{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:N5333PMSPQUMVU22MU7WTYXO3Y","short_pith_number":"pith:N5333PMS","schema_version":"1.0","canonical_sha256":"6f77bdbd927c28cad35a653f69e2eede0aeebec48c0cb711f027f414381710d6","source":{"kind":"arxiv","id":"2607.16444","version":1},"attestation_state":"computed","paper":{"title":"Bernoulli problem for the fractional $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OC"],"primary_cat":"math.AP","authors_text":"Diego Marcon, Rafael Costa","submitted_at":"2026-07-17T18:46:02Z","abstract_excerpt":"We study regularity properties of minimizers for the one-phase Alt--Caffarelli problem associated with the fractional $p$-Laplacian in the range $p\\geq2$. We consider minimizers of the fractional $p$-energy penalized by the measure of the positivity set, with prescribed nonnegative exterior datum. We prove existence of minimizers and derive their basic variational properties: minimizers are nonnegative and are weak subsolutions of the homogeneous fractional $p$-Laplace equation. The main regularity argument combines fractional $p$-harmonic replacements, energy-gap estimates, nonlocal tail boun"},"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":"2607.16444","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-07-17T18:46:02Z","cross_cats_sorted":["math.FA","math.OC"],"title_canon_sha256":"2aa7da8b2606c8dc6999bf531e8876e3a5350c3294d495c57cb23f65d5acb6e5","abstract_canon_sha256":"35d61e1924c1eb658d4e234b02430ec246d7de1df55bf54e9fa571c777d8f500"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T00:20:18.934756Z","signature_b64":"Vb50QH//m4vMwKK19wwjeIJQ2g/QuRivTDf4tpzLPPY4b5SC4SvCTyfOMkDH2kSHEo4Iqcc4ersxzq0fkq43CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f77bdbd927c28cad35a653f69e2eede0aeebec48c0cb711f027f414381710d6","last_reissued_at":"2026-07-21T00:20:18.933920Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T00:20:18.933920Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bernoulli problem for the fractional $p$-Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.OC"],"primary_cat":"math.AP","authors_text":"Diego Marcon, Rafael Costa","submitted_at":"2026-07-17T18:46:02Z","abstract_excerpt":"We study regularity properties of minimizers for the one-phase Alt--Caffarelli problem associated with the fractional $p$-Laplacian in the range $p\\geq2$. We consider minimizers of the fractional $p$-energy penalized by the measure of the positivity set, with prescribed nonnegative exterior datum. We prove existence of minimizers and derive their basic variational properties: minimizers are nonnegative and are weak subsolutions of the homogeneous fractional $p$-Laplace equation. The main regularity argument combines fractional $p$-harmonic replacements, energy-gap estimates, nonlocal tail boun"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16444","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.16444/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2607.16444","created_at":"2026-07-21T00:20:18.934342+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.16444v1","created_at":"2026-07-21T00:20:18.934342+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16444","created_at":"2026-07-21T00:20:18.934342+00:00"},{"alias_kind":"pith_short_12","alias_value":"N5333PMSPQUM","created_at":"2026-07-21T00:20:18.934342+00:00"},{"alias_kind":"pith_short_16","alias_value":"N5333PMSPQUMVU22","created_at":"2026-07-21T00:20:18.934342+00:00"},{"alias_kind":"pith_short_8","alias_value":"N5333PMS","created_at":"2026-07-21T00:20:18.934342+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/N5333PMSPQUMVU22MU7WTYXO3Y","json":"https://pith.science/pith/N5333PMSPQUMVU22MU7WTYXO3Y.json","graph_json":"https://pith.science/api/pith-number/N5333PMSPQUMVU22MU7WTYXO3Y/graph.json","events_json":"https://pith.science/api/pith-number/N5333PMSPQUMVU22MU7WTYXO3Y/events.json","paper":"https://pith.science/paper/N5333PMS"},"agent_actions":{"view_html":"https://pith.science/pith/N5333PMSPQUMVU22MU7WTYXO3Y","download_json":"https://pith.science/pith/N5333PMSPQUMVU22MU7WTYXO3Y.json","view_paper":"https://pith.science/paper/N5333PMS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.16444&json=true","fetch_graph":"https://pith.science/api/pith-number/N5333PMSPQUMVU22MU7WTYXO3Y/graph.json","fetch_events":"https://pith.science/api/pith-number/N5333PMSPQUMVU22MU7WTYXO3Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/N5333PMSPQUMVU22MU7WTYXO3Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/N5333PMSPQUMVU22MU7WTYXO3Y/action/storage_attestation","attest_author":"https://pith.science/pith/N5333PMSPQUMVU22MU7WTYXO3Y/action/author_attestation","sign_citation":"https://pith.science/pith/N5333PMSPQUMVU22MU7WTYXO3Y/action/citation_signature","submit_replication":"https://pith.science/pith/N5333PMSPQUMVU22MU7WTYXO3Y/action/replication_record"}},"created_at":"2026-07-21T00:20:18.934342+00:00","updated_at":"2026-07-21T00:20:18.934342+00:00"}