{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MYF3FRO5J7ZOF6W75WFBCTNS2X","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":"eff9a42666391b9f38c0f636c28ad9bb57f596e2a91eb2c4cf6cc95ee76dcc58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-02-06T12:57:47Z","title_canon_sha256":"707508470b74a864cea1448a2d92dcec1fea6417ece064f8515d7b9ed75b890b"},"schema_version":"1.0","source":{"id":"1802.01920","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01920","created_at":"2026-05-18T00:15:42Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01920v2","created_at":"2026-05-18T00:15:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01920","created_at":"2026-05-18T00:15:42Z"},{"alias_kind":"pith_short_12","alias_value":"MYF3FRO5J7ZO","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_16","alias_value":"MYF3FRO5J7ZOF6W7","created_at":"2026-05-18T12:32:40Z"},{"alias_kind":"pith_short_8","alias_value":"MYF3FRO5","created_at":"2026-05-18T12:32:40Z"}],"graph_snapshots":[{"event_id":"sha256:d87eff3bd14eb830fb48b53a6f3d773e05820c39a0d01df0f5ba266c0360501d","target":"graph","created_at":"2026-05-18T00:15:42Z","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":"For a given computational problem, a certificate is a piece of data that one (the prover) attaches to the output with the aim of allowing efficient verification (by the verifier) that this output is correct. Here, we consider the minimal approximant basis problem, for which the fastest known algorithms output a polynomial matrix of dimensions $m \\times m$ and average degree $D/m$ using $O\\tilde{~}(m^\\omega \\frac{D}{m})$ field operations. We propose a certificate which, for typical instances of the problem, is computed by the prover using $O(m^\\omega \\frac{D}{m})$ additional field operations an","authors_text":"Pascal Giorgi, Vincent Neiger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-02-06T12:57:47Z","title":"Certification of minimal approximant bases"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01920","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":"sha256:886feb8958c9e98efd8d78f498a9b180f2674c69669bfca589db0eaa9517cfe6","target":"record","created_at":"2026-05-18T00:15:42Z","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":"eff9a42666391b9f38c0f636c28ad9bb57f596e2a91eb2c4cf6cc95ee76dcc58","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2018-02-06T12:57:47Z","title_canon_sha256":"707508470b74a864cea1448a2d92dcec1fea6417ece064f8515d7b9ed75b890b"},"schema_version":"1.0","source":{"id":"1802.01920","kind":"arxiv","version":2}},"canonical_sha256":"660bb2c5dd4ff2e2fadfed8a114db2d5d7b919e384957248902e3a211585304d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"660bb2c5dd4ff2e2fadfed8a114db2d5d7b919e384957248902e3a211585304d","first_computed_at":"2026-05-18T00:15:42.854475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:42.854475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SN6Cd+mij8aoIEy0M5LPcU6rc4I+5ELe9/8Z362A3bh78QSY0ozCQEoHvh/9PzUvKukhwSxotC8blNtglBE8Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:42.854972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.01920","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:886feb8958c9e98efd8d78f498a9b180f2674c69669bfca589db0eaa9517cfe6","sha256:d87eff3bd14eb830fb48b53a6f3d773e05820c39a0d01df0f5ba266c0360501d"],"state_sha256":"de77a501447ffd6ed480bbf4e20150c0ffec732130d4bcf0ee9ea6fb3e2f8012"}