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This spectral gap holds for all, including unbounded, maximum degree $\\Delta$. Consequently, we have the following mixing time bounds for the models satisfying the uniqueness condition with a slack $\\delta\\in(0,1)$:\n  $\\bullet$ $C(\\delta) n^2\\log n$ mixing time for the hardcore model with fugacity $\\lambda\\le (1-\\delta)\\lambda_c(\\Delta)= (1-\\delta)\\frac{(\\Delta - 1)^{\\Delta - 1}}{(\\Delta - 2)^\\Delta}$;\n  $\\bullet$ $C(\\"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2105.15005","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2021-05-31T14:40:34Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"426f92392c20e4a39cf17ddf5f53391d0188f49cffa186e355d28d5f4971999f","abstract_canon_sha256":"d495494479b53a5588aa5274647d5e7379c7a5b8df69a93148b9d22adda13f57"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:33:21.947391Z","signature_b64":"KgpK1pQMhxYch2kc3Q4A+O7OAkzYMbKcGAkM2TYpGBUCp9EHv4HKYbNg73EG6wORbVYSe7tVx1jgefAC+KQAAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06f0859dbd762f6775d5a0779645a87a0061969b606f9735c3f4487001de6823","last_reissued_at":"2026-07-05T03:33:21.946942Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:33:21.946942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rapid mixing of Glauber dynamics via spectral independence for all degrees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"cs.DS","authors_text":"Weiming Feng, Xiaoyu Chen, Xinyuan Zhang, Yitong Yin","submitted_at":"2021-05-31T14:40:34Z","abstract_excerpt":"We prove an optimal $\\Omega(n^{-1})$ lower bound on the spectral gap of Glauber dynamics for anti-ferromagnetic two-spin systems with $n$ vertices in the tree uniqueness regime. This spectral gap holds for all, including unbounded, maximum degree $\\Delta$. Consequently, we have the following mixing time bounds for the models satisfying the uniqueness condition with a slack $\\delta\\in(0,1)$:\n  $\\bullet$ $C(\\delta) n^2\\log n$ mixing time for the hardcore model with fugacity $\\lambda\\le (1-\\delta)\\lambda_c(\\Delta)= (1-\\delta)\\frac{(\\Delta - 1)^{\\Delta - 1}}{(\\Delta - 2)^\\Delta}$;\n  $\\bullet$ $C(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.15005","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.15005/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2105.15005","created_at":"2026-07-05T03:33:21.947008+00:00"},{"alias_kind":"arxiv_version","alias_value":"2105.15005v3","created_at":"2026-07-05T03:33:21.947008+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.15005","created_at":"2026-07-05T03:33:21.947008+00:00"},{"alias_kind":"pith_short_12","alias_value":"A3YILHN5OYXW","created_at":"2026-07-05T03:33:21.947008+00:00"},{"alias_kind":"pith_short_16","alias_value":"A3YILHN5OYXWO5OV","created_at":"2026-07-05T03:33:21.947008+00:00"},{"alias_kind":"pith_short_8","alias_value":"A3YILHN5","created_at":"2026-07-05T03:33:21.947008+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/A3YILHN5OYXWO5OVUB3ZMRNIPI","json":"https://pith.science/pith/A3YILHN5OYXWO5OVUB3ZMRNIPI.json","graph_json":"https://pith.science/api/pith-number/A3YILHN5OYXWO5OVUB3ZMRNIPI/graph.json","events_json":"https://pith.science/api/pith-number/A3YILHN5OYXWO5OVUB3ZMRNIPI/events.json","paper":"https://pith.science/paper/A3YILHN5"},"agent_actions":{"view_html":"https://pith.science/pith/A3YILHN5OYXWO5OVUB3ZMRNIPI","download_json":"https://pith.science/pith/A3YILHN5OYXWO5OVUB3ZMRNIPI.json","view_paper":"https://pith.science/paper/A3YILHN5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2105.15005&json=true","fetch_graph":"https://pith.science/api/pith-number/A3YILHN5OYXWO5OVUB3ZMRNIPI/graph.json","fetch_events":"https://pith.science/api/pith-number/A3YILHN5OYXWO5OVUB3ZMRNIPI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A3YILHN5OYXWO5OVUB3ZMRNIPI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A3YILHN5OYXWO5OVUB3ZMRNIPI/action/storage_attestation","attest_author":"https://pith.science/pith/A3YILHN5OYXWO5OVUB3ZMRNIPI/action/author_attestation","sign_citation":"https://pith.science/pith/A3YILHN5OYXWO5OVUB3ZMRNIPI/action/citation_signature","submit_replication":"https://pith.science/pith/A3YILHN5OYXWO5OVUB3ZMRNIPI/action/replication_record"}},"created_at":"2026-07-05T03:33:21.947008+00:00","updated_at":"2026-07-05T03:33:21.947008+00:00"}