{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NJHGQQ3HZTMRPHDDSDS7LBCSWC","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":"0ad62238a58ea42fcf9f43ba600934df88735f8a5b6c1a57b08aca32d767e405","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-04T03:11:54Z","title_canon_sha256":"9cf4a152028ac9498483138188955fadc2bed8a15e0f04fe952d6c2d0f561efd"},"schema_version":"1.0","source":{"id":"2605.05243","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.05243","created_at":"2026-05-22T01:04:04Z"},{"alias_kind":"arxiv_version","alias_value":"2605.05243v2","created_at":"2026-05-22T01:04:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.05243","created_at":"2026-05-22T01:04:04Z"},{"alias_kind":"pith_short_12","alias_value":"NJHGQQ3HZTMR","created_at":"2026-05-22T01:04:04Z"},{"alias_kind":"pith_short_16","alias_value":"NJHGQQ3HZTMRPHDD","created_at":"2026-05-22T01:04:04Z"},{"alias_kind":"pith_short_8","alias_value":"NJHGQQ3H","created_at":"2026-05-22T01:04:04Z"}],"graph_snapshots":[{"event_id":"sha256:2c424b2225005a52298cb07292b0051d20bbfb54a5f93e1e141bc45938f7c75f","target":"graph","created_at":"2026-05-22T01:04:04Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"For d ≥ 4 the minimum of ||x||_p / ||x||_2 over non-zero zero-sum x equals 2^{1/p-1/2} when 0 < p ≤ 1, equals the min of that quantity and ((d-1)^{p/2} + (d-1)^{1-p/2})/d^{p/2})^{1/p} when 1 < p < 2, and the analogous maximum statement holds for q > 2."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The proof must correctly identify and compare the two candidate extremal configurations (the two-support vector and the equitable (d-1)-support vector) and show no other zero-sum vector yields a smaller or larger ratio; this case analysis is not visible in the abstract."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Proves that the minimum and maximum of ||x||_p / ||x||_2 over non-zero zero-sum x in R^d equal the stated closed-form expressions for all d ≥ 4."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"The conjectured sharp bounds on p-norm to 2-norm ratios for zero-sum vectors hold for all dimensions four and higher."}],"snapshot_sha256":"7ca6f1d23df7364dca4daf1199fff5fc51f9ab8e95c002953aee07cca90bba5c"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-20T16:36:42.607288Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-20T04:01:22.356213Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T16:37:36.391377Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.05243/integrity.json","findings":[],"snapshot_sha256":"206b1be5a2e01f818ab810a65da1ce0888d2935ff7ca09524370efedd90346ad","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $d\\ge 3$ and $p>0$. Let $\\|x\\|_p$ denote the $\\ell_p$ (quasi-)norm of a $d$-dimensional vector $x$. Holevo and Utkin \\cite{HU26} conjectured that for $0<p\\le 1$, \\[ \\min \\left\\{\\frac{\\|x\\|_p}{\\|x\\|_2}:\\vec{0}\\neq x\\in\\mathbb R^d,\\ \\sum_{i=1}^d x_i=0\\right\\} =2^{1/p-1/2}; \\] for $1<p<2$, \\[ \\min \\left\\{\\frac{\\|x\\|_p}{\\|x\\|_2}:\\vec{0}\\neq x\\in\\mathbb R^d,\\ \\sum_{i=1}^d x_i=0\\right\\} = \\min\\left\\{2^{1/p-1/2},\\left(\\frac{(d-1)^{p/2}+(d-1)^{1-p/2}}{d^{p/2}}\\right)^{1/p}\\right\\}; \\] and for $2<q<\\infty$ \\[ \\max\\left\\{\\frac{\\|x\\|_q}{\\|x\\|_2}:\\vec{0}\\neq x\\in\\mathbb R^d,\\ \\sum_{i=1}^d x_i=0\\right\\","authors_text":"Haonan Zhang","cross_cats":["math-ph","math.FA","math.MP"],"headline":"The conjectured sharp bounds on p-norm to 2-norm ratios for zero-sum vectors hold for all dimensions four and higher.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-04T03:11:54Z","title":"Proof of the Holevo--Utkin conjecture on sharp $\\ell_p$ norms for zero-sum vectors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.05243","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-08T17:19:21.557797Z","id":"e8d2d0ba-8e2b-43ad-9a2b-10705592c9a9","model_set":{"reader":"grok-4.3"},"one_line_summary":"Proves that the minimum and maximum of ||x||_p / ||x||_2 over non-zero zero-sum x in R^d equal the stated closed-form expressions for all d ≥ 4.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"The conjectured sharp bounds on p-norm to 2-norm ratios for zero-sum vectors hold for all dimensions four and higher.","strongest_claim":"For d ≥ 4 the minimum of ||x||_p / ||x||_2 over non-zero zero-sum x equals 2^{1/p-1/2} when 0 < p ≤ 1, equals the min of that quantity and ((d-1)^{p/2} + (d-1)^{1-p/2})/d^{p/2})^{1/p} when 1 < p < 2, and the analogous maximum statement holds for q > 2.","weakest_assumption":"The proof must correctly identify and compare the two candidate extremal configurations (the two-support vector and the equitable (d-1)-support vector) and show no other zero-sum vector yields a smaller or larger ratio; this case analysis is not visible in the abstract."}},"verdict_id":"e8d2d0ba-8e2b-43ad-9a2b-10705592c9a9"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c4544611cd9b4a2f85f00f98ddd9ef32bb58b20f838019219a2672d91fe7ea39","target":"record","created_at":"2026-05-22T01:04:04Z","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":"0ad62238a58ea42fcf9f43ba600934df88735f8a5b6c1a57b08aca32d767e405","cross_cats_sorted":["math-ph","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2026-05-04T03:11:54Z","title_canon_sha256":"9cf4a152028ac9498483138188955fadc2bed8a15e0f04fe952d6c2d0f561efd"},"schema_version":"1.0","source":{"id":"2605.05243","kind":"arxiv","version":2}},"canonical_sha256":"6a4e684367ccd9179c6390e5f58452b09f6d9b02ad4c972350d04dbd0e6c6cae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a4e684367ccd9179c6390e5f58452b09f6d9b02ad4c972350d04dbd0e6c6cae","first_computed_at":"2026-05-22T01:04:04.510376Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:04.510376Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CYgCCO+aRvORg33JcG0UqXu7lvvbQCD5ZpjL7TfuM3PCeD+m6596tqgK7uYygbffr4FR8nXmN+IhdAmrz/ZsBw==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:04.511186Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.05243","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c4544611cd9b4a2f85f00f98ddd9ef32bb58b20f838019219a2672d91fe7ea39","sha256:2c424b2225005a52298cb07292b0051d20bbfb54a5f93e1e141bc45938f7c75f"],"state_sha256":"27b11a6e208d00a46000fe6bb4f2ca7226f705067254a31c56a5016d3fa8c3ef"}