{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:V6FAJESXMOW2AUE43HNA5RQZNL","short_pith_number":"pith:V6FAJESX","schema_version":"1.0","canonical_sha256":"af8a04925763ada0509cd9da0ec6196ae3de75919906169538eb2c438b8db4c4","source":{"kind":"arxiv","id":"1703.00678","version":2},"attestation_state":"computed","paper":{"title":"On the measure and the structure of the free boundary of the lower dimensional obstacle problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Emanuele Spadaro, Matteo Focardi","submitted_at":"2017-03-02T09:33:22Z","abstract_excerpt":"We provide a thorough description of the free boundary for the lower dimensional obstacle problem in $\\mathbb{R}^{n+1}$ up to sets of null $\\mathcal{H}^{n-1}$ measure. In particular, we prove (i) local finiteness of the $(n-1)$-dimensional Hausdorff measure of the free boundary, (ii) $\\mathcal{H}^{n-1}$-rectifiability of the free boundary, (iii) classification of the frequencies up to a set of dimension at most (n-2) and classification of the blow-ups at $\\mathcal{H}^{n-1}$ almost every free boundary point."},"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":"1703.00678","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-02T09:33:22Z","cross_cats_sorted":[],"title_canon_sha256":"b7ba7a6110766e2eb0b811a5e5e49e6c6fd79290dfb8a3edc5fa306e7c7dfda1","abstract_canon_sha256":"c679f1f4c55a2bd85ba76cc51ab5a7dfd8e916e993e56a96e31136e08be909ee"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:33.970578Z","signature_b64":"UyJ6CBmFsOM5Fw9JWbHYm/8xqNX7nsot5Ak5C63koVcEiXqgBpZ+gVLPr3GuypawT070EhWtd+ichAL6SbdIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af8a04925763ada0509cd9da0ec6196ae3de75919906169538eb2c438b8db4c4","last_reissued_at":"2026-05-18T00:16:33.969981Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:33.969981Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the measure and the structure of the free boundary of the lower dimensional obstacle problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Emanuele Spadaro, Matteo Focardi","submitted_at":"2017-03-02T09:33:22Z","abstract_excerpt":"We provide a thorough description of the free boundary for the lower dimensional obstacle problem in $\\mathbb{R}^{n+1}$ up to sets of null $\\mathcal{H}^{n-1}$ measure. In particular, we prove (i) local finiteness of the $(n-1)$-dimensional Hausdorff measure of the free boundary, (ii) $\\mathcal{H}^{n-1}$-rectifiability of the free boundary, (iii) classification of the frequencies up to a set of dimension at most (n-2) and classification of the blow-ups at $\\mathcal{H}^{n-1}$ almost every free boundary point."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00678","kind":"arxiv","version":2},"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":"1703.00678","created_at":"2026-05-18T00:16:33.970063+00:00"},{"alias_kind":"arxiv_version","alias_value":"1703.00678v2","created_at":"2026-05-18T00:16:33.970063+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.00678","created_at":"2026-05-18T00:16:33.970063+00:00"},{"alias_kind":"pith_short_12","alias_value":"V6FAJESXMOW2","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"V6FAJESXMOW2AUE4","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"V6FAJESX","created_at":"2026-05-18T12:31:49.984773+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/V6FAJESXMOW2AUE43HNA5RQZNL","json":"https://pith.science/pith/V6FAJESXMOW2AUE43HNA5RQZNL.json","graph_json":"https://pith.science/api/pith-number/V6FAJESXMOW2AUE43HNA5RQZNL/graph.json","events_json":"https://pith.science/api/pith-number/V6FAJESXMOW2AUE43HNA5RQZNL/events.json","paper":"https://pith.science/paper/V6FAJESX"},"agent_actions":{"view_html":"https://pith.science/pith/V6FAJESXMOW2AUE43HNA5RQZNL","download_json":"https://pith.science/pith/V6FAJESXMOW2AUE43HNA5RQZNL.json","view_paper":"https://pith.science/paper/V6FAJESX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1703.00678&json=true","fetch_graph":"https://pith.science/api/pith-number/V6FAJESXMOW2AUE43HNA5RQZNL/graph.json","fetch_events":"https://pith.science/api/pith-number/V6FAJESXMOW2AUE43HNA5RQZNL/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/V6FAJESXMOW2AUE43HNA5RQZNL/action/timestamp_anchor","attest_storage":"https://pith.science/pith/V6FAJESXMOW2AUE43HNA5RQZNL/action/storage_attestation","attest_author":"https://pith.science/pith/V6FAJESXMOW2AUE43HNA5RQZNL/action/author_attestation","sign_citation":"https://pith.science/pith/V6FAJESXMOW2AUE43HNA5RQZNL/action/citation_signature","submit_replication":"https://pith.science/pith/V6FAJESXMOW2AUE43HNA5RQZNL/action/replication_record"}},"created_at":"2026-05-18T00:16:33.970063+00:00","updated_at":"2026-05-18T00:16:33.970063+00:00"}