{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:ND4DWM2ORZUAN6ERDGCCUYC6JC","short_pith_number":"pith:ND4DWM2O","canonical_record":{"source":{"id":"1706.04903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-15T14:47:30Z","cross_cats_sorted":[],"title_canon_sha256":"a2283d31d412e55946c650eb2554519116550a55713c84b38b2e6bbfc0fbb9c0","abstract_canon_sha256":"7815b6d1631cbaa3cc47847404d70231322a64cbfba9e6976bcc3c87eda33abf"},"schema_version":"1.0"},"canonical_sha256":"68f83b334e8e6806f89119842a605e488f04dc0f2a54a6a797f600f4190141f0","source":{"kind":"arxiv","id":"1706.04903","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04903","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04903v1","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04903","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"ND4DWM2ORZUA","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"ND4DWM2ORZUAN6ER","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"ND4DWM2O","created_at":"2026-05-18T12:31:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:ND4DWM2ORZUAN6ERDGCCUYC6JC","target":"record","payload":{"canonical_record":{"source":{"id":"1706.04903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-15T14:47:30Z","cross_cats_sorted":[],"title_canon_sha256":"a2283d31d412e55946c650eb2554519116550a55713c84b38b2e6bbfc0fbb9c0","abstract_canon_sha256":"7815b6d1631cbaa3cc47847404d70231322a64cbfba9e6976bcc3c87eda33abf"},"schema_version":"1.0"},"canonical_sha256":"68f83b334e8e6806f89119842a605e488f04dc0f2a54a6a797f600f4190141f0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:42:18.594571Z","signature_b64":"hMYwMl6XlQ3zntgV0vdsHU6OwhztOsNtJZQx67bVLUilnxonX4fy+C157mYVgNXrNOXrB1eCJc6CLn/VcyfYDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"68f83b334e8e6806f89119842a605e488f04dc0f2a54a6a797f600f4190141f0","last_reissued_at":"2026-05-18T00:42:18.593854Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:42:18.593854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.04903","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":"2026-05-18T00:42:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5l56IgvjGBnub1k9PqlNF1cKn7yUyroCcxbKY5xpIlOpzXHonnaJxexcsSh0W9Qm0LCgc5unoULaoDwjP6b8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:15:56.461705Z"},"content_sha256":"a5da32fc52a54f29811861fec2bb87dbb9a442930b4cec76e3df91811ebadbc2","schema_version":"1.0","event_id":"sha256:a5da32fc52a54f29811861fec2bb87dbb9a442930b4cec76e3df91811ebadbc2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:ND4DWM2ORZUAN6ERDGCCUYC6JC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A remark on Hamilton cycles with few colors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alexey Pokrovskiy, Benny Sudakov, Igor Balla","submitted_at":"2017-06-15T14:47:30Z","abstract_excerpt":"Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge colouring of $K_n$ with $n$ colours contains a Hamilton cycle with $\\leq O(\\log n)$ colours. They proved that there is always a Hamilton cycle with $\\leq 8\\sqrt n$ colours. In this note we improve this bound to $O(\\log^3 n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04903","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":"2026-05-18T00:42:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lpcdqNzWhv2jHwhq6bospgmRABN21E3JOTE5LkfQYXKD9Ver3jCcjW40HvogJ1xpumJ4ZRqXHPxVdPVR2gYyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T10:15:56.462044Z"},"content_sha256":"eac21e862fb8466c798c394f07529639ad9abe2e599a678e772acebf2f2ee3de","schema_version":"1.0","event_id":"sha256:eac21e862fb8466c798c394f07529639ad9abe2e599a678e772acebf2f2ee3de"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ND4DWM2ORZUAN6ERDGCCUYC6JC/bundle.json","state_url":"https://pith.science/pith/ND4DWM2ORZUAN6ERDGCCUYC6JC