{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UDZLDL4CDARFD7J7H3RDU2AD55","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":"70496010433c52ffe3e443fc425f2c2f84c583247d853ebb358dbac06817d931","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-09-21T07:03:22Z","title_canon_sha256":"90409da225f734cbdd2c005ed34e3f7ee2c9fb9b5d8558142fabaa7cdcc9ae5e"},"schema_version":"1.0","source":{"id":"1109.4481","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4481","created_at":"2026-05-18T04:12:34Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4481v1","created_at":"2026-05-18T04:12:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4481","created_at":"2026-05-18T04:12:34Z"},{"alias_kind":"pith_short_12","alias_value":"UDZLDL4CDARF","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UDZLDL4CDARFD7J7","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UDZLDL4C","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:b0a3c4353a5471e1ee498dc44ee46672fa4e5fa6e7fda2eb740719d55beb85d3","target":"graph","created_at":"2026-05-18T04:12:34Z","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":"We consider the distances between a line and a set of points in the plane defined by the L^p-norms of the vector consisting of the euclidian distance between the single points and the line. We determine lines with minimal geometric L^p-distance to the vertices of an equilateral triangle for all 1<= p<=\\infty. The investigation of the L^p-distances for p\\ne 1,2,\\infty establishes the passage between the well-known sets of optimal lines for p=1,2,\\infty. The set of optimal lines consists of three lines each parallel to one of the triangle sides for 1<= p < 4/3 and 2<p<=\\infty and of the three pe","authors_text":"Annett Puettmann","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-09-21T07:03:22Z","title":"Geometrically L^p-optimal lines of vertices of an equilateral triangle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4481","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:e4064b448b8fbe01cc9553c0605ea0a1324f62174954e7017baf0d4cef905a46","target":"record","created_at":"2026-05-18T04:12:34Z","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":"70496010433c52ffe3e443fc425f2c2f84c583247d853ebb358dbac06817d931","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2011-09-21T07:03:22Z","title_canon_sha256":"90409da225f734cbdd2c005ed34e3f7ee2c9fb9b5d8558142fabaa7cdcc9ae5e"},"schema_version":"1.0","source":{"id":"1109.4481","kind":"arxiv","version":1}},"canonical_sha256":"a0f2b1af82182251fd3f3ee23a6803ef47c41161cfb38b64334f5409eb779e7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0f2b1af82182251fd3f3ee23a6803ef47c41161cfb38b64334f5409eb779e7b","first_computed_at":"2026-05-18T04:12:34.638353Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:12:34.638353Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VbtkE2CSWCT/ezGzKKfGAHrZltc54X3n4AS1W0KdkYDe8Kn7AUMbEHNHiui+CwjrkBA6nZD++FgPZ8KTVen1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:12:34.638870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4481","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4064b448b8fbe01cc9553c0605ea0a1324f62174954e7017baf0d4cef905a46","sha256:b0a3c4353a5471e1ee498dc44ee46672fa4e5fa6e7fda2eb740719d55beb85d3"],"state_sha256":"7dbd0cb67f7ac459dcc69e3e082f8ae4350f07ea965b4ee6692e0fd010fe0cc5"}