{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3H3DE4A2PE4ZEUU3PVI5OWG26U","short_pith_number":"pith:3H3DE4A2","canonical_record":{"source":{"id":"1201.5810","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2012-01-27T16:01:53Z","cross_cats_sorted":["cs.NA","math.AC"],"title_canon_sha256":"5fbe2a3d7463925e92a70712b5a4a8f1c54e9d5a7afe8b5154b4788f0e14a584","abstract_canon_sha256":"51615d49815193362b5e2ff1cbcb87cf108f1e3cdd7b7926347344ccc306e885"},"schema_version":"1.0"},"canonical_sha256":"d9f632701a793992529b7d51d758daf53be3da01ae85ebbd145c62dd5688691a","source":{"kind":"arxiv","id":"1201.5810","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5810","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5810v1","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5810","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"3H3DE4A2PE4Z","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3H3DE4A2PE4ZEUU3","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3H3DE4A2","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3H3DE4A2PE4ZEUU3PVI5OWG26U","target":"record","payload":{"canonical_record":{"source":{"id":"1201.5810","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2012-01-27T16:01:53Z","cross_cats_sorted":["cs.NA","math.AC"],"title_canon_sha256":"5fbe2a3d7463925e92a70712b5a4a8f1c54e9d5a7afe8b5154b4788f0e14a584","abstract_canon_sha256":"51615d49815193362b5e2ff1cbcb87cf108f1e3cdd7b7926347344ccc306e885"},"schema_version":"1.0"},"canonical_sha256":"d9f632701a793992529b7d51d758daf53be3da01ae85ebbd145c62dd5688691a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:44.465393Z","signature_b64":"MhGZ8l+hn6pQk20KzYO4RA4BkvjtIW28A4jDMe8GQiqvNlA7nwhnTK1E+w+JLnUknJe/lhfviGUWuTrdmTjBDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9f632701a793992529b7d51d758daf53be3da01ae85ebbd145c62dd5688691a","last_reissued_at":"2026-05-18T04:03:44.464369Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:44.464369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.5810","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":"2026-05-18T04:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A19i4gbAZldplrxxr2MMSKp9TBdDZ+5c1UbCgaO37/gr0OzDvQ4sr3N583xK5B42TytsaQ5DR1aBMAxnYxKvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:50:09.875720Z"},"content_sha256":"f393a9f9354a877727d86af7174a818d30cb9f1b0204fd66f594a0638378dd1c","schema_version":"1.0","event_id":"sha256:f393a9f9354a877727d86af7174a818d30cb9f1b0204fd66f594a0638378dd1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3H3DE4A2PE4ZEUU3PVI5OWG26U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A General Solver Based on Sparse Resultants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AC"],"primary_cat":"cs.SC","authors_text":"Ioannis Z. Emiris","submitted_at":"2012-01-27T16:01:53Z","abstract_excerpt":"Sparse (or toric) elimination exploits the structure of polynomials by measuring their complexity in terms of Newton polytopes instead of total degree. The sparse, or Newton, resultant generalizes the classical homogeneous resultant and its degree is a function of the mixed volumes of the Newton polytopes. We sketch the sparse resultant constructions of Canny and Emiris and show how they reduce the problem of root-finding to an eigenproblem. A novel method for achieving this reduction is presented which does not increase the dimension of the problem. Together with an implementation of the spar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5810","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":"2026-05-18T04:03:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hvbFLhfWJfN/e44SVX1FyUdHW3cFsjlDhfmH644RP8yhRGU6eypIWx1p2LSIkTXFbZhXNS79gCzJo4yYs9VADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T14:50:09.876076Z"},"content_sha256":"9780a05f3a6b6b899305c7428fe130b5845e034a9e16b84ab21e1e9ddcb734c5","schema_version":"1.0","event_id":"sha256:9780a05f3a6b6b899305c7428fe130b5845e034a9e16b84ab21e1e9ddcb734c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3H3DE4A2PE4ZEUU3PVI5OWG26U/bundle.json","state_url":"https://pith.science/pith/3H3DE4A2PE4ZEUU3PVI5OWG26U