{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:WG5RLNXUS2XNBHGTN2YLADJOQ5","short_pith_number":"pith:WG5RLNXU","schema_version":"1.0","canonical_sha256":"b1bb15b6f496aed09cd36eb0b00d2e87404d696d416330fcb7e0c0f882938006","source":{"kind":"arxiv","id":"2308.08041","version":1},"attestation_state":"computed","paper":{"title":"Typical sofic entropy and local limits for free group shift systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Christopher Shriver","submitted_at":"2023-08-15T21:06:04Z","abstract_excerpt":"We show that for any invariant measure $\\mu$ on a free group shift system, there are two numbers $h^\\flat \\leq h^\\sharp$ which in some sense are the typical upper and lower sofic entropy values. We also give a condition under which $h^\\flat = h^\\sharp = \\mathrm{f}(\\mu)$, where $\\mathrm{f}$ is the annealed entropy (also called the f invariant). This can be used to compute typical local limits of finitary Gibbs states over sequences of random regular graphs. As examples, we work out typical local limits of the Ising and Potts models.\n  We also show that, for Markov chains, the Kesten--Stigum sec"},"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":"2308.08041","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-08-15T21:06:04Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"030bcdb88da55609289134c162962a51f4127d1a7f594cfcab195db8365c8fbb","abstract_canon_sha256":"fe7c25b9434d796039e9fb9a8a8beaf92f3b7f844994d13ff1fed1ecc56b192c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:41:53.442783Z","signature_b64":"2sCEjT48k7J5t0C5S+iiRLmhMaBls9U2AIUoTiNXd7yGyr5LMnz7/ebO9kgLAGZl6pnnIMwsxmK3ipANf+SGCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b1bb15b6f496aed09cd36eb0b00d2e87404d696d416330fcb7e0c0f882938006","last_reissued_at":"2026-07-05T06:41:53.442301Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:41:53.442301Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Typical sofic entropy and local limits for free group shift systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.PR","authors_text":"Christopher Shriver","submitted_at":"2023-08-15T21:06:04Z","abstract_excerpt":"We show that for any invariant measure $\\mu$ on a free group shift system, there are two numbers $h^\\flat \\leq h^\\sharp$ which in some sense are the typical upper and lower sofic entropy values. We also give a condition under which $h^\\flat = h^\\sharp = \\mathrm{f}(\\mu)$, where $\\mathrm{f}$ is the annealed entropy (also called the f invariant). This can be used to compute typical local limits of finitary Gibbs states over sequences of random regular graphs. As examples, we work out typical local limits of the Ising and Potts models.\n  We also show that, for Markov chains, the Kesten--Stigum sec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.08041","kind":"arxiv","version":1},"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/2308.08041/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":"2308.08041","created_at":"2026-07-05T06:41:53.442370+00:00"},{"alias_kind":"arxiv_version","alias_value":"2308.08041v1","created_at":"2026-07-05T06:41:53.442370+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.08041","created_at":"2026-07-05T06:41:53.442370+00:00"},{"alias_kind":"pith_short_12","alias_value":"WG5RLNXUS2XN","created_at":"2026-07-05T06:41:53.442370+00:00"},{"alias_kind":"pith_short_16","alias_value":"WG5RLNXUS2XNBHGT","created_at":"2026-07-05T06:41:53.442370+00:00"},{"alias_kind":"pith_short_8","alias_value":"WG5RLNXU","created_at":"2026-07-05T06:41:53.442370+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.24283","citing_title":"Characterizing the limiting critical Potts measures on locally regular-tree-like expander graphs","ref_index":29,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/WG5RLNXUS2XNBHGTN2YLADJOQ5","json":"https://pith.science/pith/WG5RLNXUS2XNBHGTN2YLADJOQ5.json","graph_json":"https://pith.science/api/pith-number/WG5RLNXUS2XNBHGTN2YLADJOQ5/graph.json","events_json":"https://pith.science/api/pith-number/WG5RLNXUS2XNBHGTN2YLADJOQ5/events.json","paper":"https://pith.science/paper/WG5RLNXU"},"agent_actions":{"view_html":"https://pith.science/pith/WG5RLNXUS2XNBHGTN2YLADJOQ5","download_json":"https://pith.science/pith/WG5RLNXUS2XNBHGTN2YLADJOQ5.json","view_paper":"https://pith.science/paper/WG5RLNXU","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2308.08041&json=true","fetch_graph":"https://pith.science/api/pith-number/WG5RLNXUS2XNBHGTN2YLADJOQ5/graph.json","fetch_events":"https://pith.science/api/pith-number/WG5RLNXUS2XNBHGTN2YLADJOQ5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WG5RLNXUS2XNBHGTN2YLADJOQ5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WG5RLNXUS2XNBHGTN2YLADJOQ5/action/storage_attestation","attest_author":"https://pith.science/pith/WG5RLNXUS2XNBHGTN2YLADJOQ5/action/author_attestation","sign_citation":"https://pith.science/pith/WG5RLNXUS2XNBHGTN2YLADJOQ5/action/citation_signature","submit_replication":"https://pith.science/pith/WG5RLNXUS2XNBHGTN2YLADJOQ5/action/replication_record"}},"created_at":"2026-07-05T06:41:53.442370+00:00","updated_at":"2026-07-05T06:41:53.442370+00:00"}