{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:O6QAXRCHQVZKLJPWE6JB5LWSW6","short_pith_number":"pith:O6QAXRCH","canonical_record":{"source":{"id":"1403.3805","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-03-15T13:49:56Z","cross_cats_sorted":[],"title_canon_sha256":"82e0090e3803676e839890ee2983d5a46bfd60e9a81f0b7dd696594fd3df6a7c","abstract_canon_sha256":"453c3c0d64e987f5b01c7d148a86760ca1abd45a160f86bbf1f82849fbd2fcbd"},"schema_version":"1.0"},"canonical_sha256":"77a00bc4478572a5a5f627921eaed2b78c0a7012ec6222acdbcc24e0695fd951","source":{"kind":"arxiv","id":"1403.3805","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3805","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3805v2","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3805","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"O6QAXRCHQVZK","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O6QAXRCHQVZKLJPW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O6QAXRCH","created_at":"2026-05-18T12:28:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:O6QAXRCHQVZKLJPWE6JB5LWSW6","target":"record","payload":{"canonical_record":{"source":{"id":"1403.3805","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-03-15T13:49:56Z","cross_cats_sorted":[],"title_canon_sha256":"82e0090e3803676e839890ee2983d5a46bfd60e9a81f0b7dd696594fd3df6a7c","abstract_canon_sha256":"453c3c0d64e987f5b01c7d148a86760ca1abd45a160f86bbf1f82849fbd2fcbd"},"schema_version":"1.0"},"canonical_sha256":"77a00bc4478572a5a5f627921eaed2b78c0a7012ec6222acdbcc24e0695fd951","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:00.429332Z","signature_b64":"1ocwom0KAUHDbf41rpnJiUO/ideu5iwUgt3yEVvxJy34HCOph7rNBKu5gVZF7wN6BS5arsFFQKjkKPgVReEZBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77a00bc4478572a5a5f627921eaed2b78c0a7012ec6222acdbcc24e0695fd951","last_reissued_at":"2026-05-18T02:44:00.428942Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:00.428942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.3805","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":"2026-05-18T02:44:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NnJy9Q1tMJBstmSK+18w6Lsy7xTDyBWJ+vpIUAO0WlkX5/VjwzQe/kDYXPE1vluhBMOPtqbQVdxGxd3x1eWoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:26:21.250255Z"},"content_sha256":"7843d833c10d7ab7ecdb7b950dbc89715f48109748ceb288b1f21fa8bcc29df2","schema_version":"1.0","event_id":"sha256:7843d833c10d7ab7ecdb7b950dbc89715f48109748ceb288b1f21fa8bcc29df2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:O6QAXRCHQVZKLJPWE6JB5LWSW6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$E$-optimal designs for second-order response surface models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Holger Dette, Yuri Grigoriev","submitted_at":"2014-03-15T13:49:56Z","abstract_excerpt":"$E$-optimal experimental designs for a second-order response surface model with $k\\geq1$ predictors are investigated. If the design space is the $k$-dimensional unit cube, Galil and Kiefer [J. Statist. Plann. Inference 1 (1977a) 121-132] determined optimal designs in a restricted class of designs (defined by the multiplicity of the minimal eigenvalue) and stated their universal optimality as a conjecture. In this paper, we prove this claim and show that these designs are in fact $E$-optimal in the class of all approximate designs. Moreover, if the design space is the unit ball, $E$-optimal des"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3805","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":"2026-05-18T02:44:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7rkHF2wSJ4eri2znXxaGBdwnfgtp0vwkoiFjW8zA5IA7Zj1L3Pxs5OsoJw6r8RMu8K6GJznlRbeL1JmGfFkZBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:26:21.250615Z"},"content_sha256":"fc7993fe432802bee2abfdaef28947fc9d44cae926a8a80feb034c1afa2f58c9","schema_version":"1.0","event_id":"sha256:fc7993fe432802bee2abfdaef28947fc9d44cae926a8a80feb034c1afa2f58c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O6QAXRCHQVZKLJPWE6JB5LWSW6/bundle.json","state_url":"https://pith.science/pith/O