{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:5TWGWXSV7BS7HRAOGYTJT6B46Y","short_pith_number":"pith:5TWGWXSV","schema_version":"1.0","canonical_sha256":"ecec6b5e55f865f3c40e362699f83cf613f0628b36d9cd080ffdd11e990d39f2","source":{"kind":"arxiv","id":"1108.5985","version":4},"attestation_state":"computed","paper":{"title":"An Oracle-based, Output-sensitive Algorithm for Projections of Resultant Polytopes","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.SC","authors_text":"Christos Konaxis, Ioannis Z. Emiris, Luis Pe\\~naranda, Vissarion Fisikopoulos","submitted_at":"2011-08-30T15:38:54Z","abstract_excerpt":"We design an algorithm to compute the Newton polytope of the resultant, known as resultant polytope, or its orthogonal projection along a given direction. The resultant is fundamental in algebraic elimination, optimization, and geometric modeling. Our algorithm exactly computes vertex- and halfspace-representations of the polytope using an oracle producing resultant vertices in a given direction, thus avoiding walking on the polytope whose dimension is alpha-n-1, where the input consists of alpha points in Z^n. Our approach is output-sensitive as it makes one oracle call per vertex and facet. "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1108.5985","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.SC","submitted_at":"2011-08-30T15:38:54Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"af8bc0879a688df9c80f38b58f2ec131b44b6a775661477f1c110456687e6694","abstract_canon_sha256":"b7b7c7c6ebffddd36ed17f1e7504686ab8c4acaeb960a1cece73087b45da0417"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:11.606588Z","signature_b64":"D4wt26VBUsnO2oKrck3pgRQj9UFnR0KlZgnJn3NwPQrRs7Q0gpVjlMLbl3sSJtbeRF2QZ9I/toAPSvtTCk65Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ecec6b5e55f865f3c40e362699f83cf613f0628b36d9cd080ffdd11e990d39f2","last_reissued_at":"2026-05-18T03:27:11.605891Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:11.605891Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Oracle-based, Output-sensitive Algorithm for Projections of Resultant Polytopes","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.SC","authors_text":"Christos Konaxis, Ioannis Z. Emiris, Luis Pe\\~naranda, Vissarion Fisikopoulos","submitted_at":"2011-08-30T15:38:54Z","abstract_excerpt":"We design an algorithm to compute the Newton polytope of the resultant, known as resultant polytope, or its orthogonal projection along a given direction. The resultant is fundamental in algebraic elimination, optimization, and geometric modeling. Our algorithm exactly computes vertex- and halfspace-representations of the polytope using an oracle producing resultant vertices in a given direction, thus avoiding walking on the polytope whose dimension is alpha-n-1, where the input consists of alpha points in Z^n. Our approach is output-sensitive as it makes one oracle call per vertex and facet. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5985","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1108.5985","created_at":"2026-05-18T03:27:11.606016+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.5985v4","created_at":"2026-05-18T03:27:11.606016+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.5985","created_at":"2026-05-18T03:27:11.606016+00:00"},{"alias_kind":"pith_short_12","alias_value":"5TWGWXSV7BS7","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"5TWGWXSV7BS7HRAO","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"5TWGWXSV","created_at":"2026-05-18T12:26:20.644004+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/5TWGWXSV7BS7HRAOGYTJT6B46Y","json":"https://pith.science/pith/5TWGWXSV7BS7HRAOGYTJT6B46Y.json","graph_json":"https://pith.science/api/pith-number/5TWGWXSV7BS7HRAOGYTJT6B46Y/graph.json","events_json":"https://pith.science/api/pith-number/5TWGWXSV7BS7HRAOGYTJT6B46Y/events.json","paper":"https://pith.science/paper/5TWGWXSV"},"agent_actions":{"view_html":"https://pith.science/pith/5TWGWXSV7BS7HRAOGYTJT6B46Y","download_json":"https://pith.science/pith/5TWGWXSV7BS7HRAOGYTJT6B46Y.json","view_paper":"https://pith.science/paper/5TWGWXSV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.5985&json=true","fetch_graph":"https://pith.science/api/pith-number/5TWGWXSV7BS7HRAOGYTJT6B46Y/graph.json","fetch_events":"https://pith.science/api/pith-number/5TWGWXSV7BS7HRAOGYTJT6B46Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5TWGWXSV7BS7HRAOGYTJT6B46Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5TWGWXSV7BS7HRAOGYTJT6B46Y/action/storage_attestation","attest_author":"https://pith.science/pith/5TWGWXSV7BS7HRAOGYTJT6B46Y/action/author_attestation","sign_citation":"https://pith.science/pith/5TWGWXSV7BS7HRAOGYTJT6B46Y/action/citation_signature","submit_replication":"https://pith.science/pith/5TWGWXSV7BS7HRAOGYTJT6B46Y/action/replication_record"}},"created_at":"2026-05-18T03:27:11.606016+00:00","updated_at":"2026-05-18T03:27:11.606016+00:00"}