{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:S2L2ONHSUKOZ43U3HCLQEZTBMJ","short_pith_number":"pith:S2L2ONHS","canonical_record":{"source":{"id":"1301.3991","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-01-17T06:16:02Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"f76de3d9bbd3379b8148c228253471e04cf3783059e8542cae7e27ca911558a1","abstract_canon_sha256":"7e537d8654df2586961ef720ac070701ae83d3efc97a27bda681c40b14821024"},"schema_version":"1.0"},"canonical_sha256":"9697a734f2a29d9e6e9b389702666162669454dd3ff4636803d46744e60f2d3e","source":{"kind":"arxiv","id":"1301.3991","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3991","created_at":"2026-05-18T03:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3991v1","created_at":"2026-05-18T03:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3991","created_at":"2026-05-18T03:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"S2L2ONHSUKOZ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S2L2ONHSUKOZ43U3","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S2L2ONHS","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:S2L2ONHSUKOZ43U3HCLQEZTBMJ","target":"record","payload":{"canonical_record":{"source":{"id":"1301.3991","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-01-17T06:16:02Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"f76de3d9bbd3379b8148c228253471e04cf3783059e8542cae7e27ca911558a1","abstract_canon_sha256":"7e537d8654df2586961ef720ac070701ae83d3efc97a27bda681c40b14821024"},"schema_version":"1.0"},"canonical_sha256":"9697a734f2a29d9e6e9b389702666162669454dd3ff4636803d46744e60f2d3e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:14.680840Z","signature_b64":"GpzG0JDJzzh5VYepVsgK/aFE5HfKtUcJ8ZOut9xXYaqae1xGsRFH4jz8KXnLtSLrz8Ji8TGNSkONZm5rC4BCBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9697a734f2a29d9e6e9b389702666162669454dd3ff4636803d46744e60f2d3e","last_reissued_at":"2026-05-18T03:36:14.680219Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:14.680219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.3991","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":"2026-05-18T03:36:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o3gl64j15FFngkYUhvzxQ+VrUjg0/RacgW1iMVST621NWnfdysfOEu6x6lr58cP34lrTbLuvFhRkOtuPk7mtDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:14:02.279079Z"},"content_sha256":"a18937b84040537a9fb57b88b8836f5b860b11940af403eacaa149ed90d0b8af","schema_version":"1.0","event_id":"sha256:a18937b84040537a9fb57b88b8836f5b860b11940af403eacaa149ed90d0b8af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:S2L2ONHSUKOZ43U3HCLQEZTBMJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generic Regular Decompositions for Parametric Polynomial Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.SC","authors_text":"Bican Xia, Xiaoxian Tang, Zhenghong Chen","submitted_at":"2013-01-17T06:16:02Z","abstract_excerpt":"This paper presents a generalization of our earlier work in [19]. In this paper, the two concepts, generic regular decomposition (GRD) and regular-decomposition-unstable (RDU) variety introduced in [19] for generic zero-dimensional systems, are extended to the case where the parametric systems are not necessarily zero-dimensional. An algorithm is provided to compute GRDs and the associated RDU varieties of parametric systems simultaneously on the basis of the algorithm for generic zero-dimensional systems proposed in [19]. Then the solutions of any parametric system can be represented by the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3991","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":"2026-05-18T03:36:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d4ez6Pyu8IF6hZOmVYaYVpSYJs1h7lWISK0KnoBN7bq9vyqatKu73/SsL0mqCqZ2jWAy4/bx4uzQyOecbWstBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:14:02.279444Z"},"content_sha256":"ea3744705c510086c694ced42341d58e7c127f180f5febbded18d178ff32aa86","schema_version":"1.0","event_id":"sha256:ea3744705c510086c694ced42341d58e7c127f180f5febbded18d178ff32aa86"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S2L2ONHSUKOZ43U3HCLQEZTBMJ/bundle.json","state_url":"https://pith.