{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:Y6ZDAIGNLV4AYJD4KIWUJJFPDV","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":"b35a3921fa0f8cb8a23bdb3af658529c3be0c4a7efacf8da410403478bf1fed9","cross_cats_sorted":["math.CO","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-08-02T20:39:06Z","title_canon_sha256":"da8b412c201d895c3ca5bf0bc5bdfd0414f6a79d3b3f8d66ae1dfd125de2c1a2"},"schema_version":"1.0","source":{"id":"2108.01161","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2108.01161","created_at":"2026-07-05T03:02:59Z"},{"alias_kind":"arxiv_version","alias_value":"2108.01161v1","created_at":"2026-07-05T03:02:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.01161","created_at":"2026-07-05T03:02:59Z"},{"alias_kind":"pith_short_12","alias_value":"Y6ZDAIGNLV4A","created_at":"2026-07-05T03:02:59Z"},{"alias_kind":"pith_short_16","alias_value":"Y6ZDAIGNLV4AYJD4","created_at":"2026-07-05T03:02:59Z"},{"alias_kind":"pith_short_8","alias_value":"Y6ZDAIGN","created_at":"2026-07-05T03:02:59Z"}],"graph_snapshots":[{"event_id":"sha256:7f0fb793790d0da2f4277099d811d01b921643aac1d9caf32663f6d2c7438b95","target":"graph","created_at":"2026-07-05T03:02:59Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2108.01161/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give an FPTAS for computing the number of matchings of size $k$ in a graph $G$ of maximum degree $\\Delta$ on $n$ vertices, for all $k \\le (1-\\delta)m^*(G)$, where $\\delta>0$ is fixed and $m^*(G)$ is the matching number of $G$, and an FPTAS for the number of independent sets of size $k \\le (1-\\delta) \\alpha_c(\\Delta) n$, where $\\alpha_c(\\Delta)$ is the NP-hardness threshold for this problem. We also provide quasi-linear time randomized algorithms to approximately sample from the uniform distribution on matchings of size $k \\leq (1-\\delta)m^*(G)$ and independent sets of size $k \\leq (1-\\delta","authors_text":"Ashwin Sah, Mehtaab Sawhney, Vishesh Jain, Will Perkins","cross_cats":["math.CO","math.PR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-08-02T20:39:06Z","title":"Approximate counting and sampling via local central limit theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.01161","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:e89e7ed651f54d8ca6904ef3496b5b3203c134bc333175e87a51a9b27bd8250d","target":"record","created_at":"2026-07-05T03:02:59Z","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":"b35a3921fa0f8cb8a23bdb3af658529c3be0c4a7efacf8da410403478bf1fed9","cross_cats_sorted":["math.CO","math.PR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2021-08-02T20:39:06Z","title_canon_sha256":"da8b412c201d895c3ca5bf0bc5bdfd0414f6a79d3b3f8d66ae1dfd125de2c1a2"},"schema_version":"1.0","source":{"id":"2108.01161","kind":"arxiv","version":1}},"canonical_sha256":"c7b23020cd5d780c247c522d44a4af1d6f1ad49c4a65606a066071157f6910bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c7b23020cd5d780c247c522d44a4af1d6f1ad49c4a65606a066071157f6910bf","first_computed_at":"2026-07-05T03:02:59.978582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:02:59.978582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aPq07CmBtGMPk8PpF9Qno4WBleWnM4nCKLIDYX9+foAKRc7w07miOG3JyjeXmIBP665olKz3IDNgeM0HORkxBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:02:59.979015Z","signed_message":"canonical_sha256_bytes"},"source_id":"2108.01161","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e89e7ed651f54d8ca6904ef3496b5b3203c134bc333175e87a51a9b27bd8250d","sha256:7f0fb793790d0da2f4277099d811d01b921643aac1d9caf32663f6d2c7438b95"],"state_sha256":"3435dc91f8d80fb8e0f0049f35345188a9ed480fdaf642d5fabd47eea71df357"}