{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:URTL6TKGGK3SXAVLQUN5FLYMUR","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":"27103a51cad47eaeed838d01fd244b272eb9174c70fcdab79c540e0ae2c51d69","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-09-02T00:57:22Z","title_canon_sha256":"70c3cb0a6d8f7225fdfe67b9de02c2029b7fb6e8fcd5e9b92a4cece8d6eda34a"},"schema_version":"1.0","source":{"id":"2409.00885","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.00885","created_at":"2026-07-05T10:41:48Z"},{"alias_kind":"arxiv_version","alias_value":"2409.00885v4","created_at":"2026-07-05T10:41:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.00885","created_at":"2026-07-05T10:41:48Z"},{"alias_kind":"pith_short_12","alias_value":"URTL6TKGGK3S","created_at":"2026-07-05T10:41:48Z"},{"alias_kind":"pith_short_16","alias_value":"URTL6TKGGK3SXAVL","created_at":"2026-07-05T10:41:48Z"},{"alias_kind":"pith_short_8","alias_value":"URTL6TKG","created_at":"2026-07-05T10:41:48Z"}],"graph_snapshots":[{"event_id":"sha256:513a0c6b638f23e62a151b329a97faeb0f206217eb8eaeb1b0a34ec1f6489982","target":"graph","created_at":"2026-07-05T10:41:48Z","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/2409.00885/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We obtain an inverse of Furstenberg's correspondence principle in the setting of countable cancellative, amenable semigroups. Besides being of intrinsic interest on its own, this result allows us to answer a variety of questions concerning sets of recurrence and van der Corput (vdC) sets, which were posed by Bergelson and Lesigne \\cite{BL}, Bergelson and Ferr\\'e Moragues \\cite{BF}, Kelly and L\\^e \\cite{KL}, and Moreira \\cite{Mor}. We also prove a spectral characterization of vdC sets and prove some of their basic properties in the context of countable amenable groups.\n  Several results in this","authors_text":"Sa\\'ul Rodr\\'iguez Mart\\'in","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-09-02T00:57:22Z","title":"An inverse of Furstenberg's correspondence principle and applications to van der Corput sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.00885","kind":"arxiv","version":4},"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":"sha256:2c11192b1189fb4721b6c6f27294eef12e7103450ef928c6b4a00fee2362324c","target":"record","created_at":"2026-07-05T10:41:48Z","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":"27103a51cad47eaeed838d01fd244b272eb9174c70fcdab79c540e0ae2c51d69","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2024-09-02T00:57:22Z","title_canon_sha256":"70c3cb0a6d8f7225fdfe67b9de02c2029b7fb6e8fcd5e9b92a4cece8d6eda34a"},"schema_version":"1.0","source":{"id":"2409.00885","kind":"arxiv","version":4}},"canonical_sha256":"a466bf4d4632b72b82ab851bd2af0ca4534a6f76871033ebd44696c849b7b975","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a466bf4d4632b72b82ab851bd2af0ca4534a6f76871033ebd44696c849b7b975","first_computed_at":"2026-07-05T10:41:48.405868Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:41:48.405868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6CKtyyMu3484qvwxlwp8iOepNHjJ+6izztCtSd4D1EYTMhflyxBut0I7ofbdqMxQac/BlN1A6p/KHBui56zcCg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:41:48.406394Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.00885","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c11192b1189fb4721b6c6f27294eef12e7103450ef928c6b4a00fee2362324c","sha256:513a0c6b638f23e62a151b329a97faeb0f206217eb8eaeb1b0a34ec1f6489982"],"state_sha256":"71f6c3e113f3c523b0a2ca2e2d9fb35513488925ab8477dbcfef4a4ad720a736"}