{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:SJEB6R62EMKT2EDY3R77DE4CVL","short_pith_number":"pith:SJEB6R62","schema_version":"1.0","canonical_sha256":"92481f47da23153d1078dc7ff19382aac96a9460e8cd2271fd06533967a78288","source":{"kind":"arxiv","id":"1607.04021","version":1},"attestation_state":"computed","paper":{"title":"Steady states of elastically-coupled extensible double-beam systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudio Giorgi, Filippo Dell'Oro, Vittorino Pata","submitted_at":"2016-07-14T08:00:28Z","abstract_excerpt":"Given $\\beta\\in\\mathbb{R}$ and $\\varrho,k>0$, we analyze an abstract version of the nonlinear stationary model in dimensionless form $$\\begin{cases} u\"\" - \\Big(\\beta+ \\varrho\\int_0^1 |u'(s)|^2\\,{\\rm d} s\\Big)u\" +k(u-v) = 0 v\"\" - \\Big(\\beta+ \\varrho\\int_0^1 |v'(s)|^2\\,{\\rm d} s\\Big)v\" -k(u-v) = 0 \\end{cases} $$ describing the equilibria of an elastically-coupled extensible double-beam system subject to evenly compressive axial loads. Necessary and sufficient conditions in order to have nontrivial solutions are established, and their explicit closed-form expressions are found. In particular, the"},"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":"1607.04021","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-07-14T08:00:28Z","cross_cats_sorted":[],"title_canon_sha256":"34cc410e19928937843cecc86b31c341244fa8222071b500bbae23f612678603","abstract_canon_sha256":"e1d6195487c897ba958c3c4a8de12cf0a8f7777929d3dde92523cfd869a0d768"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:11:04.304650Z","signature_b64":"Cd7+5YO1epMrTgGAenyf7yzsd/3ImRroMC39JDBazI8mCcN/8DQuITAFnU5z8Bz6AZCtm/QQLupSp9LH0VW4CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92481f47da23153d1078dc7ff19382aac96a9460e8cd2271fd06533967a78288","last_reissued_at":"2026-05-18T01:11:04.304127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:11:04.304127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Steady states of elastically-coupled extensible double-beam systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Claudio Giorgi, Filippo Dell'Oro, Vittorino Pata","submitted_at":"2016-07-14T08:00:28Z","abstract_excerpt":"Given $\\beta\\in\\mathbb{R}$ and $\\varrho,k>0$, we analyze an abstract version of the nonlinear stationary model in dimensionless form $$\\begin{cases} u\"\" - \\Big(\\beta+ \\varrho\\int_0^1 |u'(s)|^2\\,{\\rm d} s\\Big)u\" +k(u-v) = 0 v\"\" - \\Big(\\beta+ \\varrho\\int_0^1 |v'(s)|^2\\,{\\rm d} s\\Big)v\" -k(u-v) = 0 \\end{cases} $$ describing the equilibria of an elastically-coupled extensible double-beam system subject to evenly compressive axial loads. Necessary and sufficient conditions in order to have nontrivial solutions are established, and their explicit closed-form expressions are found. In particular, the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04021","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":"1607.04021","created_at":"2026-05-18T01:11:04.304230+00:00"},{"alias_kind":"arxiv_version","alias_value":"1607.04021v1","created_at":"2026-05-18T01:11:04.304230+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.04021","created_at":"2026-05-18T01:11:04.304230+00:00"},{"alias_kind":"pith_short_12","alias_value":"SJEB6R62EMKT","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_16","alias_value":"SJEB6R62EMKT2EDY","created_at":"2026-05-18T12:30:44.179134+00:00"},{"alias_kind":"pith_short_8","alias_value":"SJEB6R62","created_at":"2026-05-18T12:30:44.179134+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/SJEB6R62EMKT2EDY3R77DE4CVL","json":"https://pith.science/pith/SJEB6R62EMKT2EDY3R77DE4CVL.json","graph_json":"https://pith.science/api/pith-number/SJEB6R62EMKT2EDY3R77DE4CVL/graph.json","events_json":"https://pith.science/api/pith-number/SJEB6R62EMKT2EDY3R77DE4CVL/events.json","paper":"https://pith.science/paper/SJEB6R62"},"agent_actions":{"view_html":"https://pith.science/pith/SJEB6R62EMKT2EDY3R77DE4CVL","download_json":"https://pith.science/pith/SJEB6R62EMKT2EDY3R77DE4CVL.json","view_paper":"https://pith.science/paper/SJEB6R62","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1607.04021&json=true","fetch_graph":"https://pith.science/api/pith-number/SJEB6R62EMKT2EDY3R77DE4CVL/graph.json","fetch_events":"https://pith.science/api/pith-number/SJEB6R62EMKT2EDY3R77DE4CVL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SJEB6R62EMKT2EDY3R77DE4CVL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SJEB6R62EMKT2EDY3R77DE4CVL/action/storage_attestation","attest_author":"https://pith.science/pith/SJEB6R62EMKT2EDY3R77DE4CVL/action/author_attestation","sign_citation":"https://pith.science/pith/SJEB6R62EMKT2EDY3R77DE4CVL/action/citation_signature","submit_replication":"https://pith.science/pith/SJEB6R62EMKT2EDY3R77DE4CVL/action/replication_record"}},"created_at":"2026-05-18T01:11:04.304230+00:00","updated_at":"2026-05-18T01:11:04.304230+00:00"}