{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:QD5D4LRG4DKE6VXAYKN2DOGBCK","short_pith_number":"pith:QD5D4LRG","canonical_record":{"source":{"id":"1905.04356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-05-10T19:44:41Z","cross_cats_sorted":[],"title_canon_sha256":"41e84abee8a94af448fc97a6cdef12a0eedd02e161ee6584e59bb9cd784fc865","abstract_canon_sha256":"d439ffb0148a4b177a21e467ccaa8534426107df3d6c9649b870b91d2945a21c"},"schema_version":"1.0"},"canonical_sha256":"80fa3e2e26e0d44f56e0c29ba1b8c112929bb91296c547984c5b1ecee834bcba","source":{"kind":"arxiv","id":"1905.04356","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.04356","created_at":"2026-05-17T23:46:25Z"},{"alias_kind":"arxiv_version","alias_value":"1905.04356v1","created_at":"2026-05-17T23:46:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04356","created_at":"2026-05-17T23:46:25Z"},{"alias_kind":"pith_short_12","alias_value":"QD5D4LRG4DKE","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QD5D4LRG4DKE6VXA","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QD5D4LRG","created_at":"2026-05-18T12:33:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:QD5D4LRG4DKE6VXAYKN2DOGBCK","target":"record","payload":{"canonical_record":{"source":{"id":"1905.04356","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-05-10T19:44:41Z","cross_cats_sorted":[],"title_canon_sha256":"41e84abee8a94af448fc97a6cdef12a0eedd02e161ee6584e59bb9cd784fc865","abstract_canon_sha256":"d439ffb0148a4b177a21e467ccaa8534426107df3d6c9649b870b91d2945a21c"},"schema_version":"1.0"},"canonical_sha256":"80fa3e2e26e0d44f56e0c29ba1b8c112929bb91296c547984c5b1ecee834bcba","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:25.203853Z","signature_b64":"vm1LJiHAg7yzN3N3i2m5dMFVZdulP4mRhf+57Lii9tKsPX6n0TP/StzTeUOBUc/a3qgfzwEwYfF9AbOXMK03DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"80fa3e2e26e0d44f56e0c29ba1b8c112929bb91296c547984c5b1ecee834bcba","last_reissued_at":"2026-05-17T23:46:25.202984Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:25.202984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1905.04356","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":"2026-05-17T23:46:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MrHCU/esjl5YAGQqTaih8dXIESu3nMpyoa3Kj3g3nMU5rdO5y6Y+Fmadc13ZVh04WNAWtmtzCT8PMju7gsq/BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:58:46.873900Z"},"content_sha256":"4bc0ad6e5340cb8c227ccc2322787737ef97a8a1ba4c0052696900dffcbf24c0","schema_version":"1.0","event_id":"sha256:4bc0ad6e5340cb8c227ccc2322787737ef97a8a1ba4c0052696900dffcbf24c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:QD5D4LRG4DKE6VXAYKN2DOGBCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Implementations of efficient univariate polynomial matrix algorithms and application to bivariate resultants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"\\'Eric Schost, Seung Gyu Hyun, Vincent Neiger","submitted_at":"2019-05-10T19:44:41Z","abstract_excerpt":"Complexity bounds for many problems on matrices with univariate polynomial entries have been improved in the last few years. Still, for most related algorithms, efficient implementations are not available, which leaves open the question of the practical impact of these algorithms, e.g. on applications such as decoding some error-correcting codes and solving polynomial systems or structured linear systems. In this paper, we discuss implementation aspects for most fundamental operations: multiplication, truncated inversion, approximants, interpolants, kernels, linear system solving, determinant,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04356","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":"2026-05-17T23:46:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GMBCDkX6zepuuXQNY3JYue8/OjZayEJHf69xWwHkqn8erkKSc2azA+ueWy5K5tDwxhdUz3RZinxlo5JCZV/xBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:58:46.874240Z"},"content_sha256":"43c8297702cb7eaeacbb03d57ad214ad8633b3d921108c556462f03205f582fa","schema_version":"1.0","event_id":"sha256:43c8297702cb7eaeacbb03d57ad214ad8633b3d921108c556462f03205f582fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QD5D4LRG4DKE6VXAYKN2DOGBCK/bundle.json","state_url":"https://pith.science/pith/QD5D4LRG4DKE6VXAYKN2DOGBCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QD5D4LRG4DKE6VXAYKN2DOGBCK/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":"2026-06-01T16:58:46Z","links":{"resolver":"https://pith.science/pith/QD5D4LRG4DKE6VXAYKN2DOGBCK","bundle":"https://pith.science/pith/QD5D4LRG4DKE6VXAYKN2DOGBCK/bundle.json","state":"https://pith.science/pith/QD5D4LRG4DKE6VXAYKN2DOGBCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QD5D4LRG4DKE6VXAYKN2DOGBCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:QD5D4LRG4DKE6VXAYKN2DOGBCK","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":"d439ffb0148a4b177a21e467ccaa8534426107df3d6c9649b870b91d2945a21c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-05-10T19:44:41Z","title_canon_sha256":"41e84abee8a94af448fc97a6cdef12a0eedd02e161ee6584e59bb9cd784fc865"},"schema_version":"1.0","source":{"id":"1905.04356","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.04356","created_at":"2026-05-17T23:46:25Z"},{"alias_kind":"arxiv_version","alias_value":"1905.04356v1","created_at":"2026-05-17T23:46:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.04356","created_at":"2026-05-17T23:46:25Z"},{"alias_kind":"pith_short_12","alias_value":"QD5D4LRG4DKE","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_16","alias_value":"QD5D4LRG4DKE6VXA","created_at":"2026-05-18T12:33:27Z"},{"alias_kind":"pith_short_8","alias_value":"QD5D4LRG","created_at":"2026-05-18T12:33:27Z"}],"graph_snapshots":[{"event_id":"sha256:43c8297702cb7eaeacbb03d57ad214ad8633b3d921108c556462f03205f582fa","target":"graph","created_at":"2026-05-17T23:46:25Z","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":"Complexity bounds for many problems on matrices with univariate polynomial entries have been improved in the last few years. Still, for most related algorithms, efficient implementations are not available, which leaves open the question of the practical impact of these algorithms, e.g. on applications such as decoding some error-correcting codes and solving polynomial systems or structured linear systems. In this paper, we discuss implementation aspects for most fundamental operations: multiplication, truncated inversion, approximants, interpolants, kernels, linear system solving, determinant,","authors_text":"\\'Eric Schost, Seung Gyu Hyun, Vincent Neiger","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-05-10T19:44:41Z","title":"Implementations of efficient univariate polynomial matrix algorithms and application to bivariate resultants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.04356","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":"sha256:4bc0ad6e5340cb8c227ccc2322787737ef97a8a1ba4c0052696900dffcbf24c0","target":"record","created_at":"2026-05-17T23:46:25Z","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":"d439ffb0148a4b177a21e467ccaa8534426107df3d6c9649b870b91d2945a21c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2019-05-10T19:44:41Z","title_canon_sha256":"41e84abee8a94af448fc97a6cdef12a0eedd02e161ee6584e59bb9cd784fc865"},"schema_version":"1.0","source":{"id":"1905.04356","kind":"arxiv","version":1}},"canonical_sha256":"80fa3e2e26e0d44f56e0c29ba1b8c112929bb91296c547984c5b1ecee834bcba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"80fa3e2e26e0d44f56e0c29ba1b8c112929bb91296c547984c5b1ecee834bcba","first_computed_at":"2026-05-17T23:46:25.202984Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:25.202984Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vm1LJiHAg7yzN3N3i2m5dMFVZdulP4mRhf+57Lii9tKsPX6n0TP/StzTeUOBUc/a3qgfzwEwYfF9AbOXMK03DQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:25.203853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.04356","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bc0ad6e5340cb8c227ccc2322787737ef97a8a1ba4c0052696900dffcbf24c0","sha256:43c8297702cb7eaeacbb03d57ad214ad8633b3d921108c556462f03205f582fa"],"state_sha256":"d464ac6e2f7482b40656c853c05a075f74be5ede61e0bfba42a22559925248d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/M8tOLB7PLFGpVudfJcCKyCh6DyVCtWhnI2ZrJ9FTpn+N3qiEvLv+7H2kmRf3Wa6sT1FPNGMVYGRZrjrQGANAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:58:46.876210Z","bundle_sha256":"bc396cee708d16bec605c0d68b1cb3946a355f79495546ad96bb609e6929d0d8"}}