{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:BLCJJSJLNWGXA7656XLTFGTF5C","short_pith_number":"pith:BLCJJSJL","schema_version":"1.0","canonical_sha256":"0ac494c92b6d8d707fddf5d7329a65e89dcd5b867936a50cd1d9a1ac43a2b56e","source":{"kind":"arxiv","id":"1805.05141","version":1},"attestation_state":"computed","paper":{"title":"Phase field models for two-dimensional branched transportation problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Benedikt Wirth","submitted_at":"2018-05-14T12:33:51Z","abstract_excerpt":"We analyse the following inverse problem. Given a nonconvex functional (from a specific, but quite general class) of normal, codimension-1 currents (which in two spatial dimensions can be interpreted as transportation networks), find the potential of a phase field energy which approximates the given functional. We prove existence of a solution as well as its characterization via a linear deconvolution problem. We also provide an explicit formula that allows to approximate the solution arbitrarily well in the supremum norm."},"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":"1805.05141","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-14T12:33:51Z","cross_cats_sorted":[],"title_canon_sha256":"a43f911f4f918726f184badbbb5b9a3b15b0e051ef18e4dd62882094c03b503f","abstract_canon_sha256":"8028d0ccf71c583cb3908e882df0eeb069f75fb71b126a0e7c614a04ff057ba1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:03.811369Z","signature_b64":"W4JitdTcPPfJ6XstcG/OFfIVxSV/eIPNO92JUNIZP7FMvahOkvdFkuKA9ZE5zxnnE/O3GmKq96IC0xP7Tlb/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0ac494c92b6d8d707fddf5d7329a65e89dcd5b867936a50cd1d9a1ac43a2b56e","last_reissued_at":"2026-05-18T00:16:03.810790Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:03.810790Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Phase field models for two-dimensional branched transportation problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Benedikt Wirth","submitted_at":"2018-05-14T12:33:51Z","abstract_excerpt":"We analyse the following inverse problem. Given a nonconvex functional (from a specific, but quite general class) of normal, codimension-1 currents (which in two spatial dimensions can be interpreted as transportation networks), find the potential of a phase field energy which approximates the given functional. We prove existence of a solution as well as its characterization via a linear deconvolution problem. We also provide an explicit formula that allows to approximate the solution arbitrarily well in the supremum norm."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05141","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":"1805.05141","created_at":"2026-05-18T00:16:03.810908+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.05141v1","created_at":"2026-05-18T00:16:03.810908+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.05141","created_at":"2026-05-18T00:16:03.810908+00:00"},{"alias_kind":"pith_short_12","alias_value":"BLCJJSJLNWGX","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"BLCJJSJLNWGXA765","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"BLCJJSJL","created_at":"2026-05-18T12:32:16.446611+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/BLCJJSJLNWGXA7656XLTFGTF5C","json":"https://pith.science/pith/BLCJJSJLNWGXA7656XLTFGTF5C.json","graph_json":"https://pith.science/api/pith-number/BLCJJSJLNWGXA7656XLTFGTF5C/graph.json","events_json":"https://pith.science/api/pith-number/BLCJJSJLNWGXA7656XLTFGTF5C/events.json","paper":"https://pith.science/paper/BLCJJSJL"},"agent_actions":{"view_html":"https://pith.science/pith/BLCJJSJLNWGXA7656XLTFGTF5C","download_json":"https://pith.science/pith/BLCJJSJLNWGXA7656XLTFGTF5C.json","view_paper":"https://pith.science/paper/BLCJJSJL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.05141&json=true","fetch_graph":"https://pith.science/api/pith-number/BLCJJSJLNWGXA7656XLTFGTF5C/graph.json","fetch_events":"https://pith.science/api/pith-number/BLCJJSJLNWGXA7656XLTFGTF5C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BLCJJSJLNWGXA7656XLTFGTF5C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BLCJJSJLNWGXA7656XLTFGTF5C/action/storage_attestation","attest_author":"https://pith.science/pith/BLCJJSJLNWGXA7656XLTFGTF5C/action/author_attestation","sign_citation":"https://pith.science/pith/BLCJJSJLNWGXA7656XLTFGTF5C/action/citation_signature","submit_replication":"https://pith.science/pith/BLCJJSJLNWGXA7656XLTFGTF5C/action/replication_record"}},"created_at":"2026-05-18T00:16:03.810908+00:00","updated_at":"2026-05-18T00:16:03.810908+00:00"}