{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:POGEZSYOMT4WB7OUGL325RG6J2","short_pith_number":"pith:POGEZSYO","canonical_record":{"source":{"id":"0710.5611","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2007-10-30T11:22:53Z","cross_cats_sorted":[],"title_canon_sha256":"dadb9e29dfa64a79c0fb030069fefb59e206341cc405eec1c40e4cecdcff1d9d","abstract_canon_sha256":"385f6222ebd15aae780ae78af6d2d8d1b7ca6779556f45860798146a6f934471"},"schema_version":"1.0"},"canonical_sha256":"7b8c4ccb0e64f960fdd432f7aec4de4eb95cbe694efea01d5b56f6872e5b9573","source":{"kind":"arxiv","id":"0710.5611","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.5611","created_at":"2026-07-04T15:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"0710.5611v1","created_at":"2026-07-04T15:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.5611","created_at":"2026-07-04T15:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"POGEZSYOMT4W","created_at":"2026-07-04T15:05:17Z"},{"alias_kind":"pith_short_16","alias_value":"POGEZSYOMT4WB7OU","created_at":"2026-07-04T15:05:17Z"},{"alias_kind":"pith_short_8","alias_value":"POGEZSYO","created_at":"2026-07-04T15:05:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:POGEZSYOMT4WB7OUGL325RG6J2","target":"record","payload":{"canonical_record":{"source":{"id":"0710.5611","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2007-10-30T11:22:53Z","cross_cats_sorted":[],"title_canon_sha256":"dadb9e29dfa64a79c0fb030069fefb59e206341cc405eec1c40e4cecdcff1d9d","abstract_canon_sha256":"385f6222ebd15aae780ae78af6d2d8d1b7ca6779556f45860798146a6f934471"},"schema_version":"1.0"},"canonical_sha256":"7b8c4ccb0e64f960fdd432f7aec4de4eb95cbe694efea01d5b56f6872e5b9573","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:05:17.529123Z","signature_b64":"+bAxl2eCUaCweNugtGilES7WO3S4LbEPtNG8rvRbv8wG4TQA8CCVCEZNX1JmyDMt5bDiMdNZHs7lKbN+MJ26DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7b8c4ccb0e64f960fdd432f7aec4de4eb95cbe694efea01d5b56f6872e5b9573","last_reissued_at":"2026-07-04T15:05:17.528687Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:05:17.528687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.5611","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":"2026-07-04T15:05:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SAYElTpipBu8z6MXej1lQ1BKTReIX4hoR2r9YO98vzqoNu8bS6b6Gk948Xoi89PxnX2mr30KVciD5fCW+5ghAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:59:59.459573Z"},"content_sha256":"5d97ee80f2dd59aa2b8a753cabe5fe24372a84793520aa30b948bc1ffd0519dd","schema_version":"1.0","event_id":"sha256:5d97ee80f2dd59aa2b8a753cabe5fe24372a84793520aa30b948bc1ffd0519dd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:POGEZSYOMT4WB7OUGL325RG6J2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal cycles for permutations","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J. Robert Johnson","submitted_at":"2007-10-30T11:22:53Z","abstract_excerpt":"A universal cycle for permutations is a word of length n! such that each of the n! possible relative orders of n distinct integers occurs as a cyclic interval of the word. We show how to construct such a universal cycle in which only n+1 distinct integers are used. This is best possible and proves a conjecture of Chung, Diaconis and Graham."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.5611","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0710.5611/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T15:05:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OR/dXLVrmy0k5dyk/V0z51ILDI6YBoEDXRjUVM3B4G3Wm7VAzz72LLEnu7cGDTFDcYFWlTGyD6tf29n4vXgYBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T07:59:59.460050Z"},"content_sha256":"1e72f3fcbf338dee1b920b36c92cc4ce034f25863498c92f93432f4a42e90afa","schema_version":"1.0","event_id":"sha256:1e72f3fcbf338dee1b920b36c92cc4ce034f25863498c92f93432f4a42e90afa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/POGEZSYOMT4WB7OUGL325RG6J2/bundle.json","state_url":"https://pith.science/pith/POGEZSYOMT4WB7OUGL325RG6J2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/POGEZSYOMT4WB7OUGL325RG6J2/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":"2026-08-16T07:59:59Z","links":{"resolver":"https://pith.science/pith/POGEZSYOMT4WB7OUGL325RG6J2","bundle":"https://pith.science/pith/POGEZSYOMT4WB7OUGL325RG6J2/bundle.json","state":"https://pith.science/pith/POGEZSYOMT4WB7OUGL325RG6J2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/POGEZSYOMT4WB7OUGL325RG6J2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:POGEZSYOMT4WB7OUGL325RG6J2","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":"385f6222ebd15aae780ae78af6d2d8d1b7ca6779556f45860798146a6f934471","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2007-10-30T11:22:53Z","title_canon_sha256":"dadb9e29dfa64a79c0fb030069fefb59e206341cc405eec1c40e4cecdcff1d9d"},"schema_version":"1.0","source":{"id":"0710.5611","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.5611","created_at":"2026-07-04T15:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"0710.5611v1","created_at":"2026-07-04T15:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.5611","created_at":"2026-07-04T15:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"POGEZSYOMT4W","created_at":"2026-07-04T15:05:17Z"},{"alias_kind":"pith_short_16","alias_value":"POGEZSYOMT4WB7OU","created_at":"2026-07-04T15:05:17Z"},{"alias_kind":"pith_short_8","alias_value":"POGEZSYO","created_at":"2026-07-04T15:05:17Z"}],"graph_snapshots":[{"event_id":"sha256:1e72f3fcbf338dee1b920b36c92cc4ce034f25863498c92f93432f4a42e90afa","target":"graph","created_at":"2026-07-04T15:05:17Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/0710.5611/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A universal cycle for permutations is a word of length n! such that each of the n! possible relative orders of n distinct integers occurs as a cyclic interval of the word. We show how to construct such a universal cycle in which only n+1 distinct integers are used. This is best possible and proves a conjecture of Chung, Diaconis and Graham.","authors_text":"J. Robert Johnson","cross_cats":[],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2007-10-30T11:22:53Z","title":"Universal cycles for permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.5611","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":"sha256:5d97ee80f2dd59aa2b8a753cabe5fe24372a84793520aa30b948bc1ffd0519dd","target":"record","created_at":"2026-07-04T15:05:17Z","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":"385f6222ebd15aae780ae78af6d2d8d1b7ca6779556f45860798146a6f934471","cross_cats_sorted":[],"license":"","primary_cat":"math.CO","submitted_at":"2007-10-30T11:22:53Z","title_canon_sha256":"dadb9e29dfa64a79c0fb030069fefb59e206341cc405eec1c40e4cecdcff1d9d"},"schema_version":"1.0","source":{"id":"0710.5611","kind":"arxiv","version":1}},"canonical_sha256":"7b8c4ccb0e64f960fdd432f7aec4de4eb95cbe694efea01d5b56f6872e5b9573","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7b8c4ccb0e64f960fdd432f7aec4de4eb95cbe694efea01d5b56f6872e5b9573","first_computed_at":"2026-07-04T15:05:17.528687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:05:17.528687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+bAxl2eCUaCweNugtGilES7WO3S4LbEPtNG8rvRbv8wG4TQA8CCVCEZNX1JmyDMt5bDiMdNZHs7lKbN+MJ26DA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:05:17.529123Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.5611","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d97ee80f2dd59aa2b8a753cabe5fe24372a84793520aa30b948bc1ffd0519dd","sha256:1e72f3fcbf338dee1b920b36c92cc4ce034f25863498c92f93432f4a42e90afa"],"state_sha256":"222b480622ad66401569108212cf10d98afffab31360145bec75339b8a74d4b2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rJxRXbgc1raCehgZwf07pgQ7MEh/CCtemgKdbRzQcE3IZCcqrDEIjwA8gEA/S6fCzj3eFjku/OSYd/j1YoaHDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T07:59:59.464249Z","bundle_sha256":"717073a430c601c642adaefd79d441f1dc5bb0a30e4e37b420551ed345dd6547"}}