{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:J4WRSKFBYLLATKW7UXWZUA7GKL","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":"961ef895f82314b7ae5a2cf181144876185d37c265597cfaf752dd8b56f3d852","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-27T20:47:56Z","title_canon_sha256":"220ce44998d2a882d84c58bec88ec4cc0ebdb50ff85d9fc450b59797cb2b5a54"},"schema_version":"1.0","source":{"id":"1601.07541","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07541","created_at":"2026-05-18T00:52:50Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07541v3","created_at":"2026-05-18T00:52:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07541","created_at":"2026-05-18T00:52:50Z"},{"alias_kind":"pith_short_12","alias_value":"J4WRSKFBYLLA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"J4WRSKFBYLLATKW7","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"J4WRSKFB","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:68a435cc8b0db839e41d903a52d2e87c6b3da2b1cd8926fe03a1c18bc9748e5d","target":"graph","created_at":"2026-05-18T00:52:50Z","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":"Given an abelian group $G$, it is natural to ask whether there exists a permutation $\\pi$ of $G$ that \"destroys\" all nontrivial 3-term arithmetic progressions (APs), in the sense that $\\pi(b) - \\pi(a) \\neq \\pi(c) - \\pi(b)$ for every ordered triple $(a,b,c) \\in G^3$ satisfying $b-a = c-b \\neq 0$. This question was resolved for infinite groups $G$ by Hegarty, who showed that there exists an AP-destroying permutation of $G$ if and only if $G/\\Omega_2(G)$ has the same cardinality as $G$, where $\\Omega_2(G)$ denotes the subgroup of all elements in $G$ whose order divides $2$. In the case when $G$ i","authors_text":"Ashvin Swaminathan, Noam D. Elkies","cross_cats":["math.CO","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-27T20:47:56Z","title":"Permutations that Destroy Arithmetic Progressions in Elementary $p$-Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07541","kind":"arxiv","version":3},"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:fcfd66a0941a2bfe163081bcec199bcc86ba2c5d6369e96aca5d0f7e724ee4a3","target":"record","created_at":"2026-05-18T00:52:50Z","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":"961ef895f82314b7ae5a2cf181144876185d37c265597cfaf752dd8b56f3d852","cross_cats_sorted":["math.CO","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-01-27T20:47:56Z","title_canon_sha256":"220ce44998d2a882d84c58bec88ec4cc0ebdb50ff85d9fc450b59797cb2b5a54"},"schema_version":"1.0","source":{"id":"1601.07541","kind":"arxiv","version":3}},"canonical_sha256":"4f2d1928a1c2d609aadfa5ed9a03e652cc6a1e5fefc7c7a256dee24b3561b890","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f2d1928a1c2d609aadfa5ed9a03e652cc6a1e5fefc7c7a256dee24b3561b890","first_computed_at":"2026-05-18T00:52:50.561072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:50.561072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CwyL13IhMzCPet/luwJlYALxQDvLsBaBgb/Cu5MvA7DR2c9dc4k5lQtdhea74yb0Dv8rZZeNzyVvFd+hP/U9Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:50.561796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07541","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fcfd66a0941a2bfe163081bcec199bcc86ba2c5d6369e96aca5d0f7e724ee4a3","sha256:68a435cc8b0db839e41d903a52d2e87c6b3da2b1cd8926fe03a1c18bc9748e5d"],"state_sha256":"8a452b897953457d6073ac52263eadd3e315ec4704dafd0cc5384ea1b23c1fa7"}