{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JWYF5NHIS6LASLPW5CUUPHB7BW","short_pith_number":"pith:JWYF5NHI","canonical_record":{"source":{"id":"1209.4662","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-20T20:37:55Z","cross_cats_sorted":[],"title_canon_sha256":"0c97086d5de8c641aba0c61a42d67edd00779b0aa5262f009af5dcb470bcfbc9","abstract_canon_sha256":"fa578a7cf18e49d1062c810f2354f8b1bb2b49513f32bea966ba8eced54c46c2"},"schema_version":"1.0"},"canonical_sha256":"4db05eb4e89796092df6e8a9479c3f0d9a9199e91dc5df525c56081b90644663","source":{"kind":"arxiv","id":"1209.4662","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4662","created_at":"2026-05-18T03:27:13Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4662v2","created_at":"2026-05-18T03:27:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4662","created_at":"2026-05-18T03:27:13Z"},{"alias_kind":"pith_short_12","alias_value":"JWYF5NHIS6LA","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JWYF5NHIS6LASLPW","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JWYF5NHI","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JWYF5NHIS6LASLPW5CUUPHB7BW","target":"record","payload":{"canonical_record":{"source":{"id":"1209.4662","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-20T20:37:55Z","cross_cats_sorted":[],"title_canon_sha256":"0c97086d5de8c641aba0c61a42d67edd00779b0aa5262f009af5dcb470bcfbc9","abstract_canon_sha256":"fa578a7cf18e49d1062c810f2354f8b1bb2b49513f32bea966ba8eced54c46c2"},"schema_version":"1.0"},"canonical_sha256":"4db05eb4e89796092df6e8a9479c3f0d9a9199e91dc5df525c56081b90644663","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:27:13.796381Z","signature_b64":"B3IdGO5PhQDYbmuRMcxwfO5I58+yTuQUNsiYa6IZPjhgJAUZuWMS/CF9Va8oubYBA1b4MrOhCp9CPSkl2KofCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4db05eb4e89796092df6e8a9479c3f0d9a9199e91dc5df525c56081b90644663","last_reissued_at":"2026-05-18T03:27:13.795690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:27:13.795690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.4662","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":"2026-05-18T03:27:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7q/92+VahsqhDVQblHa4cBmJKUBtuqG0AwJlbpHxHev2jHNbsyudnaJGj94ejNPa3kvKrP2DajDvql1SWgkdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:33:04.276403Z"},"content_sha256":"f3dbcda111ea25152bf8b2424dc410ed4b1714417f370cc3c0f184a1b3a4452e","schema_version":"1.0","event_id":"sha256:f3dbcda111ea25152bf8b2424dc410ed4b1714417f370cc3c0f184a1b3a4452e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JWYF5NHIS6LASLPW5CUUPHB7BW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An inductive approach to constructing Universal Cycles on the k-subsets of [n]","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yevgeniy Rudoy","submitted_at":"2012-09-20T20:37:55Z","abstract_excerpt":"In this paper, we introduce a method of constructing Universal Cycles on sets by taking \"sums\" and \"products\" of smaller cycles. We demonstrate this new approach by proving that if there exist Universal Cycles on the 4-subsets of [18] and the 4-subsets of [26], then for any integer n which is greater than or equal 18 and equivalent to 2 mod 8, there exists a Universal Cycle on the 4-subsets of [n]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4662","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":"2026-05-18T03:27:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fso9DlCLot/CLxRShZ2s2dvU6uVjPjgJkU1HXs0dPUYdcPlktgz2eojAYE92G7WySWQ8KZC6S14wB4azUyq8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:33:04.276770Z"},"content_sha256":"af7abdcf095b3d68e5f815f650f201da9b0d0b5781514927e574bf4ba0c5ad47","schema_version":"1.0","event_id":"sha256:af7abdcf095b3d68e5f815f650f201da9b0d0b5781514927e574bf4ba0c5ad47"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JWYF5NHIS6LASLPW5CUUPHB7BW/bundle.json","state_url":"https://pith.science