{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:RKSH2XVE54QN4HR2IVLY7JLEGL","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":"4364448638a4f6ca8ca18c2d45e0f284e3991c5ddbe2192a98cccf0594560bf9","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-03-04T20:04:23Z","title_canon_sha256":"4cd2a05c27b1c7f955c93ade878878f1cc175a6bb719594dc33d9ff6fa10f3d4"},"schema_version":"1.0","source":{"id":"2603.04572","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2603.04572","created_at":"2026-05-26T01:03:26Z"},{"alias_kind":"arxiv_version","alias_value":"2603.04572v2","created_at":"2026-05-26T01:03:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2603.04572","created_at":"2026-05-26T01:03:26Z"},{"alias_kind":"pith_short_12","alias_value":"RKSH2XVE54QN","created_at":"2026-05-26T01:03:26Z"},{"alias_kind":"pith_short_16","alias_value":"RKSH2XVE54QN4HR2","created_at":"2026-05-26T01:03:26Z"},{"alias_kind":"pith_short_8","alias_value":"RKSH2XVE","created_at":"2026-05-26T01:03:26Z"}],"graph_snapshots":[{"event_id":"sha256:e3ef65c3a39ec3eefaa5b858d3876c809815f5405552352b3019752b2b39cf87","target":"graph","created_at":"2026-05-26T01:03:26Z","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/2603.04572/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $A$ be a nonempty subset of finite abelian group $G$ of order $n$. For an integer $h \\geq 2$, the restricted $h$-fold sumset $h^\\wedge A$ is the set of all sums of $h$ distinct elements of $A$. It is known that if $G$ is a group of order $n$ and $A$ is a subset of $G$ such that $|A|$ is close to $\\frac{n}{2}$, then $h^{\\wedge}A = G$ under some conditions on $h$ and $n$. The constant $\\frac{1}{2}$ is optimal for groups of even order but not for groups of odd order. For an integer $h \\geq 4$, let $\\alpha_h$ be the unique positive root of the polynomial $3^{h - 2} x^{h - 1} + x - 1$. In this ","authors_text":"Raj Kumar Mistri, Vivekanand Goswami","cross_cats":["math.CO","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-03-04T20:04:23Z","title":"Restricted set addition in finite abelian groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.04572","kind":"arxiv","version":2},"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":"sha256:243b424fb69ddaeee8c177f5c442b27f079ff27bc4f7f37b240af225354c49fc","target":"record","created_at":"2026-05-26T01:03:26Z","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":"4364448638a4f6ca8ca18c2d45e0f284e3991c5ddbe2192a98cccf0594560bf9","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-03-04T20:04:23Z","title_canon_sha256":"4cd2a05c27b1c7f955c93ade878878f1cc175a6bb719594dc33d9ff6fa10f3d4"},"schema_version":"1.0","source":{"id":"2603.04572","kind":"arxiv","version":2}},"canonical_sha256":"8aa47d5ea4ef20de1e3a45578fa56432e0a9cce1ccc4632380341c7753fd4c3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8aa47d5ea4ef20de1e3a45578fa56432e0a9cce1ccc4632380341c7753fd4c3c","first_computed_at":"2026-05-26T01:03:26.999624Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:03:26.999624Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ee/51I0k5S581tjk4JEZXW76WKztcQuuh42T51+5jG51Cj02XxcKx8/AnkcGnZMS0JxXZU65Kh83/pWn3wAyAg==","signature_status":"signed_v1","signed_at":"2026-05-26T01:03:27.000512Z","signed_message":"canonical_sha256_bytes"},"source_id":"2603.04572","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:243b424fb69ddaeee8c177f5c442b27f079ff27bc4f7f37b240af225354c49fc","sha256:e3ef65c3a39ec3eefaa5b858d3876c809815f5405552352b3019752b2b39cf87"],"state_sha256":"9b91ff9bded37c9171e806462fa9f0889260cde1a403c82ae857f9ece76026d0"}