{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ALMYDHOC34IB5RGRPFQO5PDARH","short_pith_number":"pith:ALMYDHOC","canonical_record":{"source":{"id":"1507.08146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-29T13:54:52Z","cross_cats_sorted":[],"title_canon_sha256":"7674b1e19d47ebbb41acd41954686a7ef03c893c3d03c329b4e8cf23e2cc0268","abstract_canon_sha256":"1f3eeef9c6497548387e8eda2ca831058a931adea4c68542129a0f1d5dc3a109"},"schema_version":"1.0"},"canonical_sha256":"02d9819dc2df101ec4d17960eebc6089d36bc1dd0410735cc45a86170f88754c","source":{"kind":"arxiv","id":"1507.08146","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08146","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08146v1","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08146","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"ALMYDHOC34IB","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ALMYDHOC34IB5RGR","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ALMYDHOC","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ALMYDHOC34IB5RGRPFQO5PDARH","target":"record","payload":{"canonical_record":{"source":{"id":"1507.08146","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-29T13:54:52Z","cross_cats_sorted":[],"title_canon_sha256":"7674b1e19d47ebbb41acd41954686a7ef03c893c3d03c329b4e8cf23e2cc0268","abstract_canon_sha256":"1f3eeef9c6497548387e8eda2ca831058a931adea4c68542129a0f1d5dc3a109"},"schema_version":"1.0"},"canonical_sha256":"02d9819dc2df101ec4d17960eebc6089d36bc1dd0410735cc45a86170f88754c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:25:46.803293Z","signature_b64":"B3m172lWhj6LXb/8/s6fBi+hBbjF7IavYuyvPLngmoj34gRcvd2yJ2QpomgClRmqBDX32MhFOa4G0wNCgKUTBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"02d9819dc2df101ec4d17960eebc6089d36bc1dd0410735cc45a86170f88754c","last_reissued_at":"2026-05-18T01:25:46.802908Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:25:46.802908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.08146","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":"2026-05-18T01:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"93BAKhyjw59J96lHClLdC6YWAIIQmcPJVEtCWjQymb5O57Sax8O8C9LiIBh7iiMexFxpEJlLlzgEkRl9qsBDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:19:06.454549Z"},"content_sha256":"69ad43c8fba8f0ef488a2034f9330be69d39ce863332d16a91af492cf71200d3","schema_version":"1.0","event_id":"sha256:69ad43c8fba8f0ef488a2034f9330be69d39ce863332d16a91af492cf71200d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ALMYDHOC34IB5RGRPFQO5PDARH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On a type of commutative algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"A.L. Agore, G. Militaru","submitted_at":"2015-07-29T13:54:52Z","abstract_excerpt":"We introduce some basic concepts for Jacobi-Jordan algebras such as: representations, crossed products or Frobenius/metabelian/co-flag objects. A new family of solutions for the quantum Yang-Baxter equation is constructed arising from any $3$-step nilpotent Jacobi-Jordan algebra. Crossed products are used to construct the classifying object for the extension problem in its global form. For a given Jacobi-Jordan algebra $A$ and a given vector space $V$ of dimension $\\mathfrak{c}$, a global non-abelian cohomological object ${\\mathbb G} {\\mathbb H}^{2} \\, (A, \\, V)$ is constructed: it classifies,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08146","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":"2026-05-18T01:25:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dyEn+dPIZU0B8SFt6qlyJJx9+yl0YfV7YSBHAJ1EQZAc6PMq4YMCk+4ENLlaWsovedy9ZoOt9I3YNv/nwvtoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T05:19:06.454889Z"},"content_sha256":"d762e9dfe40cee4082456ba41f7d5bdcaf6d0df485f017836c393b1892194ec4","schema_version":"1.0","event_id":"sha256:d762e9dfe40cee4082456ba41f7d5bdcaf6d0df485f017836c393b1892194ec4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ALMYDHOC34IB5RGRPFQO5PDARH/bundle.json","state_url":"https://pith.science/pith/ALMYDHOC34IB5RGRPFQO5PDARH