{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:SZMWZE2PQ2AS273WXXD35GTIV5","short_pith_number":"pith:SZMWZE2P","canonical_record":{"source":{"id":"math/0205299","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2002-05-28T17:35:10Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"7bf46290ba71fc30c5a057ccd4616201a778e6a5b69ce02be0bae8594ba2269e","abstract_canon_sha256":"b3cafeb1e3fbce5276bb747aadddb31992d0df2c7a1f3bf799fc83432cb0c754"},"schema_version":"1.0"},"canonical_sha256":"96596c934f86812d7f76bdc7be9a68af7231d758d724d82b1989902157a8f44b","source":{"kind":"arxiv","id":"math/0205299","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205299","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205299v1","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205299","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"SZMWZE2PQ2AS","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"SZMWZE2PQ2AS273W","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"SZMWZE2P","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:SZMWZE2PQ2AS273WXXD35GTIV5","target":"record","payload":{"canonical_record":{"source":{"id":"math/0205299","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2002-05-28T17:35:10Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"7bf46290ba71fc30c5a057ccd4616201a778e6a5b69ce02be0bae8594ba2269e","abstract_canon_sha256":"b3cafeb1e3fbce5276bb747aadddb31992d0df2c7a1f3bf799fc83432cb0c754"},"schema_version":"1.0"},"canonical_sha256":"96596c934f86812d7f76bdc7be9a68af7231d758d724d82b1989902157a8f44b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:35:38.605337Z","signature_b64":"pZbgG0kHZjhVTCcbNfzCQncZFddIKrHmvWFmQY0LLR/OfvJ/wFDHs1fTv3MgbZ3D5SBRpES5QziLek9iniB9BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96596c934f86812d7f76bdc7be9a68af7231d758d724d82b1989902157a8f44b","last_reissued_at":"2026-05-18T02:35:38.604882Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:35:38.604882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0205299","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":"2026-05-18T02:35:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yMJu5i6Bs00dnv6se2U7hqvVvNy/Hxm+R4Np2y5+mJsTXFvMWoeqNt0QeyOBtI+kQykw+O3qwJEBw2vj1CUnDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:31:40.153774Z"},"content_sha256":"cbaafcc48db3954c90b89a95fca277c2857b77d94fb37357cf8fe8d7241a10cc","schema_version":"1.0","event_id":"sha256:cbaafcc48db3954c90b89a95fca277c2857b77d94fb37357cf8fe8d7241a10cc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:SZMWZE2PQ2AS273WXXD35GTIV5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Lattice of N-Run Orthogonal Arrays","license":"","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"E. M. Rains, John Stufken, N. J. A. Sloane","submitted_at":"2002-05-28T17:35:10Z","abstract_excerpt":"If the number of runs in a (mixed-level) orthogonal array of strength 2 is specified, what numbers of levels and factors are possible? The collection of possible sets of parameters for orthogonal arrays with N runs has a natural lattice structure, induced by the ``expansive replacement'' construction method. In particular the dual atoms in this lattice are the most important parameter sets, since any other parameter set for an N-run orthogonal array can be constructed from them. To get a sense for the number of dual atoms, and to begin to understand the lattice as a function of N, we investiga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205299","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":"2026-05-18T02:35:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b2msbN2MkUhGDhQIppP0Lv4/bgNoauAeLmvOuFQI7YysmlFBFSfeC5CWIXZO1NkinZIozaZc7MeBIoedCDvlDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T17:31:40.154189Z"},"content_sha256":"cacc425b789e86281ade6ac90d32a034132ccfcf05b6ddd83fc4af66dd179e03","schema_version":"1.0","event_id":"sha256:cacc425b789e86281ade6ac90d32a034132ccfcf05b6ddd83fc4af66dd179e03"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SZMWZE2PQ2AS273WXXD35GTIV5/bundle.json","state_url":"https://pith.science/pith/SZMWZE2PQ2AS273WXXD35GTIV5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