{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:MVIHMWYLGHUKIMVYNFS2P6SMWA","short_pith_number":"pith:MVIHMWYL","canonical_record":{"source":{"id":"1703.04118","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-12T13:41:54Z","cross_cats_sorted":["math.GR","math.NT"],"title_canon_sha256":"da3d371d7019efa258785e67e7de8a72ac4124b130562c2bf0437076b2074899","abstract_canon_sha256":"0eaa2fc25d610a1941ea073ef7512312dda542812ff33397b95f1a91a04d2eef"},"schema_version":"1.0"},"canonical_sha256":"6550765b0b31e8a432b86965a7fa4cb00bf5de18bb0da1d03d47f8d5ad33b333","source":{"kind":"arxiv","id":"1703.04118","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04118","created_at":"2026-05-18T00:45:19Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04118v2","created_at":"2026-05-18T00:45:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04118","created_at":"2026-05-18T00:45:19Z"},{"alias_kind":"pith_short_12","alias_value":"MVIHMWYLGHUK","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MVIHMWYLGHUKIMVY","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MVIHMWYL","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:MVIHMWYLGHUKIMVYNFS2P6SMWA","target":"record","payload":{"canonical_record":{"source":{"id":"1703.04118","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-12T13:41:54Z","cross_cats_sorted":["math.GR","math.NT"],"title_canon_sha256":"da3d371d7019efa258785e67e7de8a72ac4124b130562c2bf0437076b2074899","abstract_canon_sha256":"0eaa2fc25d610a1941ea073ef7512312dda542812ff33397b95f1a91a04d2eef"},"schema_version":"1.0"},"canonical_sha256":"6550765b0b31e8a432b86965a7fa4cb00bf5de18bb0da1d03d47f8d5ad33b333","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:19.579722Z","signature_b64":"ClPKFyxAQ5RzlYNgMXMbgFBilei0zJfKPh5ZJaLb40KYkijw4loF7AMLqi/HZ/B0fMrvPLuYp1dt1oaOkGPOCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6550765b0b31e8a432b86965a7fa4cb00bf5de18bb0da1d03d47f8d5ad33b333","last_reissued_at":"2026-05-18T00:45:19.579050Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:19.579050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.04118","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:45:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B0xV5ZJ+ylZvWoHLn7jA+Spx9D+JrGKzXxzTsa6ORn3qiK8LCBDM+Mmj1nUph2zL8gGUUa5RFovzwygtrE4jCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:12:44.373052Z"},"content_sha256":"1e5396078dc6dadb53c408dbd3ea6dd63493181859c9b107c45e9ddc18bfe8e4","schema_version":"1.0","event_id":"sha256:1e5396078dc6dadb53c408dbd3ea6dd63493181859c9b107c45e9ddc18bfe8e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:MVIHMWYLGHUKIMVYNFS2P6SMWA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Symmetric Complete Sum-free Sets in Cyclic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.NT"],"primary_cat":"math.CO","authors_text":"Dan Levy, Ishay Haviv","submitted_at":"2017-03-12T13:41:54Z","abstract_excerpt":"We present constructions of symmetric complete sum-free sets in general finite cyclic groups. It is shown that the relative sizes of the sets are dense in $[0,\\frac{1}{3}]$, answering a question of Cameron, and that the number of those contained in the cyclic group of order $n$ is exponential in $n$. For primes $p$, we provide a full characterization of the symmetric complete sum-free subsets of $\\mathbb{Z}_p$ of size at least $(\\frac{1}{3}-c) \\cdot p$, where $c>0$ is a universal constant."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04118","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:45:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QtyVmFFauQ5e+4weUb8+5V5zqwjoMHjWasCqRUWpHqf41n8yBPj5Kpyb3YYc9B2bBEDuFMtJsG50bLPuM/OXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T17:12:44.373456Z"},"content_sha256":"7cb11fa970bcf853d5e84a82dae08892aec9f17c2b879bd74293d4692fd04f62","schema_version":"1.0","event_id":"sha256:7cb11fa970bcf853d5e84a82dae08892aec9f17c2b879bd74293d4692fd04f62"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MVIHMWYLGHUKIMVYNFS2P6SMWA/bundle.json","state_url":"https://pith.science/pith