{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:HMBJM6PJ57HYDLG7RI5AFD7F37","short_pith_number":"pith:HMBJM6PJ","canonical_record":{"source":{"id":"2007.11830","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2020-07-23T07:31:04Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"ad4ddfebff145af6012290e2f8a1bd79e800b0e3caaaec32dade1575033681ee","abstract_canon_sha256":"73e1d572a03b3ec86a6e8ea1c786df12d383224ead53ac60edf87442e9c8d56f"},"schema_version":"1.0"},"canonical_sha256":"3b029679e9efcf81acdf8a3a028fe5dfe7ecc0e5a4fd07a73ed732f0fd102ead","source":{"kind":"arxiv","id":"2007.11830","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.11830","created_at":"2026-07-05T07:33:05Z"},{"alias_kind":"arxiv_version","alias_value":"2007.11830v2","created_at":"2026-07-05T07:33:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.11830","created_at":"2026-07-05T07:33:05Z"},{"alias_kind":"pith_short_12","alias_value":"HMBJM6PJ57HY","created_at":"2026-07-05T07:33:05Z"},{"alias_kind":"pith_short_16","alias_value":"HMBJM6PJ57HYDLG7","created_at":"2026-07-05T07:33:05Z"},{"alias_kind":"pith_short_8","alias_value":"HMBJM6PJ","created_at":"2026-07-05T07:33:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:HMBJM6PJ57HYDLG7RI5AFD7F37","target":"record","payload":{"canonical_record":{"source":{"id":"2007.11830","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2020-07-23T07:31:04Z","cross_cats_sorted":["cs.NA","math.NA"],"title_canon_sha256":"ad4ddfebff145af6012290e2f8a1bd79e800b0e3caaaec32dade1575033681ee","abstract_canon_sha256":"73e1d572a03b3ec86a6e8ea1c786df12d383224ead53ac60edf87442e9c8d56f"},"schema_version":"1.0"},"canonical_sha256":"3b029679e9efcf81acdf8a3a028fe5dfe7ecc0e5a4fd07a73ed732f0fd102ead","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:33:05.713726Z","signature_b64":"gR4qG3I/oC96ZjCmyy5XFYfK0NZqS4zfz5yAU2KFhper27Od5ewTfpFw//oFNdJhC6Rp5vhMa3DDG8OQVaVKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b029679e9efcf81acdf8a3a028fe5dfe7ecc0e5a4fd07a73ed732f0fd102ead","last_reissued_at":"2026-07-05T07:33:05.713322Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:33:05.713322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2007.11830","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:33:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fQF4jVoVlnvIS3UuqDD88AiWKfp5b2C7rFM/uKa2aMXiC1440X8Cg8llArh/PHxgSfsF0UnWc6B7l5aiGsbsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:55:05.456534Z"},"content_sha256":"b317b67fb0c85c86895ffcb4b899fbbe1b3da7b143cd3a51e2603598378391e7","schema_version":"1.0","event_id":"sha256:b317b67fb0c85c86895ffcb4b899fbbe1b3da7b143cd3a51e2603598378391e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:HMBJM6PJ57HYDLG7RI5AFD7F37","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Groebner basis structure of ideal interpolation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.NA"],"primary_cat":"cs.SC","authors_text":"Xue Jiang, Yihe Gong","submitted_at":"2020-07-23T07:31:04Z","abstract_excerpt":"We study the relationship between certain Groebner bases for zero dimensional ideals, and the interpolation condition functionals of ideal interpolation. Ideal interpolation is defined by a linear idempotent projector whose kernel is a polynomial ideal. In this paper, we propose the notion of \"reverse\" complete reduced basis. Based on the notion, we present a fast algorithm to compute the reduced Groebner basis for the kernel of ideal projector under an arbitrary compatible ordering. As an application, we show that knowing the affine variety makes available information concerning the reduced G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.11830","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2007.11830/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:33:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0/wv69AxDzm7a+xlTm1Zrwin6eu05JO5TXr4sMFeYrncUhVBvj33Ws+jT7qs2jl8UdSyhx8z+c4G9DJH13QrBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T20:55:05.456908Z"},"content_sha256":"c21c453e6609d40133c014de0a7f41a9803fcf2437ce5bf1f9022f41402ceb5d","schema_version":"1.0","event_id":"sha256:c21c453e6609d40133c014de0a7f41a9803fcf2437ce5bf1f9022f41402ceb5d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HMBJM6PJ57HYDLG7RI5AFD7F37/bundle.json","state_url":"https://pith.science/pith/HMBJM