{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PZWDW6DA5EG2KF3LMUF53WKIF3","short_pith_number":"pith:PZWDW6DA","canonical_record":{"source":{"id":"1403.2894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-12T11:47:31Z","cross_cats_sorted":[],"title_canon_sha256":"c41e5af77b8fd5ef067e98e234426bae6cfee435af03aaf932194322ba963f85","abstract_canon_sha256":"02b5d0ec6199e14b839808f74c5b920f3f54cb72d9e186057cd80091117a4d69"},"schema_version":"1.0"},"canonical_sha256":"7e6c3b7860e90da5176b650bddd9482ece0c2385e58252d635596eeec70e2b06","source":{"kind":"arxiv","id":"1403.2894","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2894","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2894v1","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2894","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"PZWDW6DA5EG2","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PZWDW6DA5EG2KF3L","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PZWDW6DA","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PZWDW6DA5EG2KF3LMUF53WKIF3","target":"record","payload":{"canonical_record":{"source":{"id":"1403.2894","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-12T11:47:31Z","cross_cats_sorted":[],"title_canon_sha256":"c41e5af77b8fd5ef067e98e234426bae6cfee435af03aaf932194322ba963f85","abstract_canon_sha256":"02b5d0ec6199e14b839808f74c5b920f3f54cb72d9e186057cd80091117a4d69"},"schema_version":"1.0"},"canonical_sha256":"7e6c3b7860e90da5176b650bddd9482ece0c2385e58252d635596eeec70e2b06","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:33.658993Z","signature_b64":"ZuRIT9UumTv26NYkulUoDXsm7d9OeeEHhspePpXh0qqmGtiP4Hdi77bgmWXixAFZJESqYu4GDeVtkKh4jMNFCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7e6c3b7860e90da5176b650bddd9482ece0c2385e58252d635596eeec70e2b06","last_reissued_at":"2026-05-18T02:56:33.658189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:33.658189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.2894","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:56:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LfnSqQx6RhC73h3PwarWzOzT5zdFtpwMhycCpbWK8d4xJzB9pp+XBGFpX+j4um8LSkDgQkw/6l2/u5m/mWQ1BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:25:14.516069Z"},"content_sha256":"9c72967c142972e31eb062df8e8793f4ba6873bfddef6187b55df8a60e7a92a6","schema_version":"1.0","event_id":"sha256:9c72967c142972e31eb062df8e8793f4ba6873bfddef6187b55df8a60e7a92a6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PZWDW6DA5EG2KF3LMUF53WKIF3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monochromatic Hamiltonian Berge-cycles in colored hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"G.R. Omidi, L. Maherani","submitted_at":"2014-03-12T11:47:31Z","abstract_excerpt":"It has been conjectured that for any fixed r and sufficiently large n, there is a monochromatic Hamiltonian Berge-cycle in every (r - 1)-coloring of the edges of the complete r-uniform hypergraph on n vertices. In this paper, we show that the statement of this conjecture is true with r-2 colors (instead of r-1 colors) by showing that there is a monochromatic Hamiltonian t-tight Berge-cycle in every b r-2 / t-1 -edge coloring of Kr n for any fixed r > t >= 2 and sufficiently large n. Also, we give a proof for this conjecture when r = 4 (the first open case). These results improve the previously"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2894","kind":"arxiv","version":1},"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":"2026-05-18T02:56:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G/0PnVXACWkA0lpGpjaeOV6SXslvux0d2SR2Ugcxs1ZePMGA8gd34e5WhhQ3DBpx0cEk8MCZA7JULXba0CylCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T20:25:14.516451Z"},"content_sha256":"dbb5cc6c22b1bcd1c4a6bc2b81b938667fb8ca182cbfd2591ce3eae33565cc24","schema_version":"1.0","event_id":"sha256:dbb5cc6c22b1bcd1c4a6bc2b81b938667fb8ca182cbfd2591ce3eae33565cc24"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PZWDW6DA5EG2KF3LMUF53WKIF3/bundle.json","state_url":"https://pith.science/pith/PZWDW6DA5EG2KF3LMUF53