{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NTWRKKVVMCP5ULIBG5NXZVRONO","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":"f9a5330a08c7d367bf7e03b5c8f22199d87610cc8aec17b4685349d4aa9e6ec9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-05-14T21:44:01Z","title_canon_sha256":"cc3affd032565374b0bc431ca7d2055e249e906f6a703f98ae162da1860b7580"},"schema_version":"1.0","source":{"id":"1605.04472","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.04472","created_at":"2026-05-18T00:10:48Z"},{"alias_kind":"arxiv_version","alias_value":"1605.04472v1","created_at":"2026-05-18T00:10:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.04472","created_at":"2026-05-18T00:10:48Z"},{"alias_kind":"pith_short_12","alias_value":"NTWRKKVVMCP5","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"NTWRKKVVMCP5ULIB","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"NTWRKKVV","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:0b71c06789e60b0df246f06b25832915ba26f841f1ca10e5be98e8f518963d3c","target":"graph","created_at":"2026-05-18T00:10:48Z","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":"Two models were recently proposed to explore the robust hardness of Gr\\\"obner basis computation. Given a polynomial system, both models allow an algorithm to selectively ignore some of the polynomials: the algorithm is only responsible for returning a Gr\\\"obner basis for the ideal generated by the remaining polynomials. For the $q$-Fractional Gr\\\"obner Basis Problem the algorithm is allowed to ignore a constant $(1-q)$-fraction of the polynomials (subject to one natural structural constraint). Here we prove a new strongest-parameter result: even if the algorithm is allowed to choose a $(3/10-\\","authors_text":"Gwen Spencer","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-05-14T21:44:01Z","title":"Extended Hardness Results for Approximate Gr\\\"obner Basis Computation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.04472","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":"sha256:49000863c77a07297b65731fb61bcf23576cdcc06ea6d9696a7307930b4e31ae","target":"record","created_at":"2026-05-18T00:10:48Z","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":"f9a5330a08c7d367bf7e03b5c8f22199d87610cc8aec17b4685349d4aa9e6ec9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2016-05-14T21:44:01Z","title_canon_sha256":"cc3affd032565374b0bc431ca7d2055e249e906f6a703f98ae162da1860b7580"},"schema_version":"1.0","source":{"id":"1605.04472","kind":"arxiv","version":1}},"canonical_sha256":"6ced152ab5609fda2d01375b7cd62e6bb5b2c3fdca28fd8c4781ff245dbc5607","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ced152ab5609fda2d01375b7cd62e6bb5b2c3fdca28fd8c4781ff245dbc5607","first_computed_at":"2026-05-18T00:10:48.178097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:10:48.178097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HGaxddLdL/t545B3vBwoAUMfd3Bt3OPVR0VWavu5ec5t3y7PusTCgApOjyuWIbeDxQutqG3mQ+rKVIN2/og+Dg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:10:48.178652Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.04472","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49000863c77a07297b65731fb61bcf23576cdcc06ea6d9696a7307930b4e31ae","sha256:0b71c06789e60b0df246f06b25832915ba26f841f1ca10e5be98e8f518963d3c"],"state_sha256":"04692edeec390eddeb6021703c346c3dce2c8976e5e7c6b9e836d0b1be972748"}