{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GDWMKOGJTKQBU6YJG6TIAP4546","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":"67810fecc4195a705c7638c860a0400597b06bf3dc8b282c2ed533c400709742","cross_cats_sorted":["cs.IT","math.CO","math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-02T23:50:07Z","title_canon_sha256":"616e9654d3265a933ed15dbb5797949844cd401fea8c0c39d187b07c3960d17c"},"schema_version":"1.0","source":{"id":"1807.00929","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.00929","created_at":"2026-05-18T00:01:38Z"},{"alias_kind":"arxiv_version","alias_value":"1807.00929v2","created_at":"2026-05-18T00:01:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.00929","created_at":"2026-05-18T00:01:38Z"},{"alias_kind":"pith_short_12","alias_value":"GDWMKOGJTKQB","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GDWMKOGJTKQBU6YJ","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GDWMKOGJ","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:fdb4b71bfd4debe7aa85afb6e78276d612127b48a18dfc32f4ae3273ba0ef07f","target":"graph","created_at":"2026-05-18T00:01:38Z","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":"We give a deterministic polynomial time $2^{O(r)}$-approximation algorithm for the number of bases of a given matroid of rank $r$ and the number of common bases of any two matroids of rank $r$. To the best of our knowledge, this is the first nontrivial deterministic approximation algorithm that works for arbitrary matroids. Based on a lower bound of Azar, Broder, and Frieze [ABF94] this is almost the best possible result assuming oracle access to independent sets of the matroid.\n  There are two main ingredients in our result: For the first, we build upon recent results of Adiprasito, Huh, and ","authors_text":"Cynthia Vinzant, Nima Anari, Shayan Oveis Gharan","cross_cats":["cs.IT","math.CO","math.IT","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-02T23:50:07Z","title":"Log-Concave Polynomials I: Entropy and a Deterministic Approximation Algorithm for Counting Bases of Matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.00929","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":"sha256:16956fb05c815d09eb4ddbddae96f9f31fa4fe1360dc2c2a0cd2e34d075457c9","target":"record","created_at":"2026-05-18T00:01:38Z","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":"67810fecc4195a705c7638c860a0400597b06bf3dc8b282c2ed533c400709742","cross_cats_sorted":["cs.IT","math.CO","math.IT","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2018-07-02T23:50:07Z","title_canon_sha256":"616e9654d3265a933ed15dbb5797949844cd401fea8c0c39d187b07c3960d17c"},"schema_version":"1.0","source":{"id":"1807.00929","kind":"arxiv","version":2}},"canonical_sha256":"30ecc538c99aa01a7b0937a6803f9de7b164de6952cab92c3bc91cfa96e3ba7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"30ecc538c99aa01a7b0937a6803f9de7b164de6952cab92c3bc91cfa96e3ba7e","first_computed_at":"2026-05-18T00:01:38.113080Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:38.113080Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/yK0LQqIwTymi/PMYE49oX93z4bFfc/6TNMd7wg6YGvTlA2SfQEDRdqjW9WMvnvXAZcrvS8W8gY0ViR/DEfjBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:38.113606Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.00929","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16956fb05c815d09eb4ddbddae96f9f31fa4fe1360dc2c2a0cd2e34d075457c9","sha256:fdb4b71bfd4debe7aa85afb6e78276d612127b48a18dfc32f4ae3273ba0ef07f"],"state_sha256":"725ffce432ade4325c7451bc5293b1cdec79f1c079a07b4f38d6d85d66cd5212"}