/MVIHMWYLGHUKIMVYNFS2P6SMWA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MVIHMWYLGHUKIMVYNFS2P6SMWA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-04T17:12:44Z","links":{"resolver":"https://pith.science/pith/MVIHMWYLGHUKIMVYNFS2P6SMWA","bundle":"https://pith.science/pith/MVIHMWYLGHUKIMVYNFS2P6SMWA/bundle.json","state":"https://pith.science/pith/MVIHMWYLGHUKIMVYNFS2P6SMWA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MVIHMWYLGHUKIMVYNFS2P6SMWA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:MVIHMWYLGHUKIMVYNFS2P6SMWA","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":"0eaa2fc25d610a1941ea073ef7512312dda542812ff33397b95f1a91a04d2eef","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-12T13:41:54Z","title_canon_sha256":"da3d371d7019efa258785e67e7de8a72ac4124b130562c2bf0437076b2074899"},"schema_version":"1.0","source":{"id":"1703.04118","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.04118","created_at":"2026-05-18T00:45:19Z"},{"alias_kind":"arxiv_version","alias_value":"1703.04118v2","created_at":"2026-05-18T00:45:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.04118","created_at":"2026-05-18T00:45:19Z"},{"alias_kind":"pith_short_12","alias_value":"MVIHMWYLGHUK","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"MVIHMWYLGHUKIMVY","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"MVIHMWYL","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:7cb11fa970bcf853d5e84a82dae08892aec9f17c2b879bd74293d4692fd04f62","target":"graph","created_at":"2026-05-18T00:45:19Z","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":"We present constructions of symmetric complete sum-free sets in general finite cyclic groups. It is shown that the relative sizes of the sets are dense in $[0,\\frac{1}{3}]$, answering a question of Cameron, and that the number of those contained in the cyclic group of order $n$ is exponential in $n$. For primes $p$, we provide a full characterization of the symmetric complete sum-free subsets of $\\mathbb{Z}_p$ of size at least $(\\frac{1}{3}-c) \\cdot p$, where $c>0$ is a universal constant.","authors_text":"Dan Levy, Ishay Haviv","cross_cats":["math.GR","math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-12T13:41:54Z","title":"Symmetric Complete Sum-free Sets in Cyclic Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04118","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":"sha256:1e5396078dc6dadb53c408dbd3ea6dd63493181859c9b107c45e9ddc18bfe8e4","target":"record","created_at":"2026-05-18T00:45:19Z","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":"0eaa2fc25d610a1941ea073ef7512312dda542812ff33397b95f1a91a04d2eef","cross_cats_sorted":["math.GR","math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-12T13:41:54Z","title_canon_sha256":"da3d371d7019efa258785e67e7de8a72ac4124b130562c2bf0437076b2074899"},"schema_version":"1.0","source":{"id":"1703.04118","kind":"arxiv","version":2}},"canonical_sha256":"6550765b0b31e8a432b86965a7fa4cb00bf5de18bb0da1d03d47f8d5ad33b333","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6550765b0b31e8a432b86965a7fa4cb00bf5de18bb0da1d03d47f8d5ad33b333","first_computed_at":"2026-05-18T00:45:19.579050Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:19.579050Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ClPKFyxAQ5RzlYNgMXMbgFBilei0zJfKPh5ZJaLb40KYkijw4loF7AMLqi/HZ/B0fMrvPLuYp1dt1oaOkGPOCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:19.579722Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04118","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e5396078dc6dadb53c408dbd3ea6dd63493181859c9b107c45e9ddc18bfe8e4","sha256:7cb11fa970bcf853d5e84a82dae08892aec9f17c2b879bd74293d4692fd04f62"],"state_sha256":"5b23e72181d94d8af56abf69dfb3d3b0451b5922227b5f1bea4c981faac1c887"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9T7bFVyeralRrKeMIeLpHmXbxo4I2vGMQ1vVY74elrvBjRDlq7Qp4xzrbq8a9ubrIcUqmHKMY2ZbbyYwevuxAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T17:12:44.375880Z","bundle_sha256":"ba05b2812626bdfc7e9eec5fe730150a940092d75e8b73bb7032c36d853e147b"}}