{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2024:QJHLSXS3V5CPR3VB3CZDO5XKHT","short_pith_number":"pith:QJHLSXS3","schema_version":"1.0","canonical_sha256":"824eb95e5baf44f8eea1d8b23776ea3ce6cabce3eb8e605c68aa86e3afb319ef","source":{"kind":"arxiv","id":"2401.08467","version":2},"attestation_state":"computed","paper":{"title":"Skew parallelogram nets and universal factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrew O. Sageman-Furnas, Jannik Steinmeier, Tim Hoffmann","submitted_at":"2024-01-16T16:18:09Z","abstract_excerpt":"We obtain many objects of discrete differential geometry as reductions of skew parallelogram nets, a system of lattice equations that may be formulated for any unit associative algebra. The Lax representation is linear in the spectral parameter, and paths in the lattice give rise to polynomial dependencies. We prove that generic polynomials in complex two by two matrices factorize, implying that skew parallelogram nets encompass all systems with such a polynomial representation. We demonstrate factorization in the context of discrete curves by constructing pairs of B\\\"acklund transformations t"},"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":"2401.08467","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2024-01-16T16:18:09Z","cross_cats_sorted":[],"title_canon_sha256":"a2f3614ce3f1caefe107aa7101545e83ab27e9e3363b8057f0ba9e35abda871b","abstract_canon_sha256":"f2e7fea58ed36ebccd08195ed75d35bd851c310e81797e4ef581cf022d06f7d1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:04:37.073598Z","signature_b64":"+hVwFNgY5mqWnYLrey6Dsag1MjyWW28+zTlxk6uveC3EWt069FXUTDFZl5cHQ+PDRyOW1wqAiElJNk9XpMtVDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"824eb95e5baf44f8eea1d8b23776ea3ce6cabce3eb8e605c68aa86e3afb319ef","last_reissued_at":"2026-07-05T08:04:37.073118Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:04:37.073118Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Skew parallelogram nets and universal factorization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Andrew O. Sageman-Furnas, Jannik Steinmeier, Tim Hoffmann","submitted_at":"2024-01-16T16:18:09Z","abstract_excerpt":"We obtain many objects of discrete differential geometry as reductions of skew parallelogram nets, a system of lattice equations that may be formulated for any unit associative algebra. The Lax representation is linear in the spectral parameter, and paths in the lattice give rise to polynomial dependencies. We prove that generic polynomials in complex two by two matrices factorize, implying that skew parallelogram nets encompass all systems with such a polynomial representation. We demonstrate factorization in the context of discrete curves by constructing pairs of B\\\"acklund transformations t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.08467","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/2401.08467/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":"2401.08467","created_at":"2026-07-05T08:04:37.073174+00:00"},{"alias_kind":"arxiv_version","alias_value":"2401.08467v2","created_at":"2026-07-05T08:04:37.073174+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2401.08467","created_at":"2026-07-05T08:04:37.073174+00:00"},{"alias_kind":"pith_short_12","alias_value":"QJHLSXS3V5CP","created_at":"2026-07-05T08:04:37.073174+00:00"},{"alias_kind":"pith_short_16","alias_value":"QJHLSXS3V5CPR3VB","created_at":"2026-07-05T08:04:37.073174+00:00"},{"alias_kind":"pith_short_8","alias_value":"QJHLSXS3","created_at":"2026-07-05T08:04:37.073174+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2501.13477","citing_title":"Discrete curve theory in space forms: planar elastic and area-constrained elastic curves","ref_index":30,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QJHLSXS3V5CPR3VB3CZDO5XKHT","json":"https://pith.science/pith/QJHLSXS3V5CPR3VB3CZDO5XKHT.json","graph_json":"https://pith.science/api/pith-number/QJHLSXS3V5CPR3VB3CZDO5XKHT/graph.json","events_json":"https://pith.science/api/pith-number/QJHLSXS3V5CPR3VB3CZDO5XKHT/events.json","paper":"https://pith.science/paper/QJHLSXS3"},"agent_actions":{"view_html":"https://pith.science/pith/QJHLSXS3V5CPR3VB3CZDO5XKHT","download_json":"https://pith.science/pith/QJHLSXS3V5CPR3VB3CZDO5XKHT.json","view_paper":"https://pith.science/paper/QJHLSXS3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2401.08467&json=true","fetch_graph":"https://pith.science/api/pith-number/QJHLSXS3V5CPR3VB3CZDO5XKHT/graph.json","fetch_events":"https://pith.science/api/pith-number/QJHLSXS3V5CPR3VB3CZDO5XKHT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QJHLSXS3V5CPR3VB3CZDO5XKHT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QJHLSXS3V5CPR3VB3CZDO5XKHT/action/storage_attestation","attest_author":"https://pith.science/pith/QJHLSXS3V5CPR3VB3CZDO5XKHT/action/author_attestation","sign_citation":"https://pith.science/pith/QJHLSXS3V5CPR3VB3CZDO5XKHT/action/citation_signature","submit_replication":"https://pith.science/pith/QJHLSXS3V5CPR3VB3CZDO5XKHT/action/replication_record"}},"created_at":"2026-07-05T08:04:37.073174+00:00","updated_at":"2026-07-05T08:04:37.073174+00:00"}