6QAXRCHQVZKLJPWE6JB5LWSW6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O6QAXRCHQVZKLJPWE6JB5LWSW6/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":"2026-06-02T19:26:21Z","links":{"resolver":"https://pith.science/pith/O6QAXRCHQVZKLJPWE6JB5LWSW6","bundle":"https://pith.science/pith/O6QAXRCHQVZKLJPWE6JB5LWSW6/bundle.json","state":"https://pith.science/pith/O6QAXRCHQVZKLJPWE6JB5LWSW6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O6QAXRCHQVZKLJPWE6JB5LWSW6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:O6QAXRCHQVZKLJPWE6JB5LWSW6","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":"453c3c0d64e987f5b01c7d148a86760ca1abd45a160f86bbf1f82849fbd2fcbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-03-15T13:49:56Z","title_canon_sha256":"82e0090e3803676e839890ee2983d5a46bfd60e9a81f0b7dd696594fd3df6a7c"},"schema_version":"1.0","source":{"id":"1403.3805","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.3805","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"1403.3805v2","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3805","created_at":"2026-05-18T02:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"O6QAXRCHQVZK","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"O6QAXRCHQVZKLJPW","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"O6QAXRCH","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:fc7993fe432802bee2abfdaef28947fc9d44cae926a8a80feb034c1afa2f58c9","target":"graph","created_at":"2026-05-18T02:44:00Z","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":"$E$-optimal experimental designs for a second-order response surface model with $k\\geq1$ predictors are investigated. If the design space is the $k$-dimensional unit cube, Galil and Kiefer [J. Statist. Plann. Inference 1 (1977a) 121-132] determined optimal designs in a restricted class of designs (defined by the multiplicity of the minimal eigenvalue) and stated their universal optimality as a conjecture. In this paper, we prove this claim and show that these designs are in fact $E$-optimal in the class of all approximate designs. Moreover, if the design space is the unit ball, $E$-optimal des","authors_text":"Holger Dette, Yuri Grigoriev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-03-15T13:49:56Z","title":"$E$-optimal designs for second-order response surface models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3805","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":"sha256:7843d833c10d7ab7ecdb7b950dbc89715f48109748ceb288b1f21fa8bcc29df2","target":"record","created_at":"2026-05-18T02:44:00Z","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":"453c3c0d64e987f5b01c7d148a86760ca1abd45a160f86bbf1f82849fbd2fcbd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2014-03-15T13:49:56Z","title_canon_sha256":"82e0090e3803676e839890ee2983d5a46bfd60e9a81f0b7dd696594fd3df6a7c"},"schema_version":"1.0","source":{"id":"1403.3805","kind":"arxiv","version":2}},"canonical_sha256":"77a00bc4478572a5a5f627921eaed2b78c0a7012ec6222acdbcc24e0695fd951","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77a00bc4478572a5a5f627921eaed2b78c0a7012ec6222acdbcc24e0695fd951","first_computed_at":"2026-05-18T02:44:00.428942Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:00.428942Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1ocwom0KAUHDbf41rpnJiUO/ideu5iwUgt3yEVvxJy34HCOph7rNBKu5gVZF7wN6BS5arsFFQKjkKPgVReEZBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:00.429332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.3805","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7843d833c10d7ab7ecdb7b950dbc89715f48109748ceb288b1f21fa8bcc29df2","sha256:fc7993fe432802bee2abfdaef28947fc9d44cae926a8a80feb034c1afa2f58c9"],"state_sha256":"27598e63b3ec05ae5b71d04052ce0f03e258efbf683c9d09e54d41765879108b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kMCXO00L/EvaUnyj4Slv4EH3dBWE2xV9QgwbhAmuFh98U2H/bUKAVXtll9ytoAxJ3uGiwUzNrOYnyQHAO5qoBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:26:21.252607Z","bundle_sha256":"0ac5bff91512dd9f9d8ee5203b972ceaccafc0e9c4eb99184fc866fc46b33238"}}