{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:37KL7OU4OZH6PI7QKDP6F2GK6E","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":"20634d3d9228f96df3464951a0bb1de08d703fce67cb0bf6940d192ac2f2873c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-24T01:39:24Z","title_canon_sha256":"24bb56060ab21c6b09195822876df0b65acd94a03edb7ebf532d4e7bfaaebff7"},"schema_version":"1.0","source":{"id":"2504.17184","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.17184","created_at":"2026-07-05T11:45:14Z"},{"alias_kind":"arxiv_version","alias_value":"2504.17184v2","created_at":"2026-07-05T11:45:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.17184","created_at":"2026-07-05T11:45:14Z"},{"alias_kind":"pith_short_12","alias_value":"37KL7OU4OZH6","created_at":"2026-07-05T11:45:14Z"},{"alias_kind":"pith_short_16","alias_value":"37KL7OU4OZH6PI7Q","created_at":"2026-07-05T11:45:14Z"},{"alias_kind":"pith_short_8","alias_value":"37KL7OU4","created_at":"2026-07-05T11:45:14Z"}],"graph_snapshots":[{"event_id":"sha256:ff64fc017aba30bd291eaba241a81e4f5dcdfe561e8006bd32c60a4504617281","target":"graph","created_at":"2026-07-05T11:45:14Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2504.17184/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper investigates the existence of $m$-stiff configurations in the unit sphere $S^{d-1}$, which are spherical $(2m-1)$-designs that lie on $m$ parallel hyperplanes. We establish two non-existence results: (1) for each fixed integer $m > 5$, there exists no $m$-stiff configuration in $S^{d-1}$ for sufficiently large $d$; (2) for each fixed integer $d > 10$, there exists no $m$-stiff configuration in $S^{d-1}$ for sufficiently large $m$. Furthermore, we provide a complete classification of the dimensions where $m$-stiff configurations exist for $m=2,3,4,5$. We also determine the non-existe","authors_text":"Eiichi Bannai, Hiroshi Nozaki, Hirotake Kurihara","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-24T01:39:24Z","title":"On the existence and non-existence of spherical $m$-stiff configurations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.17184","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:c2251c55c8149fcb22f390b4e503621a0981297b3b177d9722d3ce8d6c78e827","target":"record","created_at":"2026-07-05T11:45:14Z","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":"20634d3d9228f96df3464951a0bb1de08d703fce67cb0bf6940d192ac2f2873c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-04-24T01:39:24Z","title_canon_sha256":"24bb56060ab21c6b09195822876df0b65acd94a03edb7ebf532d4e7bfaaebff7"},"schema_version":"1.0","source":{"id":"2504.17184","kind":"arxiv","version":2}},"canonical_sha256":"dfd4bfba9c764fe7a3f050dfe2e8caf13ec63d395f8f167a37ad732bba3e2460","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dfd4bfba9c764fe7a3f050dfe2e8caf13ec63d395f8f167a37ad732bba3e2460","first_computed_at":"2026-07-05T11:45:14.795139Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:45:14.795139Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jmivciWl7XpASb/NL9rfRQNf8x9TYmCYXJbJlWCstD89QIsUJPxMGCmIf8PMP/JuGlvi1LL0ffMRkeYcTFlbBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:45:14.795801Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.17184","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c2251c55c8149fcb22f390b4e503621a0981297b3b177d9722d3ce8d6c78e827","sha256:ff64fc017aba30bd291eaba241a81e4f5dcdfe561e8006bd32c60a4504617281"],"state_sha256":"9d5ed2ce29425fbc9f0478e9c7ec6d080a009656e6624f4cc8a9c6a0de5e3f3b"}