{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:GDGHQXNG5LFWMZ2NDM65MANP6C","short_pith_number":"pith:GDGHQXNG","schema_version":"1.0","canonical_sha256":"30cc785da6eacb66674d1b3dd601aff0994c5e883e4aeadc823ad0159647c832","source":{"kind":"arxiv","id":"1505.00073","version":1},"attestation_state":"computed","paper":{"title":"Bijective Deformations in $\\mathbb{R}^n$ via Integral Curve Coordinates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GR","authors_text":"Lisa Huynh, Yotam Gingold","submitted_at":"2015-05-01T02:47:12Z","abstract_excerpt":"We introduce Integral Curve Coordinates, which identify each point in a bounded domain with a parameter along an integral curve of the gradient of a function $f$ on that domain; suitable functions have exactly one critical point, a maximum, in the domain, and the gradient of the function on the boundary points inward. Because every integral curve intersects the boundary exactly once, Integral Curve Coordinates provide a natural bijective mapping from one domain to another given a bijection of the boundary. Our approach can be applied to shapes in any dimension, provided that the boundary of th"},"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":"1505.00073","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.GR","submitted_at":"2015-05-01T02:47:12Z","cross_cats_sorted":[],"title_canon_sha256":"5d89777741aedab068d1bdb05b99e686e78bd00f84472ad7143b7815515fa725","abstract_canon_sha256":"95670b0785906a38be685bfacc8b6396cbfc71304e8d6b9868b029f5ce857947"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:13.647572Z","signature_b64":"tJ4ltESj/7MUDgNDiMer4Ze+dxhc1K/kBxt++jIqCrIZxVkzkgN0Txr0nvu2zoo3UqDnoAtt+hqaei5vqZ9IAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30cc785da6eacb66674d1b3dd601aff0994c5e883e4aeadc823ad0159647c832","last_reissued_at":"2026-05-18T02:17:13.646812Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:13.646812Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bijective Deformations in $\\mathbb{R}^n$ via Integral Curve Coordinates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.GR","authors_text":"Lisa Huynh, Yotam Gingold","submitted_at":"2015-05-01T02:47:12Z","abstract_excerpt":"We introduce Integral Curve Coordinates, which identify each point in a bounded domain with a parameter along an integral curve of the gradient of a function $f$ on that domain; suitable functions have exactly one critical point, a maximum, in the domain, and the gradient of the function on the boundary points inward. Because every integral curve intersects the boundary exactly once, Integral Curve Coordinates provide a natural bijective mapping from one domain to another given a bijection of the boundary. Our approach can be applied to shapes in any dimension, provided that the boundary of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00073","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":"1505.00073","created_at":"2026-05-18T02:17:13.646942+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.00073v1","created_at":"2026-05-18T02:17:13.646942+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.00073","created_at":"2026-05-18T02:17:13.646942+00:00"},{"alias_kind":"pith_short_12","alias_value":"GDGHQXNG5LFW","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_16","alias_value":"GDGHQXNG5LFWMZ2N","created_at":"2026-05-18T12:29:22.688609+00:00"},{"alias_kind":"pith_short_8","alias_value":"GDGHQXNG","created_at":"2026-05-18T12:29:22.688609+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/GDGHQXNG5LFWMZ2NDM65MANP6C","json":"https://pith.science/pith/GDGHQXNG5LFWMZ2NDM65MANP6C.json","graph_json":"https://pith.science/api/pith-number/GDGHQXNG5LFWMZ2NDM65MANP6C/graph.json","events_json":"https://pith.science/api/pith-number/GDGHQXNG5LFWMZ2NDM65MANP6C/events.json","paper":"https://pith.science/paper/GDGHQXNG"},"agent_actions":{"view_html":"https://pith.science/pith/GDGHQXNG5LFWMZ2NDM65MANP6C","download_json":"https://pith.science/pith/GDGHQXNG5LFWMZ2NDM65MANP6C.json","view_paper":"https://pith.science/paper/GDGHQXNG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.00073&json=true","fetch_graph":"https://pith.science/api/pith-number/GDGHQXNG5LFWMZ2NDM65MANP6C/graph.json","fetch_events":"https://pith.science/api/pith-number/GDGHQXNG5LFWMZ2NDM65MANP6C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GDGHQXNG5LFWMZ2NDM65MANP6C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GDGHQXNG5LFWMZ2NDM65MANP6C/action/storage_attestation","attest_author":"https://pith.science/pith/GDGHQXNG5LFWMZ2NDM65MANP6C/action/author_attestation","sign_citation":"https://pith.science/pith/GDGHQXNG5LFWMZ2NDM65MANP6C/action/citation_signature","submit_replication":"https://pith.science/pith/GDGHQXNG5LFWMZ2NDM65MANP6C/action/replication_record"}},"created_at":"2026-05-18T02:17:13.646942+00:00","updated_at":"2026-05-18T02:17:13.646942+00:00"}