SZMWZE2PQ2AS273WXXD35GTIV5/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":"2026-06-07T17:31:40Z","links":{"resolver":"https://pith.science/pith/SZMWZE2PQ2AS273WXXD35GTIV5","bundle":"https://pith.science/pith/SZMWZE2PQ2AS273WXXD35GTIV5/bundle.json","state":"https://pith.science/pith/SZMWZE2PQ2AS273WXXD35GTIV5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SZMWZE2PQ2AS273WXXD35GTIV5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:SZMWZE2PQ2AS273WXXD35GTIV5","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":"b3cafeb1e3fbce5276bb747aadddb31992d0df2c7a1f3bf799fc83432cb0c754","cross_cats_sorted":["cs.IT","math.IT"],"license":"","primary_cat":"math.CO","submitted_at":"2002-05-28T17:35:10Z","title_canon_sha256":"7bf46290ba71fc30c5a057ccd4616201a778e6a5b69ce02be0bae8594ba2269e"},"schema_version":"1.0","source":{"id":"math/0205299","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0205299","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"math/0205299v1","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0205299","created_at":"2026-05-18T02:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"SZMWZE2PQ2AS","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"SZMWZE2PQ2AS273W","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"SZMWZE2P","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:cacc425b789e86281ade6ac90d32a034132ccfcf05b6ddd83fc4af66dd179e03","target":"graph","created_at":"2026-05-18T02:35:38Z","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":"If the number of runs in a (mixed-level) orthogonal array of strength 2 is specified, what numbers of levels and factors are possible? The collection of possible sets of parameters for orthogonal arrays with N runs has a natural lattice structure, induced by the ``expansive replacement'' construction method. In particular the dual atoms in this lattice are the most important parameter sets, since any other parameter set for an N-run orthogonal array can be constructed from them. To get a sense for the number of dual atoms, and to begin to understand the lattice as a function of N, we investiga","authors_text":"E. M. Rains, John Stufken, N. J. A. Sloane","cross_cats":["cs.IT","math.IT"],"headline":"","license":"","primary_cat":"math.CO","submitted_at":"2002-05-28T17:35:10Z","title":"The Lattice of N-Run Orthogonal Arrays"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0205299","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:cbaafcc48db3954c90b89a95fca277c2857b77d94fb37357cf8fe8d7241a10cc","target":"record","created_at":"2026-05-18T02:35:38Z","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":"b3cafeb1e3fbce5276bb747aadddb31992d0df2c7a1f3bf799fc83432cb0c754","cross_cats_sorted":["cs.IT","math.IT"],"license":"","primary_cat":"math.CO","submitted_at":"2002-05-28T17:35:10Z","title_canon_sha256":"7bf46290ba71fc30c5a057ccd4616201a778e6a5b69ce02be0bae8594ba2269e"},"schema_version":"1.0","source":{"id":"math/0205299","kind":"arxiv","version":1}},"canonical_sha256":"96596c934f86812d7f76bdc7be9a68af7231d758d724d82b1989902157a8f44b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96596c934f86812d7f76bdc7be9a68af7231d758d724d82b1989902157a8f44b","first_computed_at":"2026-05-18T02:35:38.604882Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:35:38.604882Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pZbgG0kHZjhVTCcbNfzCQncZFddIKrHmvWFmQY0LLR/OfvJ/wFDHs1fTv3MgbZ3D5SBRpES5QziLek9iniB9BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:35:38.605337Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0205299","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbaafcc48db3954c90b89a95fca277c2857b77d94fb37357cf8fe8d7241a10cc","sha256:cacc425b789e86281ade6ac90d32a034132ccfcf05b6ddd83fc4af66dd179e03"],"state_sha256":"f8d9a088ed79714f4c98b0263b9ca21c3f9e2e101f358c359ecde6e50cc04aa8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ECMNI1qV08MpN4QpH0Ao9Hqwug48OO5a5KdViFXsl4pTfK5Nr263p0AB8Tdg37pB/SWY4Y5UH2VyOMQQGHr/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T17:31:40.157379Z","bundle_sha256":"5c2374c1c03e00178af79422fa3a593f90a18958eb6236eb2fb46e32367731bd"}}