{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DXSNSUJWGXNSKV2TUT2JICBDMI","short_pith_number":"pith:DXSNSUJW","schema_version":"1.0","canonical_sha256":"1de4d9513635db255753a4f4940823623b932ac2575e8a11ac1927541eaaa73d","source":{"kind":"arxiv","id":"1703.06717","version":1},"attestation_state":"computed","paper":{"title":"$G 1$-smooth splines on quad meshes with 4-split macro-patch elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ahmed Blidia (AROMATH), Bernard Mourrain (AROMATH), Nelly Villamizar","submitted_at":"2017-03-20T12:47:58Z","abstract_excerpt":"We analyze the space of differentiable functions on a quad-mesh  $\\cM$, which are composed of 4-split spline macro-patch elements on  each quadrangular face.  We describe explicit transition maps across  shared edges, that satisfy conditions which ensure that the space of  differentiable functions is ample on a quad-mesh of arbitrary  topology.  These transition maps define a finite dimensional vector  space of $G^{1}$ spline functions of bi-degree $\\le (k,k)$ on each  quadrangular face of $\\cM$.  We determine the dimension of this space  of $G^{1}$ spline functions for $k$ big enough and prov"},"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":"1703.06717","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-03-20T12:47:58Z","cross_cats_sorted":[],"title_canon_sha256":"44777c627fb556ed759f59e5082f99fda87cf7d609235075f10728f36afb5a17","abstract_canon_sha256":"0cfbc7e7fe7bfd81d245ed86d720aba209694dd7c1919fa1f41bcf73efd6024d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:48:21.956644Z","signature_b64":"cSi2rMYQ/B8stv69k+S7dyWkGSpg18HFeQ2M35nTf6eT6JbzyR0VGIGWZNszqdVgycNwZpskEktY95NrD43yCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1de4d9513635db255753a4f4940823623b932ac2575e8a11ac1927541eaaa73d","last_reissued_at":"2026-05-18T00:48:21.956037Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:48:21.956037Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$G 1$-smooth splines on quad meshes with 4-split macro-patch elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Ahmed Blidia (AROMATH), Bernard Mourrain (AROMATH), Nelly Villamizar","submitted_at":"2017-03-20T12:47:58Z","abstract_excerpt":"We analyze the space of differentiable functions on a quad-mesh  $\\cM$, which are composed of 4-split spline macro-patch elements on  each quadrangular face.  We describe explicit transition maps across  shared edges, that satisfy conditions which ensure that the space of  differentiable functions is ample on a quad-mesh of arbitrary  topology.  These transition maps define a finite dimensional vector  space of $G^{1}$ spline functions of bi-degree $\\le (k,k)$ on each  quadrangular face of $\\cM$.  We determine the dimension of this space  of $G^{1}$ spline functions for $k$ big enough and prov"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.06717","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":"1703.06717","created_at":"2026-05-18T00:48:21.956138+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.06717v1","created_at":"2026-05-18T00:48:21.956138+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.06717","created_at":"2026-05-18T00:48:21.956138+00:00"},{"alias_kind":"pith_short_12","alias_value":"DXSNSUJWGXNS","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"DXSNSUJWGXNSKV2T","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"DXSNSUJW","created_at":"2026-05-18T12:31:12.930513+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/DXSNSUJWGXNSKV2TUT2JICBDMI","json":"https://pith.science/pith/DXSNSUJWGXNSKV2TUT2JICBDMI.json","graph_json":"https://pith.science/api/pith-number/DXSNSUJWGXNSKV2TUT2JICBDMI/graph.json","events_json":"https://pith.science/api/pith-number/DXSNSUJWGXNSKV2TUT2JICBDMI/events.json","paper":"https://pith.science/paper/DXSNSUJW"},"agent_actions":{"view_html":"https://pith.science/pith/DXSNSUJWGXNSKV2TUT2JICBDMI","download_json":"https://pith.science/pith/DXSNSUJWGXNSKV2TUT2JICBDMI.json","view_paper":"https://pith.science/paper/DXSNSUJW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.06717&json=true","fetch_graph":"https://pith.science/api/pith-number/DXSNSUJWGXNSKV2TUT2JICBDMI/graph.json","fetch_events":"https://pith.science/api/pith-number/DXSNSUJWGXNSKV2TUT2JICBDMI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DXSNSUJWGXNSKV2TUT2JICBDMI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DXSNSUJWGXNSKV2TUT2JICBDMI/action/storage_attestation","attest_author":"https://pith.science/pith/DXSNSUJWGXNSKV2TUT2JICBDMI/action/author_attestation","sign_citation":"https://pith.science/pith/DXSNSUJWGXNSKV2TUT2JICBDMI/action/citation_signature","submit_replication":"https://pith.science/pith/DXSNSUJWGXNSKV2TUT2JICBDMI/action/replication_record"}},"created_at":"2026-05-18T00:48:21.956138+00:00","updated_at":"2026-05-18T00:48:21.956138+00:00"}