{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:52OOF2MPUZBOLLAAIVSHDAPYGF","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":"9f8c43f40593813be8ac6e6af426f502a92a0069557b87b971c9e72a5728546d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-02T20:17:46Z","title_canon_sha256":"80d8c939b3ac3accf37dc0fb2486a287a635c4b876f4ec25a92f344cd60d5481"},"schema_version":"1.0","source":{"id":"1612.00822","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.00822","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"arxiv_version","alias_value":"1612.00822v1","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.00822","created_at":"2026-05-18T00:25:27Z"},{"alias_kind":"pith_short_12","alias_value":"52OOF2MPUZBO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"52OOF2MPUZBOLLAA","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"52OOF2MP","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:8278817b71437671d5bb31a18031b80c37183dc757e8f9def28e3ea6bda193c3","target":"graph","created_at":"2026-05-18T00:25:27Z","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"},"paper":{"abstract_excerpt":"This paper concerns the smoothness of Tauberian constants of maximal operators in the discrete and ergodic settings. In particular, we define the discrete strong maximal operator $\\tilde{M}_S$ on $\\mathbb{Z}^n$ by \\[\n  \\tilde{M}_S f(m) := \\sup_{0 \\in R \\subset \\mathbb{R}^n}\\frac{1}{\\#(R \\cap \\mathbb{Z}^n)}\\sum_{ j\\in R \\cap \\mathbb{Z}^n} |f(m+j)|,\\qquad m\\in \\mathbb{Z}^n, \\] where the supremum is taken over all open rectangles in $\\mathbb{R}^n$ containing the origin whose sides are parallel to the coordinate axes. We show that the associated Tauberian constant $\\tilde{C}_S(\\alpha)$, defined by","authors_text":"Ioannis Parissis, Paul A. Hagelstein","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-02T20:17:46Z","title":"H\\\"older continuity of Tauberian constants associated with discrete and ergodic strong maximal operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.00822","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:f805b9526d5e5f7dd67d63c013d1e94be949f4cc28013239df6b158c046c9464","target":"record","created_at":"2026-05-18T00:25:27Z","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":"9f8c43f40593813be8ac6e6af426f502a92a0069557b87b971c9e72a5728546d","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-12-02T20:17:46Z","title_canon_sha256":"80d8c939b3ac3accf37dc0fb2486a287a635c4b876f4ec25a92f344cd60d5481"},"schema_version":"1.0","source":{"id":"1612.00822","kind":"arxiv","version":1}},"canonical_sha256":"ee9ce2e98fa642e5ac0045647181f8315677ced6dbd48c6a9f2d4638b2687bd5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee9ce2e98fa642e5ac0045647181f8315677ced6dbd48c6a9f2d4638b2687bd5","first_computed_at":"2026-05-18T00:25:27.085847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:27.085847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D+h3p8mxmDWk1uFk5UhNcjnP6pcK/q2oU4mezpBD3d/VzyEf32n8WImLBfSSmj51XqQjcXnLq/f/hXyzSH/UDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:27.086506Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.00822","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f805b9526d5e5f7dd67d63c013d1e94be949f4cc28013239df6b158c046c9464","sha256:8278817b71437671d5bb31a18031b80c37183dc757e8f9def28e3ea6bda193c3"],"state_sha256":"fb43b85f9bcb09a38f857f896d1504ac5efbd9b5523fc35bd3e06c3aaafe0515"}