{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UV42LPZKHMCXGKSX3M6O4SZEYU","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":"bbdabcfb036fd1edfd37bbdd1e48ff5b6036221c2f9f51cfac0031eba7c39e26","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2013-12-23T11:27:19Z","title_canon_sha256":"25a2811a03f4f4218f0a6140f260bd3ec4352bf7477b85bbc6ee81eac62d32d1"},"schema_version":"1.0","source":{"id":"1312.6524","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6524","created_at":"2026-05-18T03:03:58Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6524v1","created_at":"2026-05-18T03:03:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6524","created_at":"2026-05-18T03:03:58Z"},{"alias_kind":"pith_short_12","alias_value":"UV42LPZKHMCX","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UV42LPZKHMCXGKSX","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UV42LPZK","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:49833dc0509d806b8395088866447219df280c534e90c7771880824afe483590","target":"graph","created_at":"2026-05-18T03:03:58Z","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":"Suppose you can color $n$ \\emph{biased} coins with $n$ colors, all coins having the same bias. It is forbidden to color both sides of a coin with the same color, but all other colors are allowed. Let $X$ be the number of different colors after a toss of the coins. We present a method to obtain an upper bound on a median of $X$. Our method is based on the analysis of the probability distribution of the number of vertices with even in-degree in graphs whose edges are given random orientations. Our analysis applies to the distribution of the number of vertices with odd degree in random sub-graphs","authors_text":"Christos Pelekis","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2013-12-23T11:27:19Z","title":"Bernoulli trials of fixed parity, random and randomly oriented graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6524","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":"sha256:0bfed6468ee9349075d860f99b7c7c65de215c7efe1814adfdb1ae676468fe07","target":"record","created_at":"2026-05-18T03:03:58Z","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":"bbdabcfb036fd1edfd37bbdd1e48ff5b6036221c2f9f51cfac0031eba7c39e26","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","primary_cat":"math.PR","submitted_at":"2013-12-23T11:27:19Z","title_canon_sha256":"25a2811a03f4f4218f0a6140f260bd3ec4352bf7477b85bbc6ee81eac62d32d1"},"schema_version":"1.0","source":{"id":"1312.6524","kind":"arxiv","version":1}},"canonical_sha256":"a579a5bf2a3b05732a57db3cee4b24c512cf47373a14ba1a1867a021c921044a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a579a5bf2a3b05732a57db3cee4b24c512cf47373a14ba1a1867a021c921044a","first_computed_at":"2026-05-18T03:03:58.009826Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:03:58.009826Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eAtkL7gFlLFe9Q64lsj+gdkWkP+BKLeO46a/Ixya1zpUhofZDnhwBGgMHgoDb+LgYZSO8NFu5KG8GGbRt1JwBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:03:58.010438Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6524","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bfed6468ee9349075d860f99b7c7c65de215c7efe1814adfdb1ae676468fe07","sha256:49833dc0509d806b8395088866447219df280c534e90c7771880824afe483590"],"state_sha256":"bdcc1847262037fea2293a258f96384865ab406041d70e745f9883b8780e4e3c"}