{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:UBKDCIIHW2OVFZFVCLEEUN4E7Q","short_pith_number":"pith:UBKDCIIH","canonical_record":{"source":{"id":"1904.04255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-08T17:33:25Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"db1d313b328704ef32edd735153f72b219c21d8cdd68cac03610fc9de8733087","abstract_canon_sha256":"2aab85fac57f290a01d93dbdaef2868d526abe28f9a113098efbab7b51fce2a9"},"schema_version":"1.0"},"canonical_sha256":"a054312107b69d52e4b512c84a3784fc338e708f1878dc7b1a4f5bcdf01b0031","source":{"kind":"arxiv","id":"1904.04255","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04255","created_at":"2026-05-17T23:48:59Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04255v1","created_at":"2026-05-17T23:48:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04255","created_at":"2026-05-17T23:48:59Z"},{"alias_kind":"pith_short_12","alias_value":"UBKDCIIHW2OV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UBKDCIIHW2OVFZFV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UBKDCIIH","created_at":"2026-05-18T12:33:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:UBKDCIIHW2OVFZFVCLEEUN4E7Q","target":"record","payload":{"canonical_record":{"source":{"id":"1904.04255","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-08T17:33:25Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"db1d313b328704ef32edd735153f72b219c21d8cdd68cac03610fc9de8733087","abstract_canon_sha256":"2aab85fac57f290a01d93dbdaef2868d526abe28f9a113098efbab7b51fce2a9"},"schema_version":"1.0"},"canonical_sha256":"a054312107b69d52e4b512c84a3784fc338e708f1878dc7b1a4f5bcdf01b0031","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:48:59.433033Z","signature_b64":"JksahjEmOtWaxfFsyYi1BkE/P61JlZlTYyNG6yPABoiTxbdSn17MbvAYcRU7jPW+5LccTR1oH/E4JUzTAwZ8CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a054312107b69d52e4b512c84a3784fc338e708f1878dc7b1a4f5bcdf01b0031","last_reissued_at":"2026-05-17T23:48:59.432665Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:48:59.432665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1904.04255","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":"2026-05-17T23:48:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oPvNipYSbz3i5+r7xI22eNR1jcnsLWI9POv3d/PAG2NdKFWCA6DQa947K1WzbMcVRPLldUGW7coagXcz3XpwDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:13:59.949442Z"},"content_sha256":"2d1e190f7bad9ef6a259807e5235bb8363195a787e221fbba04ae504dbbfe3fa","schema_version":"1.0","event_id":"sha256:2d1e190f7bad9ef6a259807e5235bb8363195a787e221fbba04ae504dbbfe3fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:UBKDCIIHW2OVFZFVCLEEUN4E7Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Refinement monoids and adaptable separated graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.RA","authors_text":"E. Pardo, J. Bosa, P. Ara","submitted_at":"2019-04-08T17:33:25Z","abstract_excerpt":"We define a subclass of separated graphs, the class of adaptable separated graphs, and study their associated monoids. We show that these monoids are primely generated conical refinement monoids, and we explicitly determine their associated I-systems. We also show that any finitely generated conical refinement monoid can be represented as the monoid of an adaptable separated graph. These results provide the first step toward an affirmative answer to the Realization Problem for von Neumann regular rings, in the finitely generated case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04255","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":"2026-05-17T23:48:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"29Vn2pCm8nfwBEVhWmO1HZsQdYCyrqwE0Fu4cDf5XUpF7gPVdstThqXCEqr/VbabQtIiDov0FLlokjsGth6ICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:13:59.949788Z"},"content_sha256":"cbd2ad6665ea1d92c385fe6c8bb41ce3ffdac25d6ffbc11838735ba25d3e6344","schema_version":"1.0","event_id":"sha256:cbd2ad6665ea1d92c385fe6c8bb41ce3ffdac25d6ffbc11838735ba25d3e6344"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UBKDCIIHW2OVFZFVCLEEUN4E7Q/bundle.json","state_url":"https://pith.science/pith/UBKDCIIHW2OVFZFVCLEEUN4E7Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UBKDCIIHW2OVFZFVCLEEUN4E7Q/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":"2026-06-03T02:13:59Z","links":{"resolver":"https://pith.science/pith/UBKDCIIHW2OVFZFVCLEEUN4E7Q","bundle":"https://pith.science/pith/UBKDCIIHW2OVFZFVCLEEUN4E7Q/bundle.json","state":"https://pith.science/pith/UBKDCIIHW2OVFZFVCLEEUN4E7Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UBKDCIIHW2OVFZFVCLEEUN4E7Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:UBKDCIIHW2OVFZFVCLEEUN4E7Q","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":"2aab85fac57f290a01d93dbdaef2868d526abe28f9a113098efbab7b51fce2a9","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-08T17:33:25Z","title_canon_sha256":"db1d313b328704ef32edd735153f72b219c21d8cdd68cac03610fc9de8733087"},"schema_version":"1.0","source":{"id":"1904.04255","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.04255","created_at":"2026-05-17T23:48:59Z"},{"alias_kind":"arxiv_version","alias_value":"1904.04255v1","created_at":"2026-05-17T23:48:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.04255","created_at":"2026-05-17T23:48:59Z"},{"alias_kind":"pith_short_12","alias_value":"UBKDCIIHW2OV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_16","alias_value":"UBKDCIIHW2OVFZFV","created_at":"2026-05-18T12:33:30Z"},{"alias_kind":"pith_short_8","alias_value":"UBKDCIIH","created_at":"2026-05-18T12:33:30Z"}],"graph_snapshots":[{"event_id":"sha256:cbd2ad6665ea1d92c385fe6c8bb41ce3ffdac25d6ffbc11838735ba25d3e6344","target":"graph","created_at":"2026-05-17T23:48:59Z","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 define a subclass of separated graphs, the class of adaptable separated graphs, and study their associated monoids. We show that these monoids are primely generated conical refinement monoids, and we explicitly determine their associated I-systems. We also show that any finitely generated conical refinement monoid can be represented as the monoid of an adaptable separated graph. These results provide the first step toward an affirmative answer to the Realization Problem for von Neumann regular rings, in the finitely generated case.","authors_text":"E. Pardo, J. Bosa, P. Ara","cross_cats":["math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-08T17:33:25Z","title":"Refinement monoids and adaptable separated graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.04255","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":"sha256:2d1e190f7bad9ef6a259807e5235bb8363195a787e221fbba04ae504dbbfe3fa","target":"record","created_at":"2026-05-17T23:48:59Z","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":"2aab85fac57f290a01d93dbdaef2868d526abe28f9a113098efbab7b51fce2a9","cross_cats_sorted":["math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-04-08T17:33:25Z","title_canon_sha256":"db1d313b328704ef32edd735153f72b219c21d8cdd68cac03610fc9de8733087"},"schema_version":"1.0","source":{"id":"1904.04255","kind":"arxiv","version":1}},"canonical_sha256":"a054312107b69d52e4b512c84a3784fc338e708f1878dc7b1a4f5bcdf01b0031","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a054312107b69d52e4b512c84a3784fc338e708f1878dc7b1a4f5bcdf01b0031","first_computed_at":"2026-05-17T23:48:59.432665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:59.432665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JksahjEmOtWaxfFsyYi1BkE/P61JlZlTYyNG6yPABoiTxbdSn17MbvAYcRU7jPW+5LccTR1oH/E4JUzTAwZ8CA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:59.433033Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.04255","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d1e190f7bad9ef6a259807e5235bb8363195a787e221fbba04ae504dbbfe3fa","sha256:cbd2ad6665ea1d92c385fe6c8bb41ce3ffdac25d6ffbc11838735ba25d3e6344"],"state_sha256":"af0c56821f6aa3c98c6c81451dc7105426a9c7d210ac3bfaa097f79e5f8259ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X9dMqliRaNQOuWiRTlmV6ZSHfm3wTruahQ4iGK98b6+HW6U0MFCjxkxoyXl1fZZ7C4r27A3hGzQn+42tr33DBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:13:59.951783Z","bundle_sha256":"9d9d9559a53c7c2f0c006328789fea67e9b1b54097ad43c4f29b2268596f416a"}}