{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RU6KPHTANULNBJBKJUULPD5L5L","short_pith_number":"pith:RU6KPHTA","canonical_record":{"source":{"id":"1907.06680","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-11T07:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"b0703b7ba41cbf25c9569599c8223d1349a7cf16f5c1d507f3cc2e51ab2402a7","abstract_canon_sha256":"8127b904415c80d72c8cfe59040e4e8eb1c127aaed100961b8646073f222726f"},"schema_version":"1.0"},"canonical_sha256":"8d3ca79e606d16d0a42a4d28b78fabeaf722b930ebcdf6e705352f3cde7e9852","source":{"kind":"arxiv","id":"1907.06680","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.06680","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"arxiv_version","alias_value":"1907.06680v1","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.06680","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"pith_short_12","alias_value":"RU6KPHTANULN","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RU6KPHTANULNBJBK","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RU6KPHTA","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RU6KPHTANULNBJBKJUULPD5L5L","target":"record","payload":{"canonical_record":{"source":{"id":"1907.06680","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-11T07:32:19Z","cross_cats_sorted":[],"title_canon_sha256":"b0703b7ba41cbf25c9569599c8223d1349a7cf16f5c1d507f3cc2e51ab2402a7","abstract_canon_sha256":"8127b904415c80d72c8cfe59040e4e8eb1c127aaed100961b8646073f222726f"},"schema_version":"1.0"},"canonical_sha256":"8d3ca79e606d16d0a42a4d28b78fabeaf722b930ebcdf6e705352f3cde7e9852","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:29.433720Z","signature_b64":"ipinBheEobS7sqAvcY35hsIl1zg/zUfpnukTquOFerBMUvq9yA1WrSnJosuFguD5NFuwgwg+T6iULaRyJsijAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d3ca79e606d16d0a42a4d28b78fabeaf722b930ebcdf6e705352f3cde7e9852","last_reissued_at":"2026-05-17T23:40:29.433091Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:29.433091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.06680","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":"2026-05-17T23:40:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jxk091QqiyUJoxzh36nX/NzXxqgM9Ngy7XHmeB3AibtV+WFuq9RDqJVF/hz/djJ0mYCOpY0qEwU7blscnx1fAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:08:07.808015Z"},"content_sha256":"9fad6d406f1b7025d1cbb28a966246bc6d4ba30b0770b73f9bbfb4316fa9d982","schema_version":"1.0","event_id":"sha256:9fad6d406f1b7025d1cbb28a966246bc6d4ba30b0770b73f9bbfb4316fa9d982"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RU6KPHTANULNBJBKJUULPD5L5L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gr\\\"obner--Shirshov bases for commutative dialgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Guangliang Zhang, Yuqun Chen","submitted_at":"2019-07-11T07:32:19Z","abstract_excerpt":"We establish Gr\\\"obner--Shirshov bases theory for commutative dialgebras. We show that for any ideal $I$ of $Di[X]$, $I$ has a unique reduced Gr\\\"obner--Shirshov basis, where $Di[X]$ is the free commutative dialgebra generated by a set $X$, in particular, $I$ has a finite Gr\\\"obner--Shirshov basis if $X$ is finite. As applications, we give normal forms of elements of an arbitrary commutative disemigroup, prove that the word problem for finitely presented commutative dialgebras (disemigroups) is solvable, and show that if $X$ is finite, then the problem whether two ideals of $Di[X]$ are identic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06680","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":"2026-05-17T23:40:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jLY8EyaX+yS+EieIDnNe1kYRRKyfJu09QmfCktmFcj2GeoTg7WHC31zLfJWbIiv4voBkJN8ZXElz/gBjlLD2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T20:08:07.808703Z"},"content_sha256":"b9e5d73befbe9607f9221726d8a96d0fff9e62b2c99b3b7e56da1b9f55973b9e","schema_version":"1.0","event_id":"sha256:b9e5d73befbe9607f9221726d8a96d0fff9e62b2c99b3b7e56da1b9f55973b9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RU6KPHTANULNBJBKJUULPD5L5L/bundle.json","state_url":"https://pith.science