science/pith/S2L2ONHSUKOZ43U3HCLQEZTBMJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S2L2ONHSUKOZ43U3HCLQEZTBMJ/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":"2026-05-28T15:14:02Z","links":{"resolver":"https://pith.science/pith/S2L2ONHSUKOZ43U3HCLQEZTBMJ","bundle":"https://pith.science/pith/S2L2ONHSUKOZ43U3HCLQEZTBMJ/bundle.json","state":"https://pith.science/pith/S2L2ONHSUKOZ43U3HCLQEZTBMJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S2L2ONHSUKOZ43U3HCLQEZTBMJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:S2L2ONHSUKOZ43U3HCLQEZTBMJ","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":"7e537d8654df2586961ef720ac070701ae83d3efc97a27bda681c40b14821024","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-01-17T06:16:02Z","title_canon_sha256":"f76de3d9bbd3379b8148c228253471e04cf3783059e8542cae7e27ca911558a1"},"schema_version":"1.0","source":{"id":"1301.3991","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.3991","created_at":"2026-05-18T03:36:14Z"},{"alias_kind":"arxiv_version","alias_value":"1301.3991v1","created_at":"2026-05-18T03:36:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.3991","created_at":"2026-05-18T03:36:14Z"},{"alias_kind":"pith_short_12","alias_value":"S2L2ONHSUKOZ","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"S2L2ONHSUKOZ43U3","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"S2L2ONHS","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:ea3744705c510086c694ced42341d58e7c127f180f5febbded18d178ff32aa86","target":"graph","created_at":"2026-05-18T03:36:14Z","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":"This paper presents a generalization of our earlier work in [19]. In this paper, the two concepts, generic regular decomposition (GRD) and regular-decomposition-unstable (RDU) variety introduced in [19] for generic zero-dimensional systems, are extended to the case where the parametric systems are not necessarily zero-dimensional. An algorithm is provided to compute GRDs and the associated RDU varieties of parametric systems simultaneously on the basis of the algorithm for generic zero-dimensional systems proposed in [19]. Then the solutions of any parametric system can be represented by the s","authors_text":"Bican Xia, Xiaoxian Tang, Zhenghong Chen","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-01-17T06:16:02Z","title":"Generic Regular Decompositions for Parametric Polynomial Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.3991","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:a18937b84040537a9fb57b88b8836f5b860b11940af403eacaa149ed90d0b8af","target":"record","created_at":"2026-05-18T03:36:14Z","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":"7e537d8654df2586961ef720ac070701ae83d3efc97a27bda681c40b14821024","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2013-01-17T06:16:02Z","title_canon_sha256":"f76de3d9bbd3379b8148c228253471e04cf3783059e8542cae7e27ca911558a1"},"schema_version":"1.0","source":{"id":"1301.3991","kind":"arxiv","version":1}},"canonical_sha256":"9697a734f2a29d9e6e9b389702666162669454dd3ff4636803d46744e60f2d3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9697a734f2a29d9e6e9b389702666162669454dd3ff4636803d46744e60f2d3e","first_computed_at":"2026-05-18T03:36:14.680219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:14.680219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GpzG0JDJzzh5VYepVsgK/aFE5HfKtUcJ8ZOut9xXYaqae1xGsRFH4jz8KXnLtSLrz8Ji8TGNSkONZm5rC4BCBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:14.680840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.3991","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a18937b84040537a9fb57b88b8836f5b860b11940af403eacaa149ed90d0b8af","sha256:ea3744705c510086c694ced42341d58e7c127f180f5febbded18d178ff32aa86"],"state_sha256":"730cb6a415f3133b7dad58d05a049c2c1ce8296a82cda601f0501fccb615d3b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hL4vqTnlWOP8Tzp37Cxiim4cxXoA6mFxNRE363BdnnL/dyIRfDcHgLxZiJ1T6spxP90wUdq/I8jqB6TSx+4kBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:14:02.281520Z","bundle_sha256":"58350b754a16d209360a66f0e3d36fdc5153c9d8e7712e81dc0f58c6b1c019bf"}}