{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:WE5VDLYI6GUDYDG7RQNJJJXEUR","short_pith_number":"pith:WE5VDLYI","canonical_record":{"source":{"id":"1809.03759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-09-11T09:15:37Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"857ca7d5c4a752bf6ad070f4149903f51c201e01adfc584280d01ca99d2f82b5","abstract_canon_sha256":"dbc0b2ae666964d71c91d2a06bd2857a919b76ecf993e84f668aa92563e45ba4"},"schema_version":"1.0"},"canonical_sha256":"b13b51af08f1a83c0cdf8c1a94a6e4a455b184ef654a13c594aab165d5872d56","source":{"kind":"arxiv","id":"1809.03759","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03759","created_at":"2026-05-18T00:05:59Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03759v1","created_at":"2026-05-18T00:05:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03759","created_at":"2026-05-18T00:05:59Z"},{"alias_kind":"pith_short_12","alias_value":"WE5VDLYI6GUD","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WE5VDLYI6GUDYDG7","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WE5VDLYI","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:WE5VDLYI6GUDYDG7RQNJJJXEUR","target":"record","payload":{"canonical_record":{"source":{"id":"1809.03759","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-09-11T09:15:37Z","cross_cats_sorted":["stat.ME","stat.TH"],"title_canon_sha256":"857ca7d5c4a752bf6ad070f4149903f51c201e01adfc584280d01ca99d2f82b5","abstract_canon_sha256":"dbc0b2ae666964d71c91d2a06bd2857a919b76ecf993e84f668aa92563e45ba4"},"schema_version":"1.0"},"canonical_sha256":"b13b51af08f1a83c0cdf8c1a94a6e4a455b184ef654a13c594aab165d5872d56","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:59.902283Z","signature_b64":"DKacpAOsRav0XL/VsyI16qprzWh67qYVaKaiRKKSLD6NiIeFSymrMYQqyA4/Q/4HG9CyeB7BDHON06BkCBOODA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b13b51af08f1a83c0cdf8c1a94a6e4a455b184ef654a13c594aab165d5872d56","last_reissued_at":"2026-05-18T00:05:59.901663Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:59.901663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.03759","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":"2026-05-18T00:05:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PqTvFOkQukyOE3ORc3qilq7rL/hh/EdIzjnPXxwr9J0qx0EhJSrfxxEEPEGAqeShR8AMtw9xEFA0oH+zErmcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T08:50:41.149215Z"},"content_sha256":"f1621e80f7ae3a1dee5d565dec7ce617cddf2ab1b5ae03d16d95f470c394e3a7","schema_version":"1.0","event_id":"sha256:f1621e80f7ae3a1dee5d565dec7ce617cddf2ab1b5ae03d16d95f470c394e3a7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:WE5VDLYI6GUDYDG7RQNJJJXEUR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the aberrations of mixed level Orthogonal Arrays with removed runs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.ME","stat.TH"],"primary_cat":"math.ST","authors_text":"Fabio Rapallo, Roberto Fontana","submitted_at":"2018-09-11T09:15:37Z","abstract_excerpt":"Given an Orthogonal Array we analyze the aberrations of the sub-fractions which are obtained by the deletion of some of its points. We provide formulae to compute the Generalized Word-Length Pattern of any sub-fraction. In the case of the deletion of one single point, we provide a simple methodology to find which the best sub-fractions are according to the Generalized Minimum Aberration criterion. We also study the effect of the deletion of 1, 2 or 3 points on some examples. The methodology does not put any restriction on the number of levels of each factor. It follows that any mixed level Ort"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03759","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":"2026-05-18T00:05:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RMRpQDS7l+vM40nvzO4KFZHIfbBooYkPANyzlcvil9oQBb5P6imlNj9YidIKL4ma5AbrLWEoNzQWgG6hzvk6DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T08:50:41.149582Z"},"content_sha256":"06c0f15d41befb7591a9f9b68aa85fe7a08cc5aa196c3ae1540fc08b6e79a070","schema_version":"1.0","event_id":"sha256:06c0f15d41befb7591a9f9b68aa85fe7a08cc5aa196c3ae1540fc08b6e79a070"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WE5VDLYI6GUDYDG7RQNJJJXEUR/bundle.json","state_url":"https://pith.science/pith/WE5VDLYI6GUDYDG7RQNJJJXEUR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WE5VDLYI6GUDYDG7RQNJJJXEUR/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":"2026-06-30T08:50:41Z","links":{"resolver":"https://pith.science/pith/WE5VDLYI6GUDYDG7RQNJJJXEUR","bundle":"https://pith.science/pith/WE5VDLYI6GUDYDG7RQNJJJXEUR/bundle.json","state":"https://pith.science/pith/WE5VDLYI6GUDYDG7RQNJJJXEUR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WE5VDLYI6GUDYDG7RQNJJJXEUR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WE5VDLYI6GUDYDG7RQNJJJXEUR","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":"dbc0b2ae666964d71c91d2a06bd2857a919b76ecf993e84f668aa92563e45ba4","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-09-11T09:15:37Z","title_canon_sha256":"857ca7d5c4a752bf6ad070f4149903f51c201e01adfc584280d01ca99d2f82b5"},"schema_version":"1.0","source":{"id":"1809.03759","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.03759","created_at":"2026-05-18T00:05:59Z"},{"alias_kind":"arxiv_version","alias_value":"1809.03759v1","created_at":"2026-05-18T00:05:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.03759","created_at":"2026-05-18T00:05:59Z"},{"alias_kind":"pith_short_12","alias_value":"WE5VDLYI6GUD","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"WE5VDLYI6GUDYDG7","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"WE5VDLYI","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:06c0f15d41befb7591a9f9b68aa85fe7a08cc5aa196c3ae1540fc08b6e79a070","target":"graph","created_at":"2026-05-18T00:05:59Z","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":"Given an Orthogonal Array we analyze the aberrations of the sub-fractions which are obtained by the deletion of some of its points. We provide formulae to compute the Generalized Word-Length Pattern of any sub-fraction. In the case of the deletion of one single point, we provide a simple methodology to find which the best sub-fractions are according to the Generalized Minimum Aberration criterion. We also study the effect of the deletion of 1, 2 or 3 points on some examples. The methodology does not put any restriction on the number of levels of each factor. It follows that any mixed level Ort","authors_text":"Fabio Rapallo, Roberto Fontana","cross_cats":["stat.ME","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-09-11T09:15:37Z","title":"On the aberrations of mixed level Orthogonal Arrays with removed runs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.03759","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:f1621e80f7ae3a1dee5d565dec7ce617cddf2ab1b5ae03d16d95f470c394e3a7","target":"record","created_at":"2026-05-18T00:05:59Z","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":"dbc0b2ae666964d71c91d2a06bd2857a919b76ecf993e84f668aa92563e45ba4","cross_cats_sorted":["stat.ME","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-09-11T09:15:37Z","title_canon_sha256":"857ca7d5c4a752bf6ad070f4149903f51c201e01adfc584280d01ca99d2f82b5"},"schema_version":"1.0","source":{"id":"1809.03759","kind":"arxiv","version":1}},"canonical_sha256":"b13b51af08f1a83c0cdf8c1a94a6e4a455b184ef654a13c594aab165d5872d56","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b13b51af08f1a83c0cdf8c1a94a6e4a455b184ef654a13c594aab165d5872d56","first_computed_at":"2026-05-18T00:05:59.901663Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:59.901663Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DKacpAOsRav0XL/VsyI16qprzWh67qYVaKaiRKKSLD6NiIeFSymrMYQqyA4/Q/4HG9CyeB7BDHON06BkCBOODA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:59.902283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.03759","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1621e80f7ae3a1dee5d565dec7ce617cddf2ab1b5ae03d16d95f470c394e3a7","sha256:06c0f15d41befb7591a9f9b68aa85fe7a08cc5aa196c3ae1540fc08b6e79a070"],"state_sha256":"39d8297e97f40cd9f9cc06d3b6a90c76e181e38d3cc25bcd68aa5a2417cbb509"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rlAezEvaHcizlcIGTIZrtrhzHASe1U8AOX5DKL2W/KAaySuEEEON7lQLRHLLQB52DoDAyc9dOpHaCPCOZeZ8Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T08:50:41.152388Z","bundle_sha256":"02a74e70076f20b7207160db51ff3f152ec51a398c18c4770b823c78f39b997b"}}