/pith/RU6KPHTANULNBJBKJUULPD5L5L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RU6KPHTANULNBJBKJUULPD5L5L/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":"2026-05-25T20:08:07Z","links":{"resolver":"https://pith.science/pith/RU6KPHTANULNBJBKJUULPD5L5L","bundle":"https://pith.science/pith/RU6KPHTANULNBJBKJUULPD5L5L/bundle.json","state":"https://pith.science/pith/RU6KPHTANULNBJBKJUULPD5L5L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RU6KPHTANULNBJBKJUULPD5L5L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RU6KPHTANULNBJBKJUULPD5L5L","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":"8127b904415c80d72c8cfe59040e4e8eb1c127aaed100961b8646073f222726f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-11T07:32:19Z","title_canon_sha256":"b0703b7ba41cbf25c9569599c8223d1349a7cf16f5c1d507f3cc2e51ab2402a7"},"schema_version":"1.0","source":{"id":"1907.06680","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.06680","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"arxiv_version","alias_value":"1907.06680v1","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.06680","created_at":"2026-05-17T23:40:29Z"},{"alias_kind":"pith_short_12","alias_value":"RU6KPHTANULN","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"RU6KPHTANULNBJBK","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"RU6KPHTA","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:b9e5d73befbe9607f9221726d8a96d0fff9e62b2c99b3b7e56da1b9f55973b9e","target":"graph","created_at":"2026-05-17T23:40:29Z","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 establish Gr\\\"obner--Shirshov bases theory for commutative dialgebras. We show that for any ideal $I$ of $Di[X]$, $I$ has a unique reduced Gr\\\"obner--Shirshov basis, where $Di[X]$ is the free commutative dialgebra generated by a set $X$, in particular, $I$ has a finite Gr\\\"obner--Shirshov basis if $X$ is finite. As applications, we give normal forms of elements of an arbitrary commutative disemigroup, prove that the word problem for finitely presented commutative dialgebras (disemigroups) is solvable, and show that if $X$ is finite, then the problem whether two ideals of $Di[X]$ are identic","authors_text":"Guangliang Zhang, Yuqun Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-11T07:32:19Z","title":"Gr\\\"obner--Shirshov bases for commutative dialgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06680","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":"sha256:9fad6d406f1b7025d1cbb28a966246bc6d4ba30b0770b73f9bbfb4316fa9d982","target":"record","created_at":"2026-05-17T23:40:29Z","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":"8127b904415c80d72c8cfe59040e4e8eb1c127aaed100961b8646073f222726f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-07-11T07:32:19Z","title_canon_sha256":"b0703b7ba41cbf25c9569599c8223d1349a7cf16f5c1d507f3cc2e51ab2402a7"},"schema_version":"1.0","source":{"id":"1907.06680","kind":"arxiv","version":1}},"canonical_sha256":"8d3ca79e606d16d0a42a4d28b78fabeaf722b930ebcdf6e705352f3cde7e9852","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d3ca79e606d16d0a42a4d28b78fabeaf722b930ebcdf6e705352f3cde7e9852","first_computed_at":"2026-05-17T23:40:29.433091Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:29.433091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ipinBheEobS7sqAvcY35hsIl1zg/zUfpnukTquOFerBMUvq9yA1WrSnJosuFguD5NFuwgwg+T6iULaRyJsijAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:29.433720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.06680","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9fad6d406f1b7025d1cbb28a966246bc6d4ba30b0770b73f9bbfb4316fa9d982","sha256:b9e5d73befbe9607f9221726d8a96d0fff9e62b2c99b3b7e56da1b9f55973b9e"],"state_sha256":"ac192a9abc0b8603272b3e0de87ba1e99b7db595bcf52edcc43aeff44694e042"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4NitvKCIjaGGi+W1AfEHSgJIlBSmI8S/7GIZmnjLUoOTKQA8bwc3cIDqe0y0T/h+qM6JdaHT2ZAH7V9O4jzXCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T20:08:07.812550Z","bundle_sha256":"1175cfac5575781996b2b767c9eb2ee77e7d388a5d102e4620946c419e1f64f4"}}