{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DQLLQCYVUKUNDVLUR537C7E4LX","short_pith_number":"pith:DQLLQCYV","canonical_record":{"source":{"id":"1602.00296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-31T18:33:33Z","cross_cats_sorted":["cs.SC","math.OA"],"title_canon_sha256":"a5bd6c69137e5e8f2b49920f11b0c10a88f2e440122e51d9bd61ac6387487fd7","abstract_canon_sha256":"a47e810d04e75fb21e28052b4fa40e1d4e5064de72f8113a71528cc15489b2eb"},"schema_version":"1.0"},"canonical_sha256":"1c16b80b15a2a8d1d5748f77f17c9c5ded20e2a143c6fa4a72ff7b401daabaa2","source":{"kind":"arxiv","id":"1602.00296","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00296","created_at":"2026-05-18T00:28:57Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00296v1","created_at":"2026-05-18T00:28:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00296","created_at":"2026-05-18T00:28:57Z"},{"alias_kind":"pith_short_12","alias_value":"DQLLQCYVUKUN","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DQLLQCYVUKUNDVLU","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DQLLQCYV","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DQLLQCYVUKUNDVLUR537C7E4LX","target":"record","payload":{"canonical_record":{"source":{"id":"1602.00296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-31T18:33:33Z","cross_cats_sorted":["cs.SC","math.OA"],"title_canon_sha256":"a5bd6c69137e5e8f2b49920f11b0c10a88f2e440122e51d9bd61ac6387487fd7","abstract_canon_sha256":"a47e810d04e75fb21e28052b4fa40e1d4e5064de72f8113a71528cc15489b2eb"},"schema_version":"1.0"},"canonical_sha256":"1c16b80b15a2a8d1d5748f77f17c9c5ded20e2a143c6fa4a72ff7b401daabaa2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:57.128877Z","signature_b64":"agOgJsxj5KmtGtDnStGlvmtMOl2hChBZ9XGbJlCn167KQ6P2ibmWP1pFmx6ihuxLc8ngUauY8dnhRDCdx/2IAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c16b80b15a2a8d1d5748f77f17c9c5ded20e2a143c6fa4a72ff7b401daabaa2","last_reissued_at":"2026-05-18T00:28:57.128409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:57.128409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.00296","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":"2026-05-18T00:28:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HuGcvTZg+MUPrcefxjxsta+Jf5fKuqZIQCGPKU5ymb7L5eHTLZ/nEKqu8+vvgZhI6tgablipKCVJt/5tDR7rBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:58:12.071459Z"},"content_sha256":"3ebc7db3bf4fb794f4918345a20d73890e4075ad6fe9f5e79d4a114d3429d5a5","schema_version":"1.0","event_id":"sha256:3ebc7db3bf4fb794f4918345a20d73890e4075ad6fe9f5e79d4a114d3429d5a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DQLLQCYVUKUNDVLUR537C7E4LX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Factorization Algorithm for G-Algebras and Applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math.OA"],"primary_cat":"math.RA","authors_text":"Albert Heinle, Viktor Levandovskyy","submitted_at":"2016-01-31T18:33:33Z","abstract_excerpt":"It has been recently discovered by Bell, Heinle and Levandovskyy that a large class of algebras, including the ubiquitous $G$-algebras, are finite factorization domains (FFD for short).\n  Utilizing this result, we contribute an algorithm to find all distinct factorizations of a given element $f \\in \\mathcal{G}$, where $\\mathcal{G}$ is any $G$-algebra, with minor assumptions on the underlying field.\n  Moreover, the property of being an FFD, in combination with the factorization algorithm, enables us to propose an analogous description of the factorized Gr\\\"obner basis algorithm for $G$-algebras"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00296","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":"2026-05-18T00:28:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ntflmzjMjLdqDQ2ZQq0s/eKuBZDoyK5mEiFeoN3HuCxR7QlHw1ie1ItFx7+5PaTexkKLE2WdJK9wDvtKdzIPCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T22:58:12.071800Z"},"content_sha256":"9528f54fdb4bda15542e149b9351d7b257cc03bc25e079f0ec8e09a8fbad4a94","schema_version":"1.0","event_id":"sha256:9528f54fdb4bda15542e149b9351d7b257cc03bc25e079f0ec8e09a8fbad4a94"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQLLQCYVUKUNDVLUR537C7E4LX/bundle.json","state_url":"https://pith.science/pith/DQLLQCYVUKUNDVLUR537C7E4LX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQLLQCYVUKUNDVLUR537C7E4LX/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":"2026-06-24T22:58:12Z","links":{"resolver":"https://pith.science/pith/DQLLQCYVUKUNDVLUR537C7E4LX","bundle":"https://pith.science/pith/DQLLQCYVUKUNDVLUR537C7E4LX/bundle.json","state":"https://pith.science/pith/DQLLQCYVUKUNDVLUR537C7E4LX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQLLQCYVUKUNDVLUR537C7E4LX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DQLLQCYVUKUNDVLUR537C7E4LX","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":"a47e810d04e75fb21e28052b4fa40e1d4e5064de72f8113a71528cc15489b2eb","cross_cats_sorted":["cs.SC","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-31T18:33:33Z","title_canon_sha256":"a5bd6c69137e5e8f2b49920f11b0c10a88f2e440122e51d9bd61ac6387487fd7"},"schema_version":"1.0","source":{"id":"1602.00296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.00296","created_at":"2026-05-18T00:28:57Z"},{"alias_kind":"arxiv_version","alias_value":"1602.00296v1","created_at":"2026-05-18T00:28:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.00296","created_at":"2026-05-18T00:28:57Z"},{"alias_kind":"pith_short_12","alias_value":"DQLLQCYVUKUN","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DQLLQCYVUKUNDVLU","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DQLLQCYV","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:9528f54fdb4bda15542e149b9351d7b257cc03bc25e079f0ec8e09a8fbad4a94","target":"graph","created_at":"2026-05-18T00:28:57Z","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":"It has been recently discovered by Bell, Heinle and Levandovskyy that a large class of algebras, including the ubiquitous $G$-algebras, are finite factorization domains (FFD for short).\n  Utilizing this result, we contribute an algorithm to find all distinct factorizations of a given element $f \\in \\mathcal{G}$, where $\\mathcal{G}$ is any $G$-algebra, with minor assumptions on the underlying field.\n  Moreover, the property of being an FFD, in combination with the factorization algorithm, enables us to propose an analogous description of the factorized Gr\\\"obner basis algorithm for $G$-algebras","authors_text":"Albert Heinle, Viktor Levandovskyy","cross_cats":["cs.SC","math.OA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-31T18:33:33Z","title":"A Factorization Algorithm for G-Algebras and Applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00296","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":"sha256:3ebc7db3bf4fb794f4918345a20d73890e4075ad6fe9f5e79d4a114d3429d5a5","target":"record","created_at":"2026-05-18T00:28:57Z","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":"a47e810d04e75fb21e28052b4fa40e1d4e5064de72f8113a71528cc15489b2eb","cross_cats_sorted":["cs.SC","math.OA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-01-31T18:33:33Z","title_canon_sha256":"a5bd6c69137e5e8f2b49920f11b0c10a88f2e440122e51d9bd61ac6387487fd7"},"schema_version":"1.0","source":{"id":"1602.00296","kind":"arxiv","version":1}},"canonical_sha256":"1c16b80b15a2a8d1d5748f77f17c9c5ded20e2a143c6fa4a72ff7b401daabaa2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c16b80b15a2a8d1d5748f77f17c9c5ded20e2a143c6fa4a72ff7b401daabaa2","first_computed_at":"2026-05-18T00:28:57.128409Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:57.128409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"agOgJsxj5KmtGtDnStGlvmtMOl2hChBZ9XGbJlCn167KQ6P2ibmWP1pFmx6ihuxLc8ngUauY8dnhRDCdx/2IAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:57.128877Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.00296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ebc7db3bf4fb794f4918345a20d73890e4075ad6fe9f5e79d4a114d3429d5a5","sha256:9528f54fdb4bda15542e149b9351d7b257cc03bc25e079f0ec8e09a8fbad4a94"],"state_sha256":"3d2d52935f026a185c7c16c7be07b41a137ebae50b337776b8d3c1210d658ce5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l+zNEoy2Dottp51G5PKSh4GeNwNTrRmDA3cdpvhHZo9NwaY9wtW2O4KOcfk9iPqC9h1FY04OVqkRyW9qiXE9Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T22:58:12.073762Z","bundle_sha256":"fc8229e5405cb3d383c03f1bad514702d7fbed103ce513445e65a5800e6a572d"}}