{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:O5QMKLRYMZCREVGSLUQOLEW4VV","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":"6462c36109fb72884873b88dee1db4c6c9c04597a1d86a37e125ab47717f916f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-06-12T04:12:14Z","title_canon_sha256":"ca1ef8698fb31028d5c400935feb44be068fe8a7650ae335832b2ea48c31154f"},"schema_version":"1.0","source":{"id":"1206.2436","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.2436","created_at":"2026-05-18T03:49:59Z"},{"alias_kind":"arxiv_version","alias_value":"1206.2436v2","created_at":"2026-05-18T03:49:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.2436","created_at":"2026-05-18T03:49:59Z"},{"alias_kind":"pith_short_12","alias_value":"O5QMKLRYMZCR","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"O5QMKLRYMZCREVGS","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"O5QMKLRY","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:417c96eef4b04c285f57496e17e943470efce46fbd1e7839419d346ffb427bff","target":"graph","created_at":"2026-05-18T03:49:59Z","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":"The PCP Theorem is one of the most stunning results in computational complexity theory, a culmination of a series of results regarding proof checking it exposes some deep structure of computational problems. As a surprising side-effect, it also gives strong non-approximability results. In this paper we initiate the study of proof checking within the scope of Parameterized Complexity. In particular we adapt and extend the PCP[n log log n, n log log n] result of Feige et al. to several parameterized classes, and discuss some corollaries.","authors_text":"Luke Mathieson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-06-12T04:12:14Z","title":"A Proof Checking View of Parameterized Complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.2436","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:b7d8e71160c082fe3e43554dfc3df288e6ce3f9d05e3ef9878858f2b05fe4dd6","target":"record","created_at":"2026-05-18T03:49:59Z","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":"6462c36109fb72884873b88dee1db4c6c9c04597a1d86a37e125ab47717f916f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CC","submitted_at":"2012-06-12T04:12:14Z","title_canon_sha256":"ca1ef8698fb31028d5c400935feb44be068fe8a7650ae335832b2ea48c31154f"},"schema_version":"1.0","source":{"id":"1206.2436","kind":"arxiv","version":2}},"canonical_sha256":"7760c52e3866451254d25d20e592dcad4d9ad840e3cc35409458b3cc2e9b2e75","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7760c52e3866451254d25d20e592dcad4d9ad840e3cc35409458b3cc2e9b2e75","first_computed_at":"2026-05-18T03:49:59.489189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:59.489189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vhoF+Nqan0sDAHKgedL9ArCxQWu6tEh0zBYcWewNzz+2RKGNc8t/hCp+H5JrfaDyWAOgIb6uQ2wWBsI1yfGhBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:59.489619Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.2436","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b7d8e71160c082fe3e43554dfc3df288e6ce3f9d05e3ef9878858f2b05fe4dd6","sha256:417c96eef4b04c285f57496e17e943470efce46fbd1e7839419d346ffb427bff"],"state_sha256":"793ab7b88baab76376f9650a4239942994717e4eecf84ca9c311921422356134"}