{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:DOGMQFFSTX6IWEB7IAS6WGU4UR","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":"a4d679fa5dade8e8f114e45d75846dc2396c91033f6e551dc37603f422b52876","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-30T03:53:29Z","title_canon_sha256":"bfc7b2a3338de04632ce669576ebabfe80fc8742c46db2d23b01d22c5cd5aaf6"},"schema_version":"1.0","source":{"id":"1708.09100","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.09100","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"arxiv_version","alias_value":"1708.09100v2","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.09100","created_at":"2026-05-18T00:18:09Z"},{"alias_kind":"pith_short_12","alias_value":"DOGMQFFSTX6I","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_16","alias_value":"DOGMQFFSTX6IWEB7","created_at":"2026-05-18T12:31:12Z"},{"alias_kind":"pith_short_8","alias_value":"DOGMQFFS","created_at":"2026-05-18T12:31:12Z"}],"graph_snapshots":[{"event_id":"sha256:f5ad9e403378bae2239f5272214bcda824a45d121047427eea6578663c7e1551","target":"graph","created_at":"2026-05-18T00:18:09Z","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":"For a finite abelian group $G$, the Erd\\H{o}s-Ginzburg-Ziv constant $\\mathfrak{s}(G)$ is the smallest $s$ such that every sequence of $s$ (not necessarily distinct) elements of $G$ has a zero-sum subsequence of length $\\operatorname{exp}(G)$. For a prime $p$, let $r(\\mathbb{F}_p^n)$ denote the size of the largest subset of $\\mathbb{F}_p^n$ without a three-term arithmetic progression. Although similar methods have been used to study $\\mathfrak{s}(G)$ and $r(\\mathbb{F}_p^n)$, no direct connection between these quantities has previously been established. We give an upper bound for $\\mathfrak{s}(G","authors_text":"Jacob Fox, Lisa Sauermann","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-30T03:53:29Z","title":"Erd\\H{o}s-Ginzburg-Ziv constants by avoiding three-term arithmetic progressions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09100","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:e6f6edc52b7344e61c8cc3c9b84fe5526dab1fa3a7294e3ee7f77ca716ff107c","target":"record","created_at":"2026-05-18T00:18:09Z","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":"a4d679fa5dade8e8f114e45d75846dc2396c91033f6e551dc37603f422b52876","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-30T03:53:29Z","title_canon_sha256":"bfc7b2a3338de04632ce669576ebabfe80fc8742c46db2d23b01d22c5cd5aaf6"},"schema_version":"1.0","source":{"id":"1708.09100","kind":"arxiv","version":2}},"canonical_sha256":"1b8cc814b29dfc8b103f4025eb1a9ca47996ffa616d33c8ec07f577a07d6801f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b8cc814b29dfc8b103f4025eb1a9ca47996ffa616d33c8ec07f577a07d6801f","first_computed_at":"2026-05-18T00:18:09.514873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:18:09.514873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tYCDGCz27EwOr3VJrS0uNFN0KS267Aduy1bUuEnVGvkdnlHUIPMA70HgVReFKK/ZdeLIPXW2yrOHjKEekzIfAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:18:09.515515Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.09100","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6f6edc52b7344e61c8cc3c9b84fe5526dab1fa3a7294e3ee7f77ca716ff107c","sha256:f5ad9e403378bae2239f5272214bcda824a45d121047427eea6578663c7e1551"],"state_sha256":"5628b1180c3b5d3e016e22a6a1d85fdf05d52f35e71e629e726bcd37bbe8c70b"}