WKIF3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PZWDW6DA5EG2KF3LMUF53WKIF3/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":"2026-06-23T20:25:14Z","links":{"resolver":"https://pith.science/pith/PZWDW6DA5EG2KF3LMUF53WKIF3","bundle":"https://pith.science/pith/PZWDW6DA5EG2KF3LMUF53WKIF3/bundle.json","state":"https://pith.science/pith/PZWDW6DA5EG2KF3LMUF53WKIF3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PZWDW6DA5EG2KF3LMUF53WKIF3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PZWDW6DA5EG2KF3LMUF53WKIF3","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":"02b5d0ec6199e14b839808f74c5b920f3f54cb72d9e186057cd80091117a4d69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-12T11:47:31Z","title_canon_sha256":"c41e5af77b8fd5ef067e98e234426bae6cfee435af03aaf932194322ba963f85"},"schema_version":"1.0","source":{"id":"1403.2894","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.2894","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"arxiv_version","alias_value":"1403.2894v1","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.2894","created_at":"2026-05-18T02:56:33Z"},{"alias_kind":"pith_short_12","alias_value":"PZWDW6DA5EG2","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PZWDW6DA5EG2KF3L","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PZWDW6DA","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:dbb5cc6c22b1bcd1c4a6bc2b81b938667fb8ca182cbfd2591ce3eae33565cc24","target":"graph","created_at":"2026-05-18T02:56:33Z","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":"It has been conjectured that for any fixed r and sufficiently large n, there is a monochromatic Hamiltonian Berge-cycle in every (r - 1)-coloring of the edges of the complete r-uniform hypergraph on n vertices. In this paper, we show that the statement of this conjecture is true with r-2 colors (instead of r-1 colors) by showing that there is a monochromatic Hamiltonian t-tight Berge-cycle in every b r-2 / t-1 -edge coloring of Kr n for any fixed r > t >= 2 and sufficiently large n. Also, we give a proof for this conjecture when r = 4 (the first open case). These results improve the previously","authors_text":"G.R. Omidi, L. Maherani","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-12T11:47:31Z","title":"Monochromatic Hamiltonian Berge-cycles in colored hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.2894","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":"sha256:9c72967c142972e31eb062df8e8793f4ba6873bfddef6187b55df8a60e7a92a6","target":"record","created_at":"2026-05-18T02:56:33Z","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":"02b5d0ec6199e14b839808f74c5b920f3f54cb72d9e186057cd80091117a4d69","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-12T11:47:31Z","title_canon_sha256":"c41e5af77b8fd5ef067e98e234426bae6cfee435af03aaf932194322ba963f85"},"schema_version":"1.0","source":{"id":"1403.2894","kind":"arxiv","version":1}},"canonical_sha256":"7e6c3b7860e90da5176b650bddd9482ece0c2385e58252d635596eeec70e2b06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7e6c3b7860e90da5176b650bddd9482ece0c2385e58252d635596eeec70e2b06","first_computed_at":"2026-05-18T02:56:33.658189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:33.658189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZuRIT9UumTv26NYkulUoDXsm7d9OeeEHhspePpXh0qqmGtiP4Hdi77bgmWXixAFZJESqYu4GDeVtkKh4jMNFCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:33.658993Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.2894","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c72967c142972e31eb062df8e8793f4ba6873bfddef6187b55df8a60e7a92a6","sha256:dbb5cc6c22b1bcd1c4a6bc2b81b938667fb8ca182cbfd2591ce3eae33565cc24"],"state_sha256":"b5baba9b8d7178cf64c779cbe5e9af9a582f1441d4ecd97cd700a4b238d7f9a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"j4HajlppyJlS9Vy0QFAkAGi6SjfxnkLH+7Sg/4uaLGYY9F9iK3/yKAN2Z52J+xuinJccFIJdZQrUvjBKdor0Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T20:25:14.518436Z","bundle_sha256":"6533b270e3ee3f4fc2519046f9db1e1c8249b476968ddd249f0847964c564e9b"}}