{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:M4KRC2NYHL4X2WZSZU7WVHD27D","short_pith_number":"pith:M4KRC2NY","schema_version":"1.0","canonical_sha256":"67151169b83af97d5b32cd3f6a9c7af8e77f8c3ea16803cd8da533d68ed6f258","source":{"kind":"arxiv","id":"1812.09543","version":1},"attestation_state":"computed","paper":{"title":"Extremal Cylinder Configurations I: Configuration $C_{\\mathfrak{m}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Oleg Ogievetsky, Senya Shlosman","submitted_at":"2018-12-22T15:16:50Z","abstract_excerpt":"We study the path $\\Gamma=\\{ C_{6,x}\\ \\vert\\ x\\in [0,1]\\}$ in the moduli space of configurations of 6 equal cylinders touching the unit sphere. Among the configurations $C_{6,x}$ is the record configuration $C_{\\mathfrak{m}}$ of \\cite{OS}. We show that $C_{\\mathfrak{m}}$ is a local sharp maximum of the distance function, so in particular the configuration $C_{\\mathfrak{m}}$ is not only unlockable but rigid. We show that if $\\frac{(1 + x) (1 + 3 x)}{3}$ is a rational number but not a square of a rational number, the configuration $C_{6,x}$ has some hidden symmetries, part of which we explain."},"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":"1812.09543","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2018-12-22T15:16:50Z","cross_cats_sorted":[],"title_canon_sha256":"d30cbe009d31709ee445122fda04fd292b63490a82b21b2f0cfd79e370578b94","abstract_canon_sha256":"683bcbff518cf4a1b189fbd627bb46a0cf777f11b8b4acae29c6f3c6dc7f0744"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:27.593056Z","signature_b64":"cgNG0CdfYAhTztJR8wnrQ+zI37/NuiRsWrNs1ZcT/B/oG5aj35n8bBXhnnkaQN5YhL4W4XGJgvhTjZSD1SQODw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67151169b83af97d5b32cd3f6a9c7af8e77f8c3ea16803cd8da533d68ed6f258","last_reissued_at":"2026-05-17T23:57:27.592418Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:27.592418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal Cylinder Configurations I: Configuration $C_{\\mathfrak{m}}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Oleg Ogievetsky, Senya Shlosman","submitted_at":"2018-12-22T15:16:50Z","abstract_excerpt":"We study the path $\\Gamma=\\{ C_{6,x}\\ \\vert\\ x\\in [0,1]\\}$ in the moduli space of configurations of 6 equal cylinders touching the unit sphere. Among the configurations $C_{6,x}$ is the record configuration $C_{\\mathfrak{m}}$ of \\cite{OS}. We show that $C_{\\mathfrak{m}}$ is a local sharp maximum of the distance function, so in particular the configuration $C_{\\mathfrak{m}}$ is not only unlockable but rigid. We show that if $\\frac{(1 + x) (1 + 3 x)}{3}$ is a rational number but not a square of a rational number, the configuration $C_{6,x}$ has some hidden symmetries, part of which we explain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09543","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":"1812.09543","created_at":"2026-05-17T23:57:27.592512+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.09543v1","created_at":"2026-05-17T23:57:27.592512+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09543","created_at":"2026-05-17T23:57:27.592512+00:00"},{"alias_kind":"pith_short_12","alias_value":"M4KRC2NYHL4X","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_16","alias_value":"M4KRC2NYHL4X2WZS","created_at":"2026-05-18T12:32:37.024351+00:00"},{"alias_kind":"pith_short_8","alias_value":"M4KRC2NY","created_at":"2026-05-18T12:32:37.024351+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/M4KRC2NYHL4X2WZSZU7WVHD27D","json":"https://pith.science/pith/M4KRC2NYHL4X2WZSZU7WVHD27D.json","graph_json":"https://pith.science/api/pith-number/M4KRC2NYHL4X2WZSZU7WVHD27D/graph.json","events_json":"https://pith.science/api/pith-number/M4KRC2NYHL4X2WZSZU7WVHD27D/events.json","paper":"https://pith.science/paper/M4KRC2NY"},"agent_actions":{"view_html":"https://pith.science/pith/M4KRC2NYHL4X2WZSZU7WVHD27D","download_json":"https://pith.science/pith/M4KRC2NYHL4X2WZSZU7WVHD27D.json","view_paper":"https://pith.science/paper/M4KRC2NY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.09543&json=true","fetch_graph":"https://pith.science/api/pith-number/M4KRC2NYHL4X2WZSZU7WVHD27D/graph.json","fetch_events":"https://pith.science/api/pith-number/M4KRC2NYHL4X2WZSZU7WVHD27D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M4KRC2NYHL4X2WZSZU7WVHD27D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M4KRC2NYHL4X2WZSZU7WVHD27D/action/storage_attestation","attest_author":"https://pith.science/pith/M4KRC2NYHL4X2WZSZU7WVHD27D/action/author_attestation","sign_citation":"https://pith.science/pith/M4KRC2NYHL4X2WZSZU7WVHD27D/action/citation_signature","submit_replication":"https://pith.science/pith/M4KRC2NYHL4X2WZSZU7WVHD27D/action/replication_record"}},"created_at":"2026-05-17T23:57:27.592512+00:00","updated_at":"2026-05-17T23:57:27.592512+00:00"}