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3H3DE4A2PE4ZEUU3PVI5OWG26U/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":"2026-05-26T14:50:09Z","links":{"resolver":"https://pith.science/pith/3H3DE4A2PE4ZEUU3PVI5OWG26U","bundle":"https://pith.science/pith/3H3DE4A2PE4ZEUU3PVI5OWG26U/bundle.json","state":"https://pith.science/pith/3H3DE4A2PE4ZEUU3PVI5OWG26U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3H3DE4A2PE4ZEUU3PVI5OWG26U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3H3DE4A2PE4ZEUU3PVI5OWG26U","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":"51615d49815193362b5e2ff1cbcb87cf108f1e3cdd7b7926347344ccc306e885","cross_cats_sorted":["cs.NA","math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2012-01-27T16:01:53Z","title_canon_sha256":"5fbe2a3d7463925e92a70712b5a4a8f1c54e9d5a7afe8b5154b4788f0e14a584"},"schema_version":"1.0","source":{"id":"1201.5810","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.5810","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"arxiv_version","alias_value":"1201.5810v1","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.5810","created_at":"2026-05-18T04:03:44Z"},{"alias_kind":"pith_short_12","alias_value":"3H3DE4A2PE4Z","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3H3DE4A2PE4ZEUU3","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3H3DE4A2","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:9780a05f3a6b6b899305c7428fe130b5845e034a9e16b84ab21e1e9ddcb734c5","target":"graph","created_at":"2026-05-18T04:03:44Z","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":"Sparse (or toric) elimination exploits the structure of polynomials by measuring their complexity in terms of Newton polytopes instead of total degree. The sparse, or Newton, resultant generalizes the classical homogeneous resultant and its degree is a function of the mixed volumes of the Newton polytopes. We sketch the sparse resultant constructions of Canny and Emiris and show how they reduce the problem of root-finding to an eigenproblem. A novel method for achieving this reduction is presented which does not increase the dimension of the problem. Together with an implementation of the spar","authors_text":"Ioannis Z. Emiris","cross_cats":["cs.NA","math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2012-01-27T16:01:53Z","title":"A General Solver Based on Sparse Resultants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.5810","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:f393a9f9354a877727d86af7174a818d30cb9f1b0204fd66f594a0638378dd1c","target":"record","created_at":"2026-05-18T04:03:44Z","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":"51615d49815193362b5e2ff1cbcb87cf108f1e3cdd7b7926347344ccc306e885","cross_cats_sorted":["cs.NA","math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2012-01-27T16:01:53Z","title_canon_sha256":"5fbe2a3d7463925e92a70712b5a4a8f1c54e9d5a7afe8b5154b4788f0e14a584"},"schema_version":"1.0","source":{"id":"1201.5810","kind":"arxiv","version":1}},"canonical_sha256":"d9f632701a793992529b7d51d758daf53be3da01ae85ebbd145c62dd5688691a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9f632701a793992529b7d51d758daf53be3da01ae85ebbd145c62dd5688691a","first_computed_at":"2026-05-18T04:03:44.464369Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:44.464369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MhGZ8l+hn6pQk20KzYO4RA4BkvjtIW28A4jDMe8GQiqvNlA7nwhnTK1E+w+JLnUknJe/lhfviGUWuTrdmTjBDA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:44.465393Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.5810","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f393a9f9354a877727d86af7174a818d30cb9f1b0204fd66f594a0638378dd1c","sha256:9780a05f3a6b6b899305c7428fe130b5845e034a9e16b84ab21e1e9ddcb734c5"],"state_sha256":"a26c5939a010e7e4126cca95e8f2bfabc719d9837fbf297025a021e9ae7a7b32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cbDHpQoiy9Gv62voYgaKpzJDTzfeXLkF01K8z2QQwWKdjzWGIyJWzWVu/BLtgNOaGZl4qg8iPHppYDTFB5IDDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T14:50:09.878382Z","bundle_sha256":"6bad75f9bd97f3a04776ecec60f1f70e07290604611336741c550166fe08605d"}}