{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:O553GILHEJ3OGSEXEJCJYUUW5K","short_pith_number":"pith:O553GILH","schema_version":"1.0","canonical_sha256":"777bb321672276e3489722449c5296eab86d26e8628a3bc034ecb46018b8176f","source":{"kind":"arxiv","id":"2505.07696","version":1},"attestation_state":"computed","paper":{"title":"Design Principles for Realizable Discrete Surface Embeddings in Physical Systems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"Christian D. Santangelo, Kyungeun Kim","submitted_at":"2025-05-12T16:05:17Z","abstract_excerpt":"The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary conditions, their discrete counterparts-represented as networks of vertices connected by edges-can exhibit multiple distinct embeddings for identical edge lengths. We present a systematic approach to constructing discrete meshes that yield a controlled number of embeddings. By analyzing the relationship between mesh connectivity and embedding multiplicity throu"},"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":"2505.07696","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2025-05-12T16:05:17Z","cross_cats_sorted":["physics.comp-ph"],"title_canon_sha256":"5badb7be42a6c68c709a69736c9d55db2d994851cb922b20c7ed3c3d1128a6ea","abstract_canon_sha256":"8e419eb2492913631b8feea92ac50ee26049faad9e343f7224123543382a4105"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:01:51.913803Z","signature_b64":"tHLp6m6+FYLFLUZmfQwlM9EacKGZchF5Dayt55rPIgGofkTUbvdCka70vtMG//0NSbL5+UElRpcYT7rFVRnVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"777bb321672276e3489722449c5296eab86d26e8628a3bc034ecb46018b8176f","last_reissued_at":"2026-07-05T11:01:51.913363Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:01:51.913363Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Design Principles for Realizable Discrete Surface Embeddings in Physical Systems","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["physics.comp-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"Christian D. Santangelo, Kyungeun Kim","submitted_at":"2025-05-12T16:05:17Z","abstract_excerpt":"The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary conditions, their discrete counterparts-represented as networks of vertices connected by edges-can exhibit multiple distinct embeddings for identical edge lengths. We present a systematic approach to constructing discrete meshes that yield a controlled number of embeddings. By analyzing the relationship between mesh connectivity and embedding multiplicity throu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07696","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2505.07696/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2505.07696","created_at":"2026-07-05T11:01:51.913421+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.07696v1","created_at":"2026-07-05T11:01:51.913421+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.07696","created_at":"2026-07-05T11:01:51.913421+00:00"},{"alias_kind":"pith_short_12","alias_value":"O553GILHEJ3O","created_at":"2026-07-05T11:01:51.913421+00:00"},{"alias_kind":"pith_short_16","alias_value":"O553GILHEJ3OGSEX","created_at":"2026-07-05T11:01:51.913421+00:00"},{"alias_kind":"pith_short_8","alias_value":"O553GILH","created_at":"2026-07-05T11:01:51.913421+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2505.07696","citing_title":"Design Principles for Realizable Discrete Surface Embeddings in Physical Systems","ref_index":1,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/O553GILHEJ3OGSEXEJCJYUUW5K","json":"https://pith.science/pith/O553GILHEJ3OGSEXEJCJYUUW5K.json","graph_json":"https://pith.science/api/pith-number/O553GILHEJ3OGSEXEJCJYUUW5K/graph.json","events_json":"https://pith.science/api/pith-number/O553GILHEJ3OGSEXEJCJYUUW5K/events.json","paper":"https://pith.science/paper/O553GILH"},"agent_actions":{"view_html":"https://pith.science/pith/O553GILHEJ3OGSEXEJCJYUUW5K","download_json":"https://pith.science/pith/O553GILHEJ3OGSEXEJCJYUUW5K.json","view_paper":"https://pith.science/paper/O553GILH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.07696&json=true","fetch_graph":"https://pith.science/api/pith-number/O553GILHEJ3OGSEXEJCJYUUW5K/graph.json","fetch_events":"https://pith.science/api/pith-number/O553GILHEJ3OGSEXEJCJYUUW5K/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/O553GILHEJ3OGSEXEJCJYUUW5K/action/timestamp_anchor","attest_storage":"https://pith.science/pith/O553GILHEJ3OGSEXEJCJYUUW5K/action/storage_attestation","attest_author":"https://pith.science/pith/O553GILHEJ3OGSEXEJCJYUUW5K/action/author_attestation","sign_citation":"https://pith.science/pith/O553GILHEJ3OGSEXEJCJYUUW5K/action/citation_signature","submit_replication":"https://pith.science/pith/O553GILHEJ3OGSEXEJCJYUUW5K/action/replication_record"}},"created_at":"2026-07-05T11:01:51.913421+00:00","updated_at":"2026-07-05T11:01:51.913421+00:00"}