{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:VPRG26SFQWASGAOHC4MZNPPIZQ","short_pith_number":"pith:VPRG26SF","schema_version":"1.0","canonical_sha256":"abe26d7a4585812301c7171996bde8cc1c44e841b00493c41f7356939e0341da","source":{"kind":"arxiv","id":"1604.05238","version":1},"attestation_state":"computed","paper":{"title":"Shadows of graphical mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Wolfgang Maurer","submitted_at":"2016-04-18T16:38:32Z","abstract_excerpt":"We consider mean curvature flow of an initial surface that is the graph of a function over some domain of definition in $R^n$. If the graph is not complete then we impose a constant Dirichlet boundary condition at the boundary of the surface. We establish longtime-existence of the flow and investigate the projection of the flowing surface onto $R^n$, the shadow of the flow. This moving shadow can be seen as a weak solution for mean curvature flow of hypersurfaces in $R^n$ with a Dirichlet boundary condition. Furthermore, we provide a lemma of independent interest to locally mollify the boundar"},"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":"1604.05238","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-04-18T16:38:32Z","cross_cats_sorted":[],"title_canon_sha256":"030527be17f2ec27c46ff43fdcd9ac7caba260c637fe00a8fc364d6eaf1643dc","abstract_canon_sha256":"8bcdfbd3de0669c642e6a04d994ad4e343b23df59968de57a068f827dc0d5e9f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:16:55.218240Z","signature_b64":"taXNMmx1GowXj752sGkbJfMu/qhPRw6S59a4uZKi3xXSkmQZ7Xmo6DnKA+VKFNqapea0CU5322byAUNrV6V5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"abe26d7a4585812301c7171996bde8cc1c44e841b00493c41f7356939e0341da","last_reissued_at":"2026-05-18T01:16:55.217565Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:16:55.217565Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Shadows of graphical mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Wolfgang Maurer","submitted_at":"2016-04-18T16:38:32Z","abstract_excerpt":"We consider mean curvature flow of an initial surface that is the graph of a function over some domain of definition in $R^n$. If the graph is not complete then we impose a constant Dirichlet boundary condition at the boundary of the surface. We establish longtime-existence of the flow and investigate the projection of the flowing surface onto $R^n$, the shadow of the flow. This moving shadow can be seen as a weak solution for mean curvature flow of hypersurfaces in $R^n$ with a Dirichlet boundary condition. Furthermore, we provide a lemma of independent interest to locally mollify the boundar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05238","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":"1604.05238","created_at":"2026-05-18T01:16:55.217669+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.05238v1","created_at":"2026-05-18T01:16:55.217669+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05238","created_at":"2026-05-18T01:16:55.217669+00:00"},{"alias_kind":"pith_short_12","alias_value":"VPRG26SFQWAS","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_16","alias_value":"VPRG26SFQWASGAOH","created_at":"2026-05-18T12:30:48.956258+00:00"},{"alias_kind":"pith_short_8","alias_value":"VPRG26SF","created_at":"2026-05-18T12:30:48.956258+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/VPRG26SFQWASGAOHC4MZNPPIZQ","json":"https://pith.science/pith/VPRG26SFQWASGAOHC4MZNPPIZQ.json","graph_json":"https://pith.science/api/pith-number/VPRG26SFQWASGAOHC4MZNPPIZQ/graph.json","events_json":"https://pith.science/api/pith-number/VPRG26SFQWASGAOHC4MZNPPIZQ/events.json","paper":"https://pith.science/paper/VPRG26SF"},"agent_actions":{"view_html":"https://pith.science/pith/VPRG26SFQWASGAOHC4MZNPPIZQ","download_json":"https://pith.science/pith/VPRG26SFQWASGAOHC4MZNPPIZQ.json","view_paper":"https://pith.science/paper/VPRG26SF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.05238&json=true","fetch_graph":"https://pith.science/api/pith-number/VPRG26SFQWASGAOHC4MZNPPIZQ/graph.json","fetch_events":"https://pith.science/api/pith-number/VPRG26SFQWASGAOHC4MZNPPIZQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VPRG26SFQWASGAOHC4MZNPPIZQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VPRG26SFQWASGAOHC4MZNPPIZQ/action/storage_attestation","attest_author":"https://pith.science/pith/VPRG26SFQWASGAOHC4MZNPPIZQ/action/author_attestation","sign_citation":"https://pith.science/pith/VPRG26SFQWASGAOHC4MZNPPIZQ/action/citation_signature","submit_replication":"https://pith.science/pith/VPRG26SFQWASGAOHC4MZNPPIZQ/action/replication_record"}},"created_at":"2026-05-18T01:16:55.217669+00:00","updated_at":"2026-05-18T01:16:55.217669+00:00"}