{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:EXD4QRCZYRTKMSJ7VGRFMJB7MI","short_pith_number":"pith:EXD4QRCZ","canonical_record":{"source":{"id":"1810.08252","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-18T19:27:03Z","cross_cats_sorted":[],"title_canon_sha256":"e7a5130f5a86cf34a04d312a9823b1e286c1e923ef3cadd8de5ef0b5427e240c","abstract_canon_sha256":"1e0e5f519c33d9deb218826f27d50a92904f0ee9398b3b0d41c5de1982879760"},"schema_version":"1.0"},"canonical_sha256":"25c7c84459c466a6493fa9a256243f620b5993b79984d4fbec66cc7cdc2bd136","source":{"kind":"arxiv","id":"1810.08252","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08252","created_at":"2026-07-05T02:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08252v4","created_at":"2026-07-05T02:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08252","created_at":"2026-07-05T02:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"EXD4QRCZYRTK","created_at":"2026-07-05T02:07:12Z"},{"alias_kind":"pith_short_16","alias_value":"EXD4QRCZYRTKMSJ7","created_at":"2026-07-05T02:07:12Z"},{"alias_kind":"pith_short_8","alias_value":"EXD4QRCZ","created_at":"2026-07-05T02:07:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:EXD4QRCZYRTKMSJ7VGRFMJB7MI","target":"record","payload":{"canonical_record":{"source":{"id":"1810.08252","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-18T19:27:03Z","cross_cats_sorted":[],"title_canon_sha256":"e7a5130f5a86cf34a04d312a9823b1e286c1e923ef3cadd8de5ef0b5427e240c","abstract_canon_sha256":"1e0e5f519c33d9deb218826f27d50a92904f0ee9398b3b0d41c5de1982879760"},"schema_version":"1.0"},"canonical_sha256":"25c7c84459c466a6493fa9a256243f620b5993b79984d4fbec66cc7cdc2bd136","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:07:12.628396Z","signature_b64":"i7WQKqE2GXzvbltqZGFVwdeSrVccnl809F9OniCFkCEI5VfJwBmaWHb2OFRao48F7lVKW0A7ORnVvWp7Z8WODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"25c7c84459c466a6493fa9a256243f620b5993b79984d4fbec66cc7cdc2bd136","last_reissued_at":"2026-07-05T02:07:12.627893Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:07:12.627893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.08252","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:07:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oVnhQlG0DZFeVs44uCd0XrKIPQJHUaz8K0aIQWL9mjH2E8ZLuIUvax1P7ktYooyiSz+AU4cyPR5UZSnhrHlMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:19:00.674027Z"},"content_sha256":"4e8e2616fed482cc137c53c68044d1cd1446724e05fbf7afaf519fc7c10e53d4","schema_version":"1.0","event_id":"sha256:4e8e2616fed482cc137c53c68044d1cd1446724e05fbf7afaf519fc7c10e53d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:EXD4QRCZYRTKMSJ7VGRFMJB7MI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Containing all permutations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michael Engen, Vincent Vatter","submitted_at":"2018-10-18T19:27:03Z","abstract_excerpt":"Numerous versions of the question \"what is the shortest object containing all permutations of a given length?\" have been asked over the past fifty years: by Karp (via Knuth) in 1972; by Chung, Diaconis, and Graham in 1992; by Ashlock and Tillotson in 1993; and by Arratia in 1999. The large variety of questions of this form, which have previously been considered in isolation, stands in stark contrast to the dearth of answers. We survey and synthesize these questions and their partial answers, introduce infinitely more related questions, and then establish an improved upper bound for one of thes"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08252","kind":"arxiv","version":4},"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/1810.08252/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":"2026-07-05T02:07:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/FlxgWIh6p5kDbIhr1/PjNBNKl2MHOwMByDcrLxq2s6/VoIgwnX6qF3Hn4WTRciJBBxrFbUgj6RN6F6qgzqjAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T14:19:00.674536Z"},"content_sha256":"40826f3dd3a0eb45f5a3936a1559d683ade1a18622a45cb97e77be15530c0c21","schema_version":"1.0","event_id":"sha256:40826f3dd3a0eb45f5a3936a1559d683ade1a18622a45cb97e77be15530c0c21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EXD4QRCZYRTKMSJ7VGRFMJB7MI/bundle.json","state_url":"https://pith.science/pith/EXD4QRCZYRTKMSJ7VGRFMJB7MI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EXD4QRCZYRTKMSJ7VGRFMJB7MI/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":"2026-08-16T14:19:00Z","links":{"resolver":"https://pith.science/pith/EXD4QRCZYRTKMSJ7VGRFMJB7MI","bundle":"https://pith.science/pith/EXD4QRCZYRTKMSJ7VGRFMJB7MI/bundle.json","state":"https://pith.science/pith/EXD4QRCZYRTKMSJ7VGRFMJB7MI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EXD4QRCZYRTKMSJ7VGRFMJB7MI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:EXD4QRCZYRTKMSJ7VGRFMJB7MI","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":"1e0e5f519c33d9deb218826f27d50a92904f0ee9398b3b0d41c5de1982879760","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-18T19:27:03Z","title_canon_sha256":"e7a5130f5a86cf34a04d312a9823b1e286c1e923ef3cadd8de5ef0b5427e240c"},"schema_version":"1.0","source":{"id":"1810.08252","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08252","created_at":"2026-07-05T02:07:12Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08252v4","created_at":"2026-07-05T02:07:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08252","created_at":"2026-07-05T02:07:12Z"},{"alias_kind":"pith_short_12","alias_value":"EXD4QRCZYRTK","created_at":"2026-07-05T02:07:12Z"},{"alias_kind":"pith_short_16","alias_value":"EXD4QRCZYRTKMSJ7","created_at":"2026-07-05T02:07:12Z"},{"alias_kind":"pith_short_8","alias_value":"EXD4QRCZ","created_at":"2026-07-05T02:07:12Z"}],"graph_snapshots":[{"event_id":"sha256:40826f3dd3a0eb45f5a3936a1559d683ade1a18622a45cb97e77be15530c0c21","target":"graph","created_at":"2026-07-05T02:07:12Z","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/1810.08252/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Numerous versions of the question \"what is the shortest object containing all permutations of a given length?\" have been asked over the past fifty years: by Karp (via Knuth) in 1972; by Chung, Diaconis, and Graham in 1992; by Ashlock and Tillotson in 1993; and by Arratia in 1999. The large variety of questions of this form, which have previously been considered in isolation, stands in stark contrast to the dearth of answers. We survey and synthesize these questions and their partial answers, introduce infinitely more related questions, and then establish an improved upper bound for one of thes","authors_text":"Michael Engen, Vincent Vatter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-18T19:27:03Z","title":"Containing all permutations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08252","kind":"arxiv","version":4},"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":"sha256:4e8e2616fed482cc137c53c68044d1cd1446724e05fbf7afaf519fc7c10e53d4","target":"record","created_at":"2026-07-05T02:07:12Z","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":"1e0e5f519c33d9deb218826f27d50a92904f0ee9398b3b0d41c5de1982879760","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-18T19:27:03Z","title_canon_sha256":"e7a5130f5a86cf34a04d312a9823b1e286c1e923ef3cadd8de5ef0b5427e240c"},"schema_version":"1.0","source":{"id":"1810.08252","kind":"arxiv","version":4}},"canonical_sha256":"25c7c84459c466a6493fa9a256243f620b5993b79984d4fbec66cc7cdc2bd136","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"25c7c84459c466a6493fa9a256243f620b5993b79984d4fbec66cc7cdc2bd136","first_computed_at":"2026-07-05T02:07:12.627893Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:07:12.627893Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i7WQKqE2GXzvbltqZGFVwdeSrVccnl809F9OniCFkCEI5VfJwBmaWHb2OFRao48F7lVKW0A7ORnVvWp7Z8WODA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:07:12.628396Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08252","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4e8e2616fed482cc137c53c68044d1cd1446724e05fbf7afaf519fc7c10e53d4","sha256:40826f3dd3a0eb45f5a3936a1559d683ade1a18622a45cb97e77be15530c0c21"],"state_sha256":"8e11b0421c9619e750bf74cf8eaeeb174f193ac03ca12bf598b8d39db76ae927"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KmY7G8h5IvCIGD4yvdhX48EW5bwUs3zUwDDX38Ech6iQYm5OxdjKMilchO5FdYgSH6DHOSPxJnySC0thVIkzDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T14:19:00.705506Z","bundle_sha256":"3775c6b7c90f6a5fc947870341200c92d3dd0f7da435871e4402fe142f6e3209"}}