{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FBTE3QKFATGRUALCRAFSUZEEPP","short_pith_number":"pith:FBTE3QKF","schema_version":"1.0","canonical_sha256":"28664dc14504cd1a0162880b2a64847bd882c861a543416e9882cc518bed8912","source":{"kind":"arxiv","id":"1708.05524","version":1},"attestation_state":"computed","paper":{"title":"On the strong non-rigidity of certain tight Euclidean designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Djoko Suprijanto, Eiichi Bannai, Etsuko Bannai","submitted_at":"2017-08-18T07:17:21Z","abstract_excerpt":"We study the non-rigidity of Euclidean $t$-designs, namely we study when Euclidean designs (in particular certain tight Euclidean designs) can be deformed keeping the property of being Euclidean $t$-designs. We show that certain tight Euclidean $t$-designs are non-rigid, and in fact satisfy a stronger form of non-rigidity which we call strong non-rigidity. This shows that there are plenty of non-isomorphic tight Euclidean $t$-designs for certain parameters, which seems to have been unnoticed before. We also include the complete classification of tight Euclidean $2$-designs."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1708.05524","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-18T07:17:21Z","cross_cats_sorted":[],"title_canon_sha256":"146c2aa17c7761a823d38a75f8b33881d40f03bab7d1eabdd5c6590425d188d0","abstract_canon_sha256":"dc68e47e5f239785e112af1c3e87c1db739846586a8cdaaa1c0eb04cca81dd6e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:49.817910Z","signature_b64":"cTwLDM2JD+8nJHWfxCHh3shoCF/jJ+PVm/TI9geASIrZNE3PJ3HqIGa8/PTbM+t5aheyoUhQNXE7fcbHgOdwCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28664dc14504cd1a0162880b2a64847bd882c861a543416e9882cc518bed8912","last_reissued_at":"2026-05-18T00:37:49.817082Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:49.817082Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the strong non-rigidity of certain tight Euclidean designs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Djoko Suprijanto, Eiichi Bannai, Etsuko Bannai","submitted_at":"2017-08-18T07:17:21Z","abstract_excerpt":"We study the non-rigidity of Euclidean $t$-designs, namely we study when Euclidean designs (in particular certain tight Euclidean designs) can be deformed keeping the property of being Euclidean $t$-designs. We show that certain tight Euclidean $t$-designs are non-rigid, and in fact satisfy a stronger form of non-rigidity which we call strong non-rigidity. This shows that there are plenty of non-isomorphic tight Euclidean $t$-designs for certain parameters, which seems to have been unnoticed before. We also include the complete classification of tight Euclidean $2$-designs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.05524","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1708.05524","created_at":"2026-05-18T00:37:49.817220+00:00"},{"alias_kind":"arxiv_version","alias_value":"1708.05524v1","created_at":"2026-05-18T00:37:49.817220+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.05524","created_at":"2026-05-18T00:37:49.817220+00:00"},{"alias_kind":"pith_short_12","alias_value":"FBTE3QKFATGR","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FBTE3QKFATGRUALC","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FBTE3QKF","created_at":"2026-05-18T12:31:15.632608+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FBTE3QKFATGRUALCRAFSUZEEPP","json":"https://pith.science/pith/FBTE3QKFATGRUALCRAFSUZEEPP.json","graph_json":"https://pith.science/api/pith-number/FBTE3QKFATGRUALCRAFSUZEEPP/graph.json","events_json":"https://pith.science/api/pith-number/FBTE3QKFATGRUALCRAFSUZEEPP/events.json","paper":"https://pith.science/paper/FBTE3QKF"},"agent_actions":{"view_html":"https://pith.science/pith/FBTE3QKFATGRUALCRAFSUZEEPP","download_json":"https://pith.science/pith/FBTE3QKFATGRUALCRAFSUZEEPP.json","view_paper":"https://pith.science/paper/FBTE3QKF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1708.05524&json=true","fetch_graph":"https://pith.science/api/pith-number/FBTE3QKFATGRUALCRAFSUZEEPP/graph.json","fetch_events":"https://pith.science/api/pith-number/FBTE3QKFATGRUALCRAFSUZEEPP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FBTE3QKFATGRUALCRAFSUZEEPP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FBTE3QKFATGRUALCRAFSUZEEPP/action/storage_attestation","attest_author":"https://pith.science/pith/FBTE3QKFATGRUALCRAFSUZEEPP/action/author_attestation","sign_citation":"https://pith.science/pith/FBTE3QKFATGRUALCRAFSUZEEPP/action/citation_signature","submit_replication":"https://pith.science/pith/FBTE3QKFATGRUALCRAFSUZEEPP/action/replication_record"}},"created_at":"2026-05-18T00:37:49.817220+00:00","updated_at":"2026-05-18T00:37:49.817220+00:00"}