{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RUELNQY3OSQQ4PEV3LFFKNVDNJ","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":"131efa95e0758414b684adaabcdf8e5cc8a3dc02fbc14d0ac76f53be0b063101","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-08T18:27:38Z","title_canon_sha256":"0a136778c3b660b88f808ae339350145c98699a7828814bd1dd133e8e72c0889"},"schema_version":"1.0","source":{"id":"1410.2209","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.2209","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"1410.2209v1","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2209","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"RUELNQY3OSQQ","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RUELNQY3OSQQ4PEV","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RUELNQY3","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:4b5d816b7633d6fae5d3612db5c38c114646caed4324320b2094dbafc7c2e390","target":"graph","created_at":"2026-05-18T02:40:47Z","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":"Assume that a group of people is going to an excursion and our task is to seat them into buses with several constraints each saying that a pair of people does not want to see each other in the same bus. This is a well-known coloring problem and it can be solved in $O^*(2^n)$ time by the inclusion-exclusion principle as shown by Bj\\\"{o}rklund, Husfeldt, and Koivisto in 2009.Another approach to solve this problem in $O^*(2^n)$ time is to use the fast Fourier transform. A graph is $k$-colorable if and only if the $k$-th power of a polynomial containing a monomial $\\prod_{i=1}^n x_i^{[i \\in I]}$ f","authors_text":"Alexander Golovnev, Alexander S. Kulikov, Ivan Mihajlin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-08T18:27:38Z","title":"Families with infants: speeding up algorithms for NP-hard problems using FFT"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2209","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":"sha256:681cc8e8759ef889f365d4f154237e2282811ba013959796b8f9ea3f4e5ebdfb","target":"record","created_at":"2026-05-18T02:40:47Z","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":"131efa95e0758414b684adaabcdf8e5cc8a3dc02fbc14d0ac76f53be0b063101","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-10-08T18:27:38Z","title_canon_sha256":"0a136778c3b660b88f808ae339350145c98699a7828814bd1dd133e8e72c0889"},"schema_version":"1.0","source":{"id":"1410.2209","kind":"arxiv","version":1}},"canonical_sha256":"8d08b6c31b74a10e3c95daca5536a36a5621481abe3d89f516e0f4d1d855d863","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d08b6c31b74a10e3c95daca5536a36a5621481abe3d89f516e0f4d1d855d863","first_computed_at":"2026-05-18T02:40:47.964811Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:47.964811Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CygR+XxOyZCqY2etQvgVqCaGWh4aLVck/fi0v8NaOk/R5v/Zu6bxXLrLw52/+0hLBatujPIr78EfEXv+9E5eAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:47.965388Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.2209","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:681cc8e8759ef889f365d4f154237e2282811ba013959796b8f9ea3f4e5ebdfb","sha256:4b5d816b7633d6fae5d3612db5c38c114646caed4324320b2094dbafc7c2e390"],"state_sha256":"324014cf6121e388e7bee14229267bb8f28e3f195565cde9d165132a235bbbed"}