{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:Z3I3Q7MASEH7MNDNL5IHKRXMX7","short_pith_number":"pith:Z3I3Q7MA","schema_version":"1.0","canonical_sha256":"ced1b87d80910ff6346d5f507546ecbfdef80039dd778f8c2634eb041f18fbb3","source":{"kind":"arxiv","id":"1807.10631","version":2},"attestation_state":"computed","paper":{"title":"An orthorhombic deformation family of Schwarz' H surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Hao Chen, Matthias Weber","submitted_at":"2018-07-26T09:25:21Z","abstract_excerpt":"The classical H surfaces of H. A. Schwarz form a 1-parameter family of triply periodic minimal surfaces (TPMS) that are usually described as close relatives to his more famous P surface. However, a crucial distinction between these surfaces is that the P surface belongs to a 5-dimensional smooth family of embedded TPMS of genus three discovered by W. Meeks, while the H surfaces are among the few known examples outside this family. We construct a 2-parameter family of embedded TPMS of genus three that contains the H family and meets the Meeks family. In particular, we prove that H surfaces can "},"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":"1807.10631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-07-26T09:25:21Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"aa1317abb5140a3c24bf3e2ef757c6d7837fb892d8b8e0e73425c10aae8e4494","abstract_canon_sha256":"73334e90e78b39dd48d50b00f0d63b65bc75261004d67270d624c7f257cc4a20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:18:27.155468Z","signature_b64":"Qq8BCc4Yee84SYZkqSYgKB3uCcJkNoatW2/hWUPVt/znNaQGBjVEG7AlFKtBYDiR73nR7vTgf/VqEQO6HATcDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ced1b87d80910ff6346d5f507546ecbfdef80039dd778f8c2634eb041f18fbb3","last_reissued_at":"2026-07-05T02:18:27.155005Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:18:27.155005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An orthorhombic deformation family of Schwarz' H surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Hao Chen, Matthias Weber","submitted_at":"2018-07-26T09:25:21Z","abstract_excerpt":"The classical H surfaces of H. A. Schwarz form a 1-parameter family of triply periodic minimal surfaces (TPMS) that are usually described as close relatives to his more famous P surface. However, a crucial distinction between these surfaces is that the P surface belongs to a 5-dimensional smooth family of embedded TPMS of genus three discovered by W. Meeks, while the H surfaces are among the few known examples outside this family. We construct a 2-parameter family of embedded TPMS of genus three that contains the H family and meets the Meeks family. In particular, we prove that H surfaces can "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10631","kind":"arxiv","version":2},"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/1807.10631/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":"1807.10631","created_at":"2026-07-05T02:18:27.155062+00:00"},{"alias_kind":"arxiv_version","alias_value":"1807.10631v2","created_at":"2026-07-05T02:18:27.155062+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.10631","created_at":"2026-07-05T02:18:27.155062+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z3I3Q7MASEH7","created_at":"2026-07-05T02:18:27.155062+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z3I3Q7MASEH7MNDN","created_at":"2026-07-05T02:18:27.155062+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z3I3Q7MA","created_at":"2026-07-05T02:18:27.155062+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.06276","citing_title":"Stacking disorder in periodic minimal surfaces","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/Z3I3Q7MASEH7MNDNL5IHKRXMX7","json":"https://pith.science/pith/Z3I3Q7MASEH7MNDNL5IHKRXMX7.json","graph_json":"https://pith.science/api/pith-number/Z3I3Q7MASEH7MNDNL5IHKRXMX7/graph.json","events_json":"https://pith.science/api/pith-number/Z3I3Q7MASEH7MNDNL5IHKRXMX7/events.json","paper":"https://pith.science/paper/Z3I3Q7MA"},"agent_actions":{"view_html":"https://pith.science/pith/Z3I3Q7MASEH7MNDNL5IHKRXMX7","download_json":"https://pith.science/pith/Z3I3Q7MASEH7MNDNL5IHKRXMX7.json","view_paper":"https://pith.science/paper/Z3I3Q7MA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1807.10631&json=true","fetch_graph":"https://pith.science/api/pith-number/Z3I3Q7MASEH7MNDNL5IHKRXMX7/graph.json","fetch_events":"https://pith.science/api/pith-number/Z3I3Q7MASEH7MNDNL5IHKRXMX7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z3I3Q7MASEH7MNDNL5IHKRXMX7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z3I3Q7MASEH7MNDNL5IHKRXMX7/action/storage_attestation","attest_author":"https://pith.science/pith/Z3I3Q7MASEH7MNDNL5IHKRXMX7/action/author_attestation","sign_citation":"https://pith.science/pith/Z3I3Q7MASEH7MNDNL5IHKRXMX7/action/citation_signature","submit_replication":"https://pith.science/pith/Z3I3Q7MASEH7MNDNL5IHKRXMX7/action/replication_record"}},"created_at":"2026-07-05T02:18:27.155062+00:00","updated_at":"2026-07-05T02:18:27.155062+00:00"}