{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:TTSJQIGRGX24VJF7LBUJT6MCM7","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":"feb3a218f608f583b9e9807bf5f37dab8e4a38dcdbe423f25792c654f114f3a2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-05-12T15:47:14Z","title_canon_sha256":"91cb03a0a184b65dbda9b2645cf551f2400bea6a801e5141bfab32d346394401"},"schema_version":"1.0","source":{"id":"2505.07682","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.07682","created_at":"2026-07-05T11:01:51Z"},{"alias_kind":"arxiv_version","alias_value":"2505.07682v1","created_at":"2026-07-05T11:01:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.07682","created_at":"2026-07-05T11:01:51Z"},{"alias_kind":"pith_short_12","alias_value":"TTSJQIGRGX24","created_at":"2026-07-05T11:01:51Z"},{"alias_kind":"pith_short_16","alias_value":"TTSJQIGRGX24VJF7","created_at":"2026-07-05T11:01:51Z"},{"alias_kind":"pith_short_8","alias_value":"TTSJQIGR","created_at":"2026-07-05T11:01:51Z"}],"graph_snapshots":[{"event_id":"sha256:7d56c6266e6c90a12eaaf0dad1aa7303bcce7777c821f9a37247b357d6436a7a","target":"graph","created_at":"2026-07-05T11:01:51Z","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/2505.07682/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the Hardy-Littlewood maximal function associated with ball averages on spaces with exponential volume growth. We focus on discrete groups with balls defined by invariant metrics associated with a variety of length functions. Under natural assumptions on the rough radial structure of the group in question, we establish a weak-type $\\mathcal{L}\\left(\\log \\mathcal{L}\\right)^{\\bf c}$ maximal inequality for the Hardy-Littlewood maximal function. We give a variety of examples where the rough radial structure assumptions hold, based on considerations from geometric group theory, or on ana","authors_text":"Amos Nevo, Koji Fujiwara","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-05-12T15:47:14Z","title":"Hardy-Littlewood maximal operator on spaces of exponential volume growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07682","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":"sha256:4a5cb80d1824ae7af5a3b585daf67181fe1fcc45c28cb2e2e04ea2372407cb7c","target":"record","created_at":"2026-07-05T11:01:51Z","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":"feb3a218f608f583b9e9807bf5f37dab8e4a38dcdbe423f25792c654f114f3a2","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DS","submitted_at":"2025-05-12T15:47:14Z","title_canon_sha256":"91cb03a0a184b65dbda9b2645cf551f2400bea6a801e5141bfab32d346394401"},"schema_version":"1.0","source":{"id":"2505.07682","kind":"arxiv","version":1}},"canonical_sha256":"9ce49820d135f5caa4bf586899f98267ce902580b30bd0752a1db94fc177096a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ce49820d135f5caa4bf586899f98267ce902580b30bd0752a1db94fc177096a","first_computed_at":"2026-07-05T11:01:51.674867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:01:51.674867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"59HVXE+rQAXQEFK8dif3WgOnk5OaFMWAgEWUCwGHE6ZzHMVqYczWzX6CAfzcJ70j+K2FNVqggHfiADKynOMzBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:01:51.675397Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.07682","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a5cb80d1824ae7af5a3b585daf67181fe1fcc45c28cb2e2e04ea2372407cb7c","sha256:7d56c6266e6c90a12eaaf0dad1aa7303bcce7777c821f9a37247b357d6436a7a"],"state_sha256":"37f13f9baf2d731ca9ff1d45b9b9860f60acd0adb379b4bfc2b77728d90f1573"}