6PJ57HYDLG7RI5AFD7F37/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HMBJM6PJ57HYDLG7RI5AFD7F37/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":"2026-07-06T20:55:05Z","links":{"resolver":"https://pith.science/pith/HMBJM6PJ57HYDLG7RI5AFD7F37","bundle":"https://pith.science/pith/HMBJM6PJ57HYDLG7RI5AFD7F37/bundle.json","state":"https://pith.science/pith/HMBJM6PJ57HYDLG7RI5AFD7F37/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HMBJM6PJ57HYDLG7RI5AFD7F37/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:HMBJM6PJ57HYDLG7RI5AFD7F37","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":"73e1d572a03b3ec86a6e8ea1c786df12d383224ead53ac60edf87442e9c8d56f","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2020-07-23T07:31:04Z","title_canon_sha256":"ad4ddfebff145af6012290e2f8a1bd79e800b0e3caaaec32dade1575033681ee"},"schema_version":"1.0","source":{"id":"2007.11830","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2007.11830","created_at":"2026-07-05T07:33:05Z"},{"alias_kind":"arxiv_version","alias_value":"2007.11830v2","created_at":"2026-07-05T07:33:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2007.11830","created_at":"2026-07-05T07:33:05Z"},{"alias_kind":"pith_short_12","alias_value":"HMBJM6PJ57HY","created_at":"2026-07-05T07:33:05Z"},{"alias_kind":"pith_short_16","alias_value":"HMBJM6PJ57HYDLG7","created_at":"2026-07-05T07:33:05Z"},{"alias_kind":"pith_short_8","alias_value":"HMBJM6PJ","created_at":"2026-07-05T07:33:05Z"}],"graph_snapshots":[{"event_id":"sha256:c21c453e6609d40133c014de0a7f41a9803fcf2437ce5bf1f9022f41402ceb5d","target":"graph","created_at":"2026-07-05T07:33:05Z","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/2007.11830/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the relationship between certain Groebner bases for zero dimensional ideals, and the interpolation condition functionals of ideal interpolation. Ideal interpolation is defined by a linear idempotent projector whose kernel is a polynomial ideal. In this paper, we propose the notion of \"reverse\" complete reduced basis. Based on the notion, we present a fast algorithm to compute the reduced Groebner basis for the kernel of ideal projector under an arbitrary compatible ordering. As an application, we show that knowing the affine variety makes available information concerning the reduced G","authors_text":"Xue Jiang, Yihe Gong","cross_cats":["cs.NA","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2020-07-23T07:31:04Z","title":"Groebner basis structure of ideal interpolation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2007.11830","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:b317b67fb0c85c86895ffcb4b899fbbe1b3da7b143cd3a51e2603598378391e7","target":"record","created_at":"2026-07-05T07:33:05Z","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":"73e1d572a03b3ec86a6e8ea1c786df12d383224ead53ac60edf87442e9c8d56f","cross_cats_sorted":["cs.NA","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2020-07-23T07:31:04Z","title_canon_sha256":"ad4ddfebff145af6012290e2f8a1bd79e800b0e3caaaec32dade1575033681ee"},"schema_version":"1.0","source":{"id":"2007.11830","kind":"arxiv","version":2}},"canonical_sha256":"3b029679e9efcf81acdf8a3a028fe5dfe7ecc0e5a4fd07a73ed732f0fd102ead","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3b029679e9efcf81acdf8a3a028fe5dfe7ecc0e5a4fd07a73ed732f0fd102ead","first_computed_at":"2026-07-05T07:33:05.713322Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:33:05.713322Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gR4qG3I/oC96ZjCmyy5XFYfK0NZqS4zfz5yAU2KFhper27Od5ewTfpFw//oFNdJhC6Rp5vhMa3DDG8OQVaVKAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:33:05.713726Z","signed_message":"canonical_sha256_bytes"},"source_id":"2007.11830","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b317b67fb0c85c86895ffcb4b899fbbe1b3da7b143cd3a51e2603598378391e7","sha256:c21c453e6609d40133c014de0a7f41a9803fcf2437ce5bf1f9022f41402ceb5d"],"state_sha256":"0bd93003107afb138bef00f21a955fbe168aca6579f492b67c29a9c2abc7bdd5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3z2e4t1vdjH1hEdPE3GM94di3ijYvzaVciOs3I8Dd/A32ICIwCjytDV7YkNBu/kWYSnvg6XYfit2jcDwooLlDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T20:55:05.458863Z","bundle_sha256":"914eccf779ad3e4af6a02574bdd050b89443566c5ee265fec08a87933384e82e"}}