/pith/JWYF5NHIS6LASLPW5CUUPHB7BW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JWYF5NHIS6LASLPW5CUUPHB7BW/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":"2026-06-22T16:33:04Z","links":{"resolver":"https://pith.science/pith/JWYF5NHIS6LASLPW5CUUPHB7BW","bundle":"https://pith.science/pith/JWYF5NHIS6LASLPW5CUUPHB7BW/bundle.json","state":"https://pith.science/pith/JWYF5NHIS6LASLPW5CUUPHB7BW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JWYF5NHIS6LASLPW5CUUPHB7BW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JWYF5NHIS6LASLPW5CUUPHB7BW","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":"fa578a7cf18e49d1062c810f2354f8b1bb2b49513f32bea966ba8eced54c46c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-20T20:37:55Z","title_canon_sha256":"0c97086d5de8c641aba0c61a42d67edd00779b0aa5262f009af5dcb470bcfbc9"},"schema_version":"1.0","source":{"id":"1209.4662","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4662","created_at":"2026-05-18T03:27:13Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4662v2","created_at":"2026-05-18T03:27:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4662","created_at":"2026-05-18T03:27:13Z"},{"alias_kind":"pith_short_12","alias_value":"JWYF5NHIS6LA","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JWYF5NHIS6LASLPW","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JWYF5NHI","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:af7abdcf095b3d68e5f815f650f201da9b0d0b5781514927e574bf4ba0c5ad47","target":"graph","created_at":"2026-05-18T03:27:13Z","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":"In this paper, we introduce a method of constructing Universal Cycles on sets by taking \"sums\" and \"products\" of smaller cycles. We demonstrate this new approach by proving that if there exist Universal Cycles on the 4-subsets of [18] and the 4-subsets of [26], then for any integer n which is greater than or equal 18 and equivalent to 2 mod 8, there exists a Universal Cycle on the 4-subsets of [n].","authors_text":"Yevgeniy Rudoy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-20T20:37:55Z","title":"An inductive approach to constructing Universal Cycles on the k-subsets of [n]"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4662","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:f3dbcda111ea25152bf8b2424dc410ed4b1714417f370cc3c0f184a1b3a4452e","target":"record","created_at":"2026-05-18T03:27:13Z","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":"fa578a7cf18e49d1062c810f2354f8b1bb2b49513f32bea966ba8eced54c46c2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-09-20T20:37:55Z","title_canon_sha256":"0c97086d5de8c641aba0c61a42d67edd00779b0aa5262f009af5dcb470bcfbc9"},"schema_version":"1.0","source":{"id":"1209.4662","kind":"arxiv","version":2}},"canonical_sha256":"4db05eb4e89796092df6e8a9479c3f0d9a9199e91dc5df525c56081b90644663","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4db05eb4e89796092df6e8a9479c3f0d9a9199e91dc5df525c56081b90644663","first_computed_at":"2026-05-18T03:27:13.795690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:27:13.795690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B3IdGO5PhQDYbmuRMcxwfO5I58+yTuQUNsiYa6IZPjhgJAUZuWMS/CF9Va8oubYBA1b4MrOhCp9CPSkl2KofCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:27:13.796381Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4662","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3dbcda111ea25152bf8b2424dc410ed4b1714417f370cc3c0f184a1b3a4452e","sha256:af7abdcf095b3d68e5f815f650f201da9b0d0b5781514927e574bf4ba0c5ad47"],"state_sha256":"065139056ef0da1afe6b35c0c33046e9e6de70c0c379b42502ec4489f98e1894"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7hcUtkqgO0hJd2KG/6k3bPi4TEy0bvKcWLysUDJ3OasiYXVskDI/kt+cy25ILhpaCBqW7nju7zw9pTvcc5tGDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:33:04.278850Z","bundle_sha256":"3341e4b4045083ff7de8141f3ee85690de188f2a8fead8de341a50a6952febc3"}}