state_url":"https://pith.science/pith/Z3BG4LX4UZI3GQFNN3CNOZ3IW5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3BG4LX4UZI3GQFNN3CNOZ3IW5/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":"2026-06-03T09:04:58Z","links":{"resolver":"https://pith.science/pith/Z3BG4LX4UZI3GQFNN3CNOZ3IW5","bundle":"https://pith.science/pith/Z3BG4LX4UZI3GQFNN3CNOZ3IW5/bundle.json","state":"https://pith.science/pith/Z3BG4LX4UZI3GQFNN3CNOZ3IW5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3BG4LX4UZI3GQFNN3CNOZ3IW5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z3BG4LX4UZI3GQFNN3CNOZ3IW5","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":"8a0d7e7e61669f0a4dcccd99f93e954631628c130de52b9543513757a63274ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-16T10:04:20Z","title_canon_sha256":"7ff4fbe825a63f1168e5af45960c8fd1c88aa5307d44bebe1b192ef6f5d3b019"},"schema_version":"1.0","source":{"id":"1309.3884","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.3884","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"arxiv_version","alias_value":"1309.3884v2","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.3884","created_at":"2026-05-18T02:31:36Z"},{"alias_kind":"pith_short_12","alias_value":"Z3BG4LX4UZI3","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z3BG4LX4UZI3GQFN","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z3BG4LX4","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:1b248d2a71e1b6c2da1bad1d205392061f90d801dd5e63ad6c823c5662d02ef2","target":"graph","created_at":"2026-05-18T02:31:36Z","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":"The class of finitely presented algebras A over a field K with a set of generators x_{1},...,x_{n} and defined by homogeneous relations of the form x_{i_1}x_{i_2}...x_{i_l}=x_{sigma(i_1)}x_{sigma(i_2)}...x_{sigma(i_l)}, where l geq 2 is a given integer and sigma runs through a subgroup H of Sym_n, is considered. It is shown that the underlying monoid S_{n,l}(H)= <x_1,x_2,...,x_n|x_{i_1}x_{i_2}...x_{i_l}=x_{sigma(i_1)}x_{sigma(i_2)}...x_{\\sigma (i_l)}, sigma in H, i_1,...,i_l in {1,...,n}> is cancellative if and only if H is semiregular and abelian. In this case S_{n,l}(H) is a submonoid of its","authors_text":"Eric Jespers, Ferran Cedo, Georg Klein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-16T10:04:20Z","title":"Finitely Presented Monoids and Algebras defined by Permutation Relations of Abelian Type, II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.3884","kind":"arxiv","version":2},"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":"sha256:187fcc39a16cae3e174693d8819b4b5b9cd150bc0456e20a03a08e726d233fae","target":"record","created_at":"2026-05-18T02:31:36Z","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":"8a0d7e7e61669f0a4dcccd99f93e954631628c130de52b9543513757a63274ea","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2013-09-16T10:04:20Z","title_canon_sha256":"7ff4fbe825a63f1168e5af45960c8fd1c88aa5307d44bebe1b192ef6f5d3b019"},"schema_version":"1.0","source":{"id":"1309.3884","kind":"arxiv","version":2}},"canonical_sha256":"cec26e2efca651b340ad6ec4d76768b76ed79a083e2df197892a669e805f3548","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cec26e2efca651b340ad6ec4d76768b76ed79a083e2df197892a669e805f3548","first_computed_at":"2026-05-18T02:31:36.165248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:31:36.165248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wafT9c0yeVJFYFekNtEIu/bkWh5MKFSlnQ+M8gz1fxUAFR1MJJOJLRTBMLIVM/5qH7Q8jRKK4u/znmepO0zPBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:31:36.165935Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.3884","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:187fcc39a16cae3e174693d8819b4b5b9cd150bc0456e20a03a08e726d233fae","sha256:1b248d2a71e1b6c2da1bad1d205392061f90d801dd5e63ad6c823c5662d02ef2"],"state_sha256":"c9aedabecdc7a15a80e4693058ee4e20604d8a0641ff6192d0a3e6d0f0a7b167"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/xPQW068vc6YnYdVZYag3RC0Sng2/hgZ/6CtW0Z/3gXazhWUvTEiEJTQ+4BVYVvq/qQFVEo5JfmEJXoUEEfoCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T09:04:58.980501Z","bundle_sha256":"0dd9742909ab594087ce3132da6e4becf726477227ea6459dc392e5bffb616ba"}}