{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:D5ACGLMA3HYJVID3XJ2Q46NCP6","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":"430741628c1d5ada7b27e2721476e632d361c1674e81cd5af3f7790b3f37302f","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-10T18:57:00Z","title_canon_sha256":"adfa194a8240fac28501d4a148ad8a19fe7aecd10e30db3e05d6ce17269f6aaa"},"schema_version":"1.0","source":{"id":"1301.2217","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.2217","created_at":"2026-05-18T01:52:13Z"},{"alias_kind":"arxiv_version","alias_value":"1301.2217v1","created_at":"2026-05-18T01:52:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.2217","created_at":"2026-05-18T01:52:13Z"},{"alias_kind":"pith_short_12","alias_value":"D5ACGLMA3HYJ","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"D5ACGLMA3HYJVID3","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"D5ACGLMA","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:d4b4a14219bdbeeab0a0068381f569653263057f276feb76831b104613877f7a","target":"graph","created_at":"2026-05-18T01:52:13Z","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"},"paper":{"abstract_excerpt":"Using classical differential geometry, the problem of elastic curves and surfaces in the presence of long-range interactions $\\Phi$, is posed. Starting from a variational principle, the balance of elastic forces and the corresponding projections ${\\bf n}_i\\cdot \\nabla\\Phi$, are found. In the case of elastic surfaces, a force coupling the mean curvature with the external potential, $K\\Phi$, appears; it is also present in the shape equation along the normal principal in the case of curves. The potential $\\Phi$ contributes to the effective tension of curves and surfaces and also to the orbital to","authors_text":"G. Chacon-Acosta, J. A. Santiago, O. Gonzalez-Gaxiola","cross_cats":["cond-mat.soft"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-10T18:57:00Z","title":"Elastic curves and surfaces under long-range forces: A geometric approach"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.2217","kind":"arxiv","version":1},"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":"sha256:0ccf941990e6c7025b338e75cde9bc73811e3834b6e57c98a3b96c7c7e8f5928","target":"record","created_at":"2026-05-18T01:52:13Z","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":"430741628c1d5ada7b27e2721476e632d361c1674e81cd5af3f7790b3f37302f","cross_cats_sorted":["cond-mat.soft"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2013-01-10T18:57:00Z","title_canon_sha256":"adfa194a8240fac28501d4a148ad8a19fe7aecd10e30db3e05d6ce17269f6aaa"},"schema_version":"1.0","source":{"id":"1301.2217","kind":"arxiv","version":1}},"canonical_sha256":"1f40232d80d9f09aa07bba750e79a27fbb2469f564f4cacb0442c12196bb55cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f40232d80d9f09aa07bba750e79a27fbb2469f564f4cacb0442c12196bb55cd","first_computed_at":"2026-05-18T01:52:13.784856Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:52:13.784856Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JWAwAwf0TwihQUzuLxZ81UPcF7Oy50LNzCwUqxMJAxy7heP/KQieyj2fO6Gnme0sGBWi8SLCFh99EGe+OevKDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:52:13.785569Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.2217","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ccf941990e6c7025b338e75cde9bc73811e3834b6e57c98a3b96c7c7e8f5928","sha256:d4b4a14219bdbeeab0a0068381f569653263057f276feb76831b104613877f7a"],"state_sha256":"7012771270c66cebe380428b2abd1fff70aed12d6d4c92db06e8dd29b8b3c056"}