{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:QPF3DQWIF75SOSSDHA5HHEHOL3","short_pith_number":"pith:QPF3DQWI","canonical_record":{"source":{"id":"1201.5787","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-01-27T14:50:38Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"fee7d469843f92f995fccf714a8541ab942972154ac30034f1ed2320413270bb","abstract_canon_sha256":"7eab57480a5a1f95e764ff6520224b7bc1d7a0a0e2b20991a8cd646474ca19e8"},"schema_version":"1.0"},"canonical_sha256":"83cbb1c2c82ffb274a43383a7390ee5ed9e1b29fd3dbb36114b9e82f23acdb7e","source":{"kind":"arxiv","id":"1201.5787","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5787","created_at":"2026-05-18T04:02:03Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5787v3","created_at":"2026-05-18T04:02:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5787","created_at":"2026-05-18T04:02:03Z"},{"alias_kind":"pith_short_12","alias_value":"QPF3DQWIF75S","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QPF3DQWIF75SOSSD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QPF3DQWI","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:QPF3DQWIF75SOSSDHA5HHEHOL3","target":"record","payload":{"canonical_record":{"source":{"id":"1201.5787","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-01-27T14:50:38Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"fee7d469843f92f995fccf714a8541ab942972154ac30034f1ed2320413270bb","abstract_canon_sha256":"7eab57480a5a1f95e764ff6520224b7bc1d7a0a0e2b20991a8cd646474ca19e8"},"schema_version":"1.0"},"canonical_sha256":"83cbb1c2c82ffb274a43383a7390ee5ed9e1b29fd3dbb36114b9e82f23acdb7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:02:03.602505Z","signature_b64":"Fag83D7f/Z4D6CUdvDnwCr8iJYomkom6adHCxaHQrl0FD0KnohRx3qH4mDuDashOasAhdpfBVMfR3+1aWXE/CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83cbb1c2c82ffb274a43383a7390ee5ed9e1b29fd3dbb36114b9e82f23acdb7e","last_reissued_at":"2026-05-18T04:02:03.601956Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:02:03.601956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.5787","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:02:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8MSThJ8mvn1g23+RtAaS6NgINC6ZTM/+WUhKz8ONQAmWEUtcHnP1DtVduZmx164piCGxDurbebeWXgDPrWgYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:28:00.950195Z"},"content_sha256":"140081324d9012737f67f20c6ad9f1afd5b00e0ea1ab9af9f400af1053042047","schema_version":"1.0","event_id":"sha256:140081324d9012737f67f20c6ad9f1afd5b00e0ea1ab9af9f400af1053042047"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:QPF3DQWIF75SOSSDHA5HHEHOL3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Factoring bivariate polynomials using adjoints","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Martin Weimann","submitted_at":"2012-01-27T14:50:38Z","abstract_excerpt":"One relates factorization of bivariate polynomials to singularities of projective plane curves. One proves that adjoint polynomials permit to solve the recombinations of the modular factors induced by the absolute and rational factorizations, and so without using Hensel's lifting. One establishes in such a way the relations between the algorithm of Duval-Ragot (locally constant functions) and of Ch\\`eze-Lecerf (lifting and recombinations), and one shows that a fast computation of adjoint polynomials leads to a fast factorization. The proof is based on cohomological sequences and residue theory"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5787","kind":"arxiv","version":3},"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":"2026-05-18T04:02:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kU4lZLly3ct1vQzaVExwmj1cNK95eQwuxERh8Yr1sWA2ZLDM0mXvfTWeekxNN5sHC+hpOTkJqwrVNd+Oz1JVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T22:28:00.950561Z"},"content_sha256":"a35afaccc3cfe82d728b9255b1ca65517c2836d793b13bc282283c6506815e1e","schema_version":"1.0","event_id":"sha256:a35afaccc3cfe82d728b9255b1ca65517c2836d793b13bc282283c6506815e1e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QPF3DQWIF75SOSSDHA5HHEHOL3/bundle.json","state_url":"https://pith.science/pith/QPF3DQWIF75SOSSDHA5HHEHOL3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QPF3DQWIF75SOSSDHA5HHEHOL3/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":"2026-06-21T22:28:00Z","links":{"resolver":"https://pith.science/pith/QPF3DQWIF75SOSSDHA5HHEHOL3","bundle":"https://pith.science/pith/QPF3DQWIF75SOSSDHA5HHEHOL3/bundle.json","state":"https://pith.science/pith/QPF3DQWIF75SOSSDHA5HHEHOL3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QPF3DQWIF75SOSSDHA5HHEHOL3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:QPF3DQWIF75SOSSDHA5HHEHOL3","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":"7eab57480a5a1f95e764ff6520224b7bc1d7a0a0e2b20991a8cd646474ca19e8","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-01-27T14:50:38Z","title_canon_sha256":"fee7d469843f92f995fccf714a8541ab942972154ac30034f1ed2320413270bb"},"schema_version":"1.0","source":{"id":"1201.5787","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5787","created_at":"2026-05-18T04:02:03Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5787v3","created_at":"2026-05-18T04:02:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5787","created_at":"2026-05-18T04:02:03Z"},{"alias_kind":"pith_short_12","alias_value":"QPF3DQWIF75S","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"QPF3DQWIF75SOSSD","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"QPF3DQWI","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:a35afaccc3cfe82d728b9255b1ca65517c2836d793b13bc282283c6506815e1e","target":"graph","created_at":"2026-05-18T04:02:03Z","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":"One relates factorization of bivariate polynomials to singularities of projective plane curves. One proves that adjoint polynomials permit to solve the recombinations of the modular factors induced by the absolute and rational factorizations, and so without using Hensel's lifting. One establishes in such a way the relations between the algorithm of Duval-Ragot (locally constant functions) and of Ch\\`eze-Lecerf (lifting and recombinations), and one shows that a fast computation of adjoint polynomials leads to a fast factorization. The proof is based on cohomological sequences and residue theory","authors_text":"Martin Weimann","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-01-27T14:50:38Z","title":"Factoring bivariate polynomials using adjoints"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5787","kind":"arxiv","version":3},"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":"sha256:140081324d9012737f67f20c6ad9f1afd5b00e0ea1ab9af9f400af1053042047","target":"record","created_at":"2026-05-18T04:02:03Z","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":"7eab57480a5a1f95e764ff6520224b7bc1d7a0a0e2b20991a8cd646474ca19e8","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-01-27T14:50:38Z","title_canon_sha256":"fee7d469843f92f995fccf714a8541ab942972154ac30034f1ed2320413270bb"},"schema_version":"1.0","source":{"id":"1201.5787","kind":"arxiv","version":3}},"canonical_sha256":"83cbb1c2c82ffb274a43383a7390ee5ed9e1b29fd3dbb36114b9e82f23acdb7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83cbb1c2c82ffb274a43383a7390ee5ed9e1b29fd3dbb36114b9e82f23acdb7e","first_computed_at":"2026-05-18T04:02:03.601956Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:02:03.601956Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fag83D7f/Z4D6CUdvDnwCr8iJYomkom6adHCxaHQrl0FD0KnohRx3qH4mDuDashOasAhdpfBVMfR3+1aWXE/CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:02:03.602505Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5787","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:140081324d9012737f67f20c6ad9f1afd5b00e0ea1ab9af9f400af1053042047","sha256:a35afaccc3cfe82d728b9255b1ca65517c2836d793b13bc282283c6506815e1e"],"state_sha256":"fc6209a8402989c2d5de265e0f674eb43e520f32080c93b64d9db2b9003b9b8a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hKsod2bgyC8iq7au+Yqq6EWCWtgPdCHBJLqQEKM+tqpx0NFdAk1FOboXOKBB5w3WbsIAwL97PmQWPaG479ZhCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T22:28:00.952483Z","bundle_sha256":"8faf2f57a0ca4c76f50a5f80facc8829be18587bdd293dac6afdabd6396518f1"}}