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ND4DWM2ORZUAN6ERDGCCUYC6JC/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":"2026-05-30T10:15:56Z","links":{"resolver":"https://pith.science/pith/ND4DWM2ORZUAN6ERDGCCUYC6JC","bundle":"https://pith.science/pith/ND4DWM2ORZUAN6ERDGCCUYC6JC/bundle.json","state":"https://pith.science/pith/ND4DWM2ORZUAN6ERDGCCUYC6JC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ND4DWM2ORZUAN6ERDGCCUYC6JC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ND4DWM2ORZUAN6ERDGCCUYC6JC","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":"7815b6d1631cbaa3cc47847404d70231322a64cbfba9e6976bcc3c87eda33abf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-15T14:47:30Z","title_canon_sha256":"a2283d31d412e55946c650eb2554519116550a55713c84b38b2e6bbfc0fbb9c0"},"schema_version":"1.0","source":{"id":"1706.04903","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.04903","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"arxiv_version","alias_value":"1706.04903v1","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.04903","created_at":"2026-05-18T00:42:18Z"},{"alias_kind":"pith_short_12","alias_value":"ND4DWM2ORZUA","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_16","alias_value":"ND4DWM2ORZUAN6ER","created_at":"2026-05-18T12:31:31Z"},{"alias_kind":"pith_short_8","alias_value":"ND4DWM2O","created_at":"2026-05-18T12:31:31Z"}],"graph_snapshots":[{"event_id":"sha256:eac21e862fb8466c798c394f07529639ad9abe2e599a678e772acebf2f2ee3de","target":"graph","created_at":"2026-05-18T00:42:18Z","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":"Akbari, Etesami, Mahini, and Mahmoody conjectured that every proper edge colouring of $K_n$ with $n$ colours contains a Hamilton cycle with $\\leq O(\\log n)$ colours. They proved that there is always a Hamilton cycle with $\\leq 8\\sqrt n$ colours. In this note we improve this bound to $O(\\log^3 n)$.","authors_text":"Alexey Pokrovskiy, Benny Sudakov, Igor Balla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-15T14:47:30Z","title":"A remark on Hamilton cycles with few colors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04903","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:a5da32fc52a54f29811861fec2bb87dbb9a442930b4cec76e3df91811ebadbc2","target":"record","created_at":"2026-05-18T00:42:18Z","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":"7815b6d1631cbaa3cc47847404d70231322a64cbfba9e6976bcc3c87eda33abf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-06-15T14:47:30Z","title_canon_sha256":"a2283d31d412e55946c650eb2554519116550a55713c84b38b2e6bbfc0fbb9c0"},"schema_version":"1.0","source":{"id":"1706.04903","kind":"arxiv","version":1}},"canonical_sha256":"68f83b334e8e6806f89119842a605e488f04dc0f2a54a6a797f600f4190141f0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68f83b334e8e6806f89119842a605e488f04dc0f2a54a6a797f600f4190141f0","first_computed_at":"2026-05-18T00:42:18.593854Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:42:18.593854Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hMYwMl6XlQ3zntgV0vdsHU6OwhztOsNtJZQx67bVLUilnxonX4fy+C157mYVgNXrNOXrB1eCJc6CLn/VcyfYDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:42:18.594571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.04903","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a5da32fc52a54f29811861fec2bb87dbb9a442930b4cec76e3df91811ebadbc2","sha256:eac21e862fb8466c798c394f07529639ad9abe2e599a678e772acebf2f2ee3de"],"state_sha256":"df83ee1c387154e6e255adc3e68198d3d280e28f8a8658adc6ecc555c1eebc6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F/qqKrY4GakM5i/zHLIOXApbZ7e9GS+HIGGn2tmQFGkN2pOaIa1dPA79IvY3odRShxI4kMYY8UZqnH4HpGZkAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T10:15:56.463949Z","bundle_sha256":"f75b023b517bc72d0ba3aafc4a037b6243ca216b90b5767ffbf022fe1422de7c"}}