{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:N4F5YH4HPKJVDRHMR3GCQSY65Y","short_pith_number":"pith:N4F5YH4H","schema_version":"1.0","canonical_sha256":"6f0bdc1f877a9351c4ec8ecc284b1eee3a29da3af6c0963150b0fbb3dacd7477","source":{"kind":"arxiv","id":"1712.00861","version":2},"attestation_state":"computed","paper":{"title":"Exponential Lower Bounds on the Generalized Erd\\H{o}s-Ginzburg-Ziv Constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jared Bitz, Sarah Griffith, Xiaoyu He","submitted_at":"2017-12-04T00:15:43Z","abstract_excerpt":"For a finite abelian group $G$, the generalized Erd\\H{o}s--Ginzburg--Ziv constant $\\mathsf s_{k}(G)$ is the smallest $m$ such that a sequence of $m$ elements in $G$ always contains a $k$-element subsequence which sums to zero. If $n = \\exp(G)$ is the exponent of $G$, the previously best known bounds for $\\mathsf s_{kn}(C_n^r)$ were linear in $n$ and $r$ when $k\\ge 2$. Via a probabilistic argument, we produce the exponential lower bound \\[ \\mathsf s_{2n}(C_n^r) > \\frac{n}{2}[1.25 - O(n^{-3/2})]^r \\] for $n > 0$. For the general case, we show \\[ \\mathsf s_{kn}(C_n^r) > \\frac{kn}{4}\\Big(1+\\frac{1"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.00861","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-12-04T00:15:43Z","cross_cats_sorted":[],"title_canon_sha256":"54402871fbdd675d516b76ab2de7a2420d150197ff6ffa7d5797156c925f1acd","abstract_canon_sha256":"d64adba64080cd1c122233da3334478017fcc83cb2bbfa2d927904a0be06e801"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:36:50.308251Z","signature_b64":"T09JO1EhEZWl0V+ljNB3BPUkeF41d4ywUQmTGbb1loPb9hCtm28YzsML6bOHl7M1Oz1Gc2GAArc5iwUHORmsBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f0bdc1f877a9351c4ec8ecc284b1eee3a29da3af6c0963150b0fbb3dacd7477","last_reissued_at":"2026-07-05T03:36:50.307741Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:36:50.307741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Exponential Lower Bounds on the Generalized Erd\\H{o}s-Ginzburg-Ziv Constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jared Bitz, Sarah Griffith, Xiaoyu He","submitted_at":"2017-12-04T00:15:43Z","abstract_excerpt":"For a finite abelian group $G$, the generalized Erd\\H{o}s--Ginzburg--Ziv constant $\\mathsf s_{k}(G)$ is the smallest $m$ such that a sequence of $m$ elements in $G$ always contains a $k$-element subsequence which sums to zero. If $n = \\exp(G)$ is the exponent of $G$, the previously best known bounds for $\\mathsf s_{kn}(C_n^r)$ were linear in $n$ and $r$ when $k\\ge 2$. Via a probabilistic argument, we produce the exponential lower bound \\[ \\mathsf s_{2n}(C_n^r) > \\frac{n}{2}[1.25 - O(n^{-3/2})]^r \\] for $n > 0$. For the general case, we show \\[ \\mathsf s_{kn}(C_n^r) > \\frac{kn}{4}\\Big(1+\\frac{1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.00861","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1712.00861/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1712.00861","created_at":"2026-07-05T03:36:50.307804+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.00861v2","created_at":"2026-07-05T03:36:50.307804+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.00861","created_at":"2026-07-05T03:36:50.307804+00:00"},{"alias_kind":"pith_short_12","alias_value":"N4F5YH4HPKJV","created_at":"2026-07-05T03:36:50.307804+00:00"},{"alias_kind":"pith_short_16","alias_value":"N4F5YH4HPKJVDRHM","created_at":"2026-07-05T03:36:50.307804+00:00"},{"alias_kind":"pith_short_8","alias_value":"N4F5YH4H","created_at":"2026-07-05T03:36:50.307804+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/N4F5YH4HPKJVDRHMR3GCQSY65Y","json":"https://pith.science/pith/N4F5YH4HPKJVDRHMR3GCQSY65Y.json","graph_json":"https://pith.science/api/pith-number/N4F5YH4HPKJVDRHMR3GCQSY65Y/graph.json","events_json":"https://pith.science/api/pith-number/N4F5YH4HPKJVDRHMR3GCQSY65Y/events.json","paper":"https://pith.science/paper/N4F5YH4H"},"agent_actions":{"view_html":"https://pith.science/pith/N4F5YH4HPKJVDRHMR3GCQSY65Y","download_json":"https://pith.science/pith/N4F5YH4HPKJVDRHMR3GCQSY65Y.json","view_paper":"https://pith.science/paper/N4F5YH4H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.00861&json=true","fetch_graph":"https://pith.science/api/pith-number/N4F5YH4HPKJVDRHMR3GCQSY65Y/graph.json","fetch_events":"https://pith.science/api/pith-number/N4F5YH4HPKJVDRHMR3GCQSY65Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N4F5YH4HPKJVDRHMR3GCQSY65Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N4F5YH4HPKJVDRHMR3GCQSY65Y/action/storage_attestation","attest_author":"https://pith.science/pith/N4F5YH4HPKJVDRHMR3GCQSY65Y/action/author_attestation","sign_citation":"https://pith.science/pith/N4F5YH4HPKJVDRHMR3GCQSY65Y/action/citation_signature","submit_replication":"https://pith.science/pith/N4F5YH4HPKJVDRHMR3GCQSY65Y/action/replication_record"}},"created_at":"2026-07-05T03:36:50.307804+00:00","updated_at":"2026-07-05T03:36:50.307804+00:00"}