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ALMYDHOC34IB5RGRPFQO5PDARH/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":"2026-06-24T05:19:06Z","links":{"resolver":"https://pith.science/pith/ALMYDHOC34IB5RGRPFQO5PDARH","bundle":"https://pith.science/pith/ALMYDHOC34IB5RGRPFQO5PDARH/bundle.json","state":"https://pith.science/pith/ALMYDHOC34IB5RGRPFQO5PDARH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ALMYDHOC34IB5RGRPFQO5PDARH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ALMYDHOC34IB5RGRPFQO5PDARH","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":"1f3eeef9c6497548387e8eda2ca831058a931adea4c68542129a0f1d5dc3a109","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-29T13:54:52Z","title_canon_sha256":"7674b1e19d47ebbb41acd41954686a7ef03c893c3d03c329b4e8cf23e2cc0268"},"schema_version":"1.0","source":{"id":"1507.08146","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.08146","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"arxiv_version","alias_value":"1507.08146v1","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.08146","created_at":"2026-05-18T01:25:46Z"},{"alias_kind":"pith_short_12","alias_value":"ALMYDHOC34IB","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"ALMYDHOC34IB5RGR","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"ALMYDHOC","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:d762e9dfe40cee4082456ba41f7d5bdcaf6d0df485f017836c393b1892194ec4","target":"graph","created_at":"2026-05-18T01:25:46Z","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 introduce some basic concepts for Jacobi-Jordan algebras such as: representations, crossed products or Frobenius/metabelian/co-flag objects. A new family of solutions for the quantum Yang-Baxter equation is constructed arising from any $3$-step nilpotent Jacobi-Jordan algebra. Crossed products are used to construct the classifying object for the extension problem in its global form. For a given Jacobi-Jordan algebra $A$ and a given vector space $V$ of dimension $\\mathfrak{c}$, a global non-abelian cohomological object ${\\mathbb G} {\\mathbb H}^{2} \\, (A, \\, V)$ is constructed: it classifies,","authors_text":"A.L. Agore, G. Militaru","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-29T13:54:52Z","title":"On a type of commutative algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.08146","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":"sha256:69ad43c8fba8f0ef488a2034f9330be69d39ce863332d16a91af492cf71200d3","target":"record","created_at":"2026-05-18T01:25:46Z","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":"1f3eeef9c6497548387e8eda2ca831058a931adea4c68542129a0f1d5dc3a109","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2015-07-29T13:54:52Z","title_canon_sha256":"7674b1e19d47ebbb41acd41954686a7ef03c893c3d03c329b4e8cf23e2cc0268"},"schema_version":"1.0","source":{"id":"1507.08146","kind":"arxiv","version":1}},"canonical_sha256":"02d9819dc2df101ec4d17960eebc6089d36bc1dd0410735cc45a86170f88754c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"02d9819dc2df101ec4d17960eebc6089d36bc1dd0410735cc45a86170f88754c","first_computed_at":"2026-05-18T01:25:46.802908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:25:46.802908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3m172lWhj6LXb/8/s6fBi+hBbjF7IavYuyvPLngmoj34gRcvd2yJ2QpomgClRmqBDX32MhFOa4G0wNCgKUTBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:25:46.803293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.08146","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69ad43c8fba8f0ef488a2034f9330be69d39ce863332d16a91af492cf71200d3","sha256:d762e9dfe40cee4082456ba41f7d5bdcaf6d0df485f017836c393b1892194ec4"],"state_sha256":"5b03b117a5d2f0d7cdf09d20002fffa4560b807f1ede95613e249318db308c3d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TfOpaNOyBh/haZSx3ANX5fbAs4M5Fpz03ZgCeszfazUNMlwNeaP1HpP0JaLPu0R3NBGrL6VHHNS5kAeLA5aBAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T05:19:06.456873Z","bundle_sha256":"9ac7efca924328bd8568125e96dc82cd1b6d9f3cc80a7ea5483030b45097b05d"}}