{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:WC43NLSKO27LUBIIGTSRYPM65B","short_pith_number":"pith:WC43NLSK","schema_version":"1.0","canonical_sha256":"b0b9b6ae4a76beba050834e51c3d9ee84a376008d8679bf8f1a695854f606a25","source":{"kind":"arxiv","id":"1403.3642","version":1},"attestation_state":"computed","paper":{"title":"A rigidity result for global Mumford-Shah minimizers in dimension three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Antoine Lemenant (LJLL)","submitted_at":"2014-03-11T05:06:40Z","abstract_excerpt":"We study global Mumford-Shah minimizers in $\\R^N$, introduced by Bonnet as blow-up limits of Mumford-Shah minimizers. We prove a new monotonicity formula for the energy of $u$ when the singular set $K$ is contained in a smooth enough cone. We then use this monotonicity to prove that for any reduced global minimizer $(u,K)$ in $\\R^3$, if $K$ is contained in a half-plane and touching its edge, then it is the half-plane itself. This partially answers to a question of Guy David."},"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":"1403.3642","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-03-11T05:06:40Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"89ea59d2cf63f21bfbd26964108ca0db2ae046ea1d92334fe3766c029c0f92ef","abstract_canon_sha256":"0fee379d8d4cb391769d02804912cc9d1ab3746ca92ff1929e223bce9c053c4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:56:19.828082Z","signature_b64":"XdcEajsPt8Tg4presogoZZYW4Ck1WRtignyoTer9QfnWViY5+s2xNZ7dWaLvfeIGIY62IZg/Ewaaq/b4Y2LLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b0b9b6ae4a76beba050834e51c3d9ee84a376008d8679bf8f1a695854f606a25","last_reissued_at":"2026-05-18T02:56:19.827476Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:56:19.827476Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A rigidity result for global Mumford-Shah minimizers in dimension three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AP","authors_text":"Antoine Lemenant (LJLL)","submitted_at":"2014-03-11T05:06:40Z","abstract_excerpt":"We study global Mumford-Shah minimizers in $\\R^N$, introduced by Bonnet as blow-up limits of Mumford-Shah minimizers. We prove a new monotonicity formula for the energy of $u$ when the singular set $K$ is contained in a smooth enough cone. We then use this monotonicity to prove that for any reduced global minimizer $(u,K)$ in $\\R^3$, if $K$ is contained in a half-plane and touching its edge, then it is the half-plane itself. This partially answers to a question of Guy David."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3642","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":"1403.3642","created_at":"2026-05-18T02:56:19.827587+00:00"},{"alias_kind":"arxiv_version","alias_value":"1403.3642v1","created_at":"2026-05-18T02:56:19.827587+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.3642","created_at":"2026-05-18T02:56:19.827587+00:00"},{"alias_kind":"pith_short_12","alias_value":"WC43NLSKO27L","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_16","alias_value":"WC43NLSKO27LUBII","created_at":"2026-05-18T12:28:54.890064+00:00"},{"alias_kind":"pith_short_8","alias_value":"WC43NLSK","created_at":"2026-05-18T12:28:54.890064+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/WC43NLSKO27LUBIIGTSRYPM65B","json":"https://pith.science/pith/WC43NLSKO27LUBIIGTSRYPM65B.json","graph_json":"https://pith.science/api/pith-number/WC43NLSKO27LUBIIGTSRYPM65B/graph.json","events_json":"https://pith.science/api/pith-number/WC43NLSKO27LUBIIGTSRYPM65B/events.json","paper":"https://pith.science/paper/WC43NLSK"},"agent_actions":{"view_html":"https://pith.science/pith/WC43NLSKO27LUBIIGTSRYPM65B","download_json":"https://pith.science/pith/WC43NLSKO27LUBIIGTSRYPM65B.json","view_paper":"https://pith.science/paper/WC43NLSK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1403.3642&json=true","fetch_graph":"https://pith.science/api/pith-number/WC43NLSKO27LUBIIGTSRYPM65B/graph.json","fetch_events":"https://pith.science/api/pith-number/WC43NLSKO27LUBIIGTSRYPM65B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WC43NLSKO27LUBIIGTSRYPM65B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WC43NLSKO27LUBIIGTSRYPM65B/action/storage_attestation","attest_author":"https://pith.science/pith/WC43NLSKO27LUBIIGTSRYPM65B/action/author_attestation","sign_citation":"https://pith.science/pith/WC43NLSKO27LUBIIGTSRYPM65B/action/citation_signature","submit_replication":"https://pith.science/pith/WC43NLSKO27LUBIIGTSRYPM65B/action/replication_record"}},"created_at":"2026-05-18T02:56:19.827587+00:00","updated_at":"2026-05-18T02:56:19.827587+00:00"}