{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:J3W2DFLVXFBTJ4IGBNYAETDBUH","short_pith_number":"pith:J3W2DFLV","schema_version":"1.0","canonical_sha256":"4eeda19575b94334f1060b70024c61a1db50009c6808dbe8de4b4b392a6d04ea","source":{"kind":"arxiv","id":"1209.0031","version":1},"attestation_state":"computed","paper":{"title":"Shape Transitions in Hyperbolic Non-Euclidean Plates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"cond-mat.soft","authors_text":"John Gemmer, Shankar Venkataramani","submitted_at":"2012-08-31T23:27:37Z","abstract_excerpt":"We present and summarize the results of recent studies on non-Euclidean plates with imposed constant negative Gaussian curvature in both the F\\\"oppl - von K\\'arm\\'an and Kirchhoff approximations. Motivated by experimental results we focus on annuli with a periodic profile. We show that in the F\\\"oppl - von K\\'arm\\'an approximation there are only two types of global minimizers -- flat and saddle shaped deformations with localized regions of stretching near the boundary of the annulus. We also show that there exists local minimizers with $n$-waves that have regions of stretching near their lines"},"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":"1209.0031","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2012-08-31T23:27:37Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"a32f3a353b352697427e16713004e867dae613b3e4c3c0c75c30f28ac5d4b7c1","abstract_canon_sha256":"7daa75a0e23bc14727d1f1531b602631c9f09c78284eaf1f10f89008c49099a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:30.226115Z","signature_b64":"zWnJdMug1w/OeAmp4fxIm6UMFSMijl7ZwaNFW98fR96Zxspt+xhHcj3k09Pd4DvBew1FKwK3IXbqjxFS+goxDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4eeda19575b94334f1060b70024c61a1db50009c6808dbe8de4b4b392a6d04ea","last_reissued_at":"2026-05-18T03:46:30.225185Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:30.225185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shape Transitions in Hyperbolic Non-Euclidean Plates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"cond-mat.soft","authors_text":"John Gemmer, Shankar Venkataramani","submitted_at":"2012-08-31T23:27:37Z","abstract_excerpt":"We present and summarize the results of recent studies on non-Euclidean plates with imposed constant negative Gaussian curvature in both the F\\\"oppl - von K\\'arm\\'an and Kirchhoff approximations. Motivated by experimental results we focus on annuli with a periodic profile. We show that in the F\\\"oppl - von K\\'arm\\'an approximation there are only two types of global minimizers -- flat and saddle shaped deformations with localized regions of stretching near the boundary of the annulus. We also show that there exists local minimizers with $n$-waves that have regions of stretching near their lines"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.0031","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":"1209.0031","created_at":"2026-05-18T03:46:30.225342+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.0031v1","created_at":"2026-05-18T03:46:30.225342+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.0031","created_at":"2026-05-18T03:46:30.225342+00:00"},{"alias_kind":"pith_short_12","alias_value":"J3W2DFLVXFBT","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_16","alias_value":"J3W2DFLVXFBTJ4IG","created_at":"2026-05-18T12:27:09.501522+00:00"},{"alias_kind":"pith_short_8","alias_value":"J3W2DFLV","created_at":"2026-05-18T12:27:09.501522+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/J3W2DFLVXFBTJ4IGBNYAETDBUH","json":"https://pith.science/pith/J3W2DFLVXFBTJ4IGBNYAETDBUH.json","graph_json":"https://pith.science/api/pith-number/J3W2DFLVXFBTJ4IGBNYAETDBUH/graph.json","events_json":"https://pith.science/api/pith-number/J3W2DFLVXFBTJ4IGBNYAETDBUH/events.json","paper":"https://pith.science/paper/J3W2DFLV"},"agent_actions":{"view_html":"https://pith.science/pith/J3W2DFLVXFBTJ4IGBNYAETDBUH","download_json":"https://pith.science/pith/J3W2DFLVXFBTJ4IGBNYAETDBUH.json","view_paper":"https://pith.science/paper/J3W2DFLV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.0031&json=true","fetch_graph":"https://pith.science/api/pith-number/J3W2DFLVXFBTJ4IGBNYAETDBUH/graph.json","fetch_events":"https://pith.science/api/pith-number/J3W2DFLVXFBTJ4IGBNYAETDBUH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J3W2DFLVXFBTJ4IGBNYAETDBUH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J3W2DFLVXFBTJ4IGBNYAETDBUH/action/storage_attestation","attest_author":"https://pith.science/pith/J3W2DFLVXFBTJ4IGBNYAETDBUH/action/author_attestation","sign_citation":"https://pith.science/pith/J3W2DFLVXFBTJ4IGBNYAETDBUH/action/citation_signature","submit_replication":"https://pith.science/pith/J3W2DFLVXFBTJ4IGBNYAETDBUH/action/replication_record"}},"created_at":"2026-05-18T03:46:30.225342+00:00","updated_at":"2026-05-18T03:46:30.225342+00:00"}