{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:BFC64MBOGSYJE7R4XI6D2VYLV5","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":"837621bb9bc6b6ccd2b6e7e1ee6bf5ff0d98f7295813fdabb136a6b297e2f45f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-02-10T21:33:26Z","title_canon_sha256":"e6eea0e5bb2b909e9c2b3c8d14df9fd142cf5d092f1a2e7a68af0e99ce7e4f27"},"schema_version":"1.0","source":{"id":"2502.07048","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.07048","created_at":"2026-07-05T11:42:25Z"},{"alias_kind":"arxiv_version","alias_value":"2502.07048v2","created_at":"2026-07-05T11:42:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.07048","created_at":"2026-07-05T11:42:25Z"},{"alias_kind":"pith_short_12","alias_value":"BFC64MBOGSYJ","created_at":"2026-07-05T11:42:25Z"},{"alias_kind":"pith_short_16","alias_value":"BFC64MBOGSYJE7R4","created_at":"2026-07-05T11:42:25Z"},{"alias_kind":"pith_short_8","alias_value":"BFC64MBO","created_at":"2026-07-05T11:42:25Z"}],"graph_snapshots":[{"event_id":"sha256:f43aba0d7454cdf7a26bf02e0774bcb72a68718bd6be2aaedf89ef4599b7b728","target":"graph","created_at":"2026-07-05T11:42:25Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2502.07048/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study bihomogeneous systems defining, non-zero dimensional, biprojective varieties for which the projection onto the first group of variables results in a finite set of points. To compute (with) the 0-dimensional projection and the corresponding quotient ring, we introduce linear maps that greatly extend the classical multiplication maps for zero-dimensional systems, but are not those associated to the elimination ideal; we also call them multiplication maps. We construct them using linear algebra on the restriction of the ideal to a carefully chosen bidegree or, if available, from an arbit","authors_text":"Carles Checa, Elias Tsigaridas, Laurent Bus\\'e, Mat\\'ias Bender","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-02-10T21:33:26Z","title":"Solving bihomogeneous polynomial systems with a zero-dimensional projection"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.07048","kind":"arxiv","version":2},"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:dd883f84163ca556002bac5f4c485ecf2e20b345e3b6a13a7b8c54755a371fa6","target":"record","created_at":"2026-07-05T11:42:25Z","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":"837621bb9bc6b6ccd2b6e7e1ee6bf5ff0d98f7295813fdabb136a6b297e2f45f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2025-02-10T21:33:26Z","title_canon_sha256":"e6eea0e5bb2b909e9c2b3c8d14df9fd142cf5d092f1a2e7a68af0e99ce7e4f27"},"schema_version":"1.0","source":{"id":"2502.07048","kind":"arxiv","version":2}},"canonical_sha256":"0945ee302e34b0927e3cba3c3d570baf7aaa849422fcbd747809e9a2419f2d40","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0945ee302e34b0927e3cba3c3d570baf7aaa849422fcbd747809e9a2419f2d40","first_computed_at":"2026-07-05T11:42:25.821254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:42:25.821254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5S7YyxjcxlsMM2YzaiD3ZmNUoMnMForjiXI9JdtC9fVWkQKydj7NDdlC8fMyu5p2Z8AhCoTUE5+a7Asd0Q71Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:42:25.821677Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.07048","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd883f84163ca556002bac5f4c485ecf2e20b345e3b6a13a7b8c54755a371fa6","sha256:f43aba0d7454cdf7a26bf02e0774bcb72a68718bd6be2aaedf89ef4599b7b728"],"state_sha256":"09d699906c9090020df35e3e191eaff7eda3c19b3f1658e1164abc68f443ebd7"}