{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:GOPUZJFHYG3VG5IBQWOKKX7JWT","short_pith_number":"pith:GOPUZJFH","schema_version":"1.0","canonical_sha256":"339f4ca4a7c1b7537501859ca55fe9b4e8b64161f64943a414a8401ec95be67b","source":{"kind":"arxiv","id":"2208.13209","version":6},"attestation_state":"computed","paper":{"title":"Subcohomology and a Livsic Theorem for Zooming Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eduardo Santana, Lamine Mbarki","submitted_at":"2022-08-28T12:27:11Z","abstract_excerpt":"In the context of continuous zooming systems $f:M \\to M$ on a compact metric space $M$, which include the non-uniformly expanding ones, possibly with the presence of a critical set, with the zooming set dense in $M$, we prove that any H\\\"older potential $\\phi : M \\to \\mathbb{R}$ for which the integrals $\\int \\phi d\\mu \\geq 0$ with respect to any $f$-invariant probability $\\mu$, admits a continuous function $\\lambda_{0} : M \\to \\mathbb{R}$ (which can be H\\\"older if some integral is positive) such that\n  \\[\n  \\phi \\geq \\lambda_{0}- \\lambda_{0} \\circ f.\n  \\]\n  This extends a result in [9] for $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":"2208.13209","kind":"arxiv","version":6},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DS","submitted_at":"2022-08-28T12:27:11Z","cross_cats_sorted":[],"title_canon_sha256":"6c97cb5e0eced739b2bc347cf0942d47b8e80272bb365269e735a9035da5917d","abstract_canon_sha256":"16d22c87dea6137ab8fc9f472ce3b89faf971d2a1f49dd9d753f4affc3f31052"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:49:01.969424Z","signature_b64":"07c6+xKL+tJ8+bZYUfX7dvY+5IqzgVCYtJFNNzJa6MJucSOipxJI+PixF8vNK8Op5XwQAApmoqTlxWVZtjg0BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"339f4ca4a7c1b7537501859ca55fe9b4e8b64161f64943a414a8401ec95be67b","last_reissued_at":"2026-07-05T10:49:01.968959Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:49:01.968959Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Subcohomology and a Livsic Theorem for Zooming Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Eduardo Santana, Lamine Mbarki","submitted_at":"2022-08-28T12:27:11Z","abstract_excerpt":"In the context of continuous zooming systems $f:M \\to M$ on a compact metric space $M$, which include the non-uniformly expanding ones, possibly with the presence of a critical set, with the zooming set dense in $M$, we prove that any H\\\"older potential $\\phi : M \\to \\mathbb{R}$ for which the integrals $\\int \\phi d\\mu \\geq 0$ with respect to any $f$-invariant probability $\\mu$, admits a continuous function $\\lambda_{0} : M \\to \\mathbb{R}$ (which can be H\\\"older if some integral is positive) such that\n  \\[\n  \\phi \\geq \\lambda_{0}- \\lambda_{0} \\circ f.\n  \\]\n  This extends a result in [9] for $C^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2208.13209","kind":"arxiv","version":6},"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/2208.13209/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":"2208.13209","created_at":"2026-07-05T10:49:01.969007+00:00"},{"alias_kind":"arxiv_version","alias_value":"2208.13209v6","created_at":"2026-07-05T10:49:01.969007+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2208.13209","created_at":"2026-07-05T10:49:01.969007+00:00"},{"alias_kind":"pith_short_12","alias_value":"GOPUZJFHYG3V","created_at":"2026-07-05T10:49:01.969007+00:00"},{"alias_kind":"pith_short_16","alias_value":"GOPUZJFHYG3VG5IB","created_at":"2026-07-05T10:49:01.969007+00:00"},{"alias_kind":"pith_short_8","alias_value":"GOPUZJFH","created_at":"2026-07-05T10:49:01.969007+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/GOPUZJFHYG3VG5IBQWOKKX7JWT","json":"https://pith.science/pith/GOPUZJFHYG3VG5IBQWOKKX7JWT.json","graph_json":"https://pith.science/api/pith-number/GOPUZJFHYG3VG5IBQWOKKX7JWT/graph.json","events_json":"https://pith.science/api/pith-number/GOPUZJFHYG3VG5IBQWOKKX7JWT/events.json","paper":"https://pith.science/paper/GOPUZJFH"},"agent_actions":{"view_html":"https://pith.science/pith/GOPUZJFHYG3VG5IBQWOKKX7JWT","download_json":"https://pith.science/pith/GOPUZJFHYG3VG5IBQWOKKX7JWT.json","view_paper":"https://pith.science/paper/GOPUZJFH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2208.13209&json=true","fetch_graph":"https://pith.science/api/pith-number/GOPUZJFHYG3VG5IBQWOKKX7JWT/graph.json","fetch_events":"https://pith.science/api/pith-number/GOPUZJFHYG3VG5IBQWOKKX7JWT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GOPUZJFHYG3VG5IBQWOKKX7JWT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GOPUZJFHYG3VG5IBQWOKKX7JWT/action/storage_attestation","attest_author":"https://pith.science/pith/GOPUZJFHYG3VG5IBQWOKKX7JWT/action/author_attestation","sign_citation":"https://pith.science/pith/GOPUZJFHYG3VG5IBQWOKKX7JWT/action/citation_signature","submit_replication":"https://pith.science/pith/GOPUZJFHYG3VG5IBQWOKKX7JWT/action/replication_record"}},"created_at":"2026-07-05T10:49:01.969007+00:00","updated_at":"2026-07-05T10:49:01.969007+00:00"}