{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:OQ7GIFU7VVVY7HJBFCUYN5PAIR","short_pith_number":"pith:OQ7GIFU7","canonical_record":{"source":{"id":"1712.04177","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-12-12T08:56:20Z","cross_cats_sorted":[],"title_canon_sha256":"94a2bb444d1b511309a0edf839f3e016287fa8398ffac94c2787fa960b7e4157","abstract_canon_sha256":"e9e737809bafa7d40c692832e5a80d76f6a07a726aee05fc6c001b480d93b116"},"schema_version":"1.0"},"canonical_sha256":"743e64169fad6b8f9d2128a986f5e044755b941a708d6e5282cf411925332ead","source":{"kind":"arxiv","id":"1712.04177","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04177","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04177v2","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04177","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"pith_short_12","alias_value":"OQ7GIFU7VVVY","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OQ7GIFU7VVVY7HJB","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OQ7GIFU7","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:OQ7GIFU7VVVY7HJBFCUYN5PAIR","target":"record","payload":{"canonical_record":{"source":{"id":"1712.04177","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-12-12T08:56:20Z","cross_cats_sorted":[],"title_canon_sha256":"94a2bb444d1b511309a0edf839f3e016287fa8398ffac94c2787fa960b7e4157","abstract_canon_sha256":"e9e737809bafa7d40c692832e5a80d76f6a07a726aee05fc6c001b480d93b116"},"schema_version":"1.0"},"canonical_sha256":"743e64169fad6b8f9d2128a986f5e044755b941a708d6e5282cf411925332ead","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:25.208972Z","signature_b64":"9mWg+FI2jCvuGNp3YrmZUiZa+MBqwfzIYnwr71ouZIPDrvi1eYaOCk3/17G6EcXMxPQwKdsw8halr+az/FuLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"743e64169fad6b8f9d2128a986f5e044755b941a708d6e5282cf411925332ead","last_reissued_at":"2026-05-17T23:56:25.208549Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:25.208549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.04177","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":"2026-05-17T23:56:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2ntEg0BFF8GbYgwIO3TnDLfXh/s6MfVAQ4rFAtSvHO7JTUSNhCi+PcmjaZQxutHw2ZEropRZEWj6pqVI1vCJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:36:27.773600Z"},"content_sha256":"13bbc20d2cd89832bd8026e38f8e73829460dc4120d2342e08656b008e4845bc","schema_version":"1.0","event_id":"sha256:13bbc20d2cd89832bd8026e38f8e73829460dc4120d2342e08656b008e4845bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:OQ7GIFU7VVVY7HJBFCUYN5PAIR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Block-Krylov techniques in the context of sparse-FGLM algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Eric Schost, Hamid Rahkooy, Seung Gyu Hyun, Vincent Neiger","submitted_at":"2017-12-12T08:56:20Z","abstract_excerpt":"Consider a zero-dimensional ideal $I$ in $\\mathbb{K}[X_1,\\dots,X_n]$. Inspired by Faug\\`ere and Mou's Sparse FGLM algorithm, we use Krylov sequences based on multiplication matrices of $I$ in order to compute a description of its zero set by means of univariate polynomials.\n  Steel recently showed how to use Coppersmith's block-Wiedemann algorithm in this context; he describes an algorithm that can be easily parallelized, but only computes parts of the output in this manner. Using generating series expressions going back to work of Bostan, Salvy, and Schost, we show how to compute the entire o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04177","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":""},"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":"2026-05-17T23:56:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gmhho9Zc9xVbn03Aj7K98zShre1tRC/hddajXDn+ZSebF8XPRfolUOOqan+0POe33I3K3GmT5kMB2V1bP88wAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T11:36:27.773941Z"},"content_sha256":"436de8b6249f3b82780c099671f6d27b69af7975dcd82c02c9d07a678bee0791","schema_version":"1.0","event_id":"sha256:436de8b6249f3b82780c099671f6d27b69af7975dcd82c02c9d07a678bee0791"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OQ7GIFU7VVVY7HJBFCUYN5PAIR/bundle.json","state_url":"https://pith.science/pith/OQ7GIFU7VVVY7HJBFCUYN5PAIR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OQ7GIFU7VVVY7HJBFCUYN5PAIR/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":"2026-06-01T11:36:27Z","links":{"resolver":"https://pith.science/pith/OQ7GIFU7VVVY7HJBFCUYN5PAIR","bundle":"https://pith.science/pith/OQ7GIFU7VVVY7HJBFCUYN5PAIR/bundle.json","state":"https://pith.science/pith/OQ7GIFU7VVVY7HJBFCUYN5PAIR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OQ7GIFU7VVVY7HJBFCUYN5PAIR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:OQ7GIFU7VVVY7HJBFCUYN5PAIR","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":"e9e737809bafa7d40c692832e5a80d76f6a07a726aee05fc6c001b480d93b116","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-12-12T08:56:20Z","title_canon_sha256":"94a2bb444d1b511309a0edf839f3e016287fa8398ffac94c2787fa960b7e4157"},"schema_version":"1.0","source":{"id":"1712.04177","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.04177","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"arxiv_version","alias_value":"1712.04177v2","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.04177","created_at":"2026-05-17T23:56:25Z"},{"alias_kind":"pith_short_12","alias_value":"OQ7GIFU7VVVY","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"OQ7GIFU7VVVY7HJB","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"OQ7GIFU7","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:436de8b6249f3b82780c099671f6d27b69af7975dcd82c02c9d07a678bee0791","target":"graph","created_at":"2026-05-17T23:56:25Z","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"},"paper":{"abstract_excerpt":"Consider a zero-dimensional ideal $I$ in $\\mathbb{K}[X_1,\\dots,X_n]$. Inspired by Faug\\`ere and Mou's Sparse FGLM algorithm, we use Krylov sequences based on multiplication matrices of $I$ in order to compute a description of its zero set by means of univariate polynomials.\n  Steel recently showed how to use Coppersmith's block-Wiedemann algorithm in this context; he describes an algorithm that can be easily parallelized, but only computes parts of the output in this manner. Using generating series expressions going back to work of Bostan, Salvy, and Schost, we show how to compute the entire o","authors_text":"Eric Schost, Hamid Rahkooy, Seung Gyu Hyun, Vincent Neiger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-12-12T08:56:20Z","title":"Block-Krylov techniques in the context of sparse-FGLM algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.04177","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":"sha256:13bbc20d2cd89832bd8026e38f8e73829460dc4120d2342e08656b008e4845bc","target":"record","created_at":"2026-05-17T23:56:25Z","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":"e9e737809bafa7d40c692832e5a80d76f6a07a726aee05fc6c001b480d93b116","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2017-12-12T08:56:20Z","title_canon_sha256":"94a2bb444d1b511309a0edf839f3e016287fa8398ffac94c2787fa960b7e4157"},"schema_version":"1.0","source":{"id":"1712.04177","kind":"arxiv","version":2}},"canonical_sha256":"743e64169fad6b8f9d2128a986f5e044755b941a708d6e5282cf411925332ead","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"743e64169fad6b8f9d2128a986f5e044755b941a708d6e5282cf411925332ead","first_computed_at":"2026-05-17T23:56:25.208549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:25.208549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9mWg+FI2jCvuGNp3YrmZUiZa+MBqwfzIYnwr71ouZIPDrvi1eYaOCk3/17G6EcXMxPQwKdsw8halr+az/FuLDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:25.208972Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.04177","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:13bbc20d2cd89832bd8026e38f8e73829460dc4120d2342e08656b008e4845bc","sha256:436de8b6249f3b82780c099671f6d27b69af7975dcd82c02c9d07a678bee0791"],"state_sha256":"90d43e1fa601fb363ac948157dfcfae2e8c7decab8c2bb2239f36a1720c094ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NjKNq15HLXC5fXvTabFXs71qCBUNSG+z77z5U9Zw/9IMOzEq++Cyr2FpfOv+PrS53jWGxf7H2Kp7NeLRt7CKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T11:36:27.775828Z","bundle_sha256":"6c10c8c41dca59119e93217e4aca83bbfbf74d6a1087cb93cbe4ee0fc7e1c3ed"}}