{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZXQZ223FTQ4IPZI55UL5XBVABA","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":"1c92761e1644d8d9eefa8f69fcc37814ae1dbb7a34b128e41147ab5df42d14f0","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-25T14:33:34Z","title_canon_sha256":"bbcc7d94889d9a10b48603089d4b04bb3c9df680539afd6d85ae7f6a253fc4f9"},"schema_version":"1.0","source":{"id":"1704.07716","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.07716","created_at":"2026-05-18T00:45:37Z"},{"alias_kind":"arxiv_version","alias_value":"1704.07716v1","created_at":"2026-05-18T00:45:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.07716","created_at":"2026-05-18T00:45:37Z"},{"alias_kind":"pith_short_12","alias_value":"ZXQZ223FTQ4I","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZXQZ223FTQ4IPZI5","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZXQZ223F","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:14084cdaf4c188f172e48291eb0c485a12ea9c1662b41020f34e4e5bdb9c4f9c","target":"graph","created_at":"2026-05-18T00:45:37Z","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":"Let $\\mathcal{B}$ denote a set of bicolorings of $[n]$, where each bicoloring is a mapping of the points in $[n]$ to $\\{-1,+1\\}$.\n  For each $B \\in \\mathcal{B}$, let $Y_B=(B(1),\\ldots,B(n))$.\n  For each $A \\subseteq [n]$, let $X_A \\in \\{0,1\\}^n$ denote the incidence vector of $A$.\n  A non-empty set $A$ is said to be an `unbiased representative' for a bicoloring $B \\in \\mathcal{B}$ if $\\left\\langle X_A,Y_B\\right\\rangle =0$.\n  Given a set $\\mathcal{B}$ of bicolorings, we study the minimum cardinality of a family $\\mathcal{A}$ consisting of subsets of $[n]$ such that every bicoloring in $\\mathcal","authors_text":"Niranjan Balachandran, Rogers Mathew, Sudebkumar Prasant Pal, Tapas Kumar Mishra","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-25T14:33:34Z","title":"System of unbiased representatives for a collection of bicolorings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.07716","kind":"arxiv","version":1},"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:d680e5c979ebfd11963ccc7629d92c142a71a10e887d7be27fbe76a18ebce914","target":"record","created_at":"2026-05-18T00:45:37Z","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":"1c92761e1644d8d9eefa8f69fcc37814ae1dbb7a34b128e41147ab5df42d14f0","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-04-25T14:33:34Z","title_canon_sha256":"bbcc7d94889d9a10b48603089d4b04bb3c9df680539afd6d85ae7f6a253fc4f9"},"schema_version":"1.0","source":{"id":"1704.07716","kind":"arxiv","version":1}},"canonical_sha256":"cde19d6b659c3887e51ded17db86a0082ea73c1cfc16f6b1a4ae8a126a28c4c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cde19d6b659c3887e51ded17db86a0082ea73c1cfc16f6b1a4ae8a126a28c4c8","first_computed_at":"2026-05-18T00:45:37.148228Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:37.148228Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mVdcCadAE4R37RM0CRqkXU1wRu1pjtGQMmbg480pcpicyunhNlZFbUPIEuCm3HKpdpfQCbYrTpc6iDpANNWOAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:37.148973Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.07716","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d680e5c979ebfd11963ccc7629d92c142a71a10e887d7be27fbe76a18ebce914","sha256:14084cdaf4c188f172e48291eb0c485a12ea9c1662b41020f34e4e5bdb9c4f9c"],"state_sha256":"19f184052b0a797c848f1c80cf2f0b563168c4451c01e60943ba1b0870f63724"}