{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:MPM5C6H5YQZVC3IPT7OYPHRE4W","short_pith_number":"pith:MPM5C6H5","schema_version":"1.0","canonical_sha256":"63d9d178fdc433516d0f9fdd879e24e5bf0fbe5ca12bda1307c54a50f915ac5c","source":{"kind":"arxiv","id":"2607.02348","version":1},"attestation_state":"computed","paper":{"title":"Eliminating positive-measure level sets by small Lipschitz perturbations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Martin Lind, Sorina Barza","submitted_at":"2026-07-02T15:51:21Z","abstract_excerpt":"We establish a new regularity phenomenon of continuous functions. Specifically, given any continuous function $f$ and arbitrary $\\epsilon>0$, we construct a Lipschitz perturbation $g_\\epsilon$ whose Lipschitz seminorm is less than $\\epsilon$ such that every level set of $f+g_\\epsilon$ has Lebesgue measure zero."},"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":"2607.02348","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2026-07-02T15:51:21Z","cross_cats_sorted":[],"title_canon_sha256":"5060c370e2719551b154691ecd47d5ed9ec7509c71f898a1d57b42755bfa4fb2","abstract_canon_sha256":"21c795e3a848fd81d6561a5ae72bd36278082f54c4c8400c736e4d2762a3cc55"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-03T01:17:49.096203Z","signature_b64":"pBM07uxTGnQBPPA237uNp6PL5fqs4jL8dAbPzHGuhmbOK7eE7bj36lfhsnQLH451siUIQQZ3Qoy2PvJjD7SoAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"63d9d178fdc433516d0f9fdd879e24e5bf0fbe5ca12bda1307c54a50f915ac5c","last_reissued_at":"2026-07-03T01:17:49.095833Z","signature_status":"signed_v1","first_computed_at":"2026-07-03T01:17:49.095833Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Eliminating positive-measure level sets by small Lipschitz perturbations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Martin Lind, Sorina Barza","submitted_at":"2026-07-02T15:51:21Z","abstract_excerpt":"We establish a new regularity phenomenon of continuous functions. Specifically, given any continuous function $f$ and arbitrary $\\epsilon>0$, we construct a Lipschitz perturbation $g_\\epsilon$ whose Lipschitz seminorm is less than $\\epsilon$ such that every level set of $f+g_\\epsilon$ has Lebesgue measure zero."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.02348","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/2607.02348/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":"2607.02348","created_at":"2026-07-03T01:17:49.095897+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.02348v1","created_at":"2026-07-03T01:17:49.095897+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.02348","created_at":"2026-07-03T01:17:49.095897+00:00"},{"alias_kind":"pith_short_12","alias_value":"MPM5C6H5YQZV","created_at":"2026-07-03T01:17:49.095897+00:00"},{"alias_kind":"pith_short_16","alias_value":"MPM5C6H5YQZVC3IP","created_at":"2026-07-03T01:17:49.095897+00:00"},{"alias_kind":"pith_short_8","alias_value":"MPM5C6H5","created_at":"2026-07-03T01:17:49.095897+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/MPM5C6H5YQZVC3IPT7OYPHRE4W","json":"https://pith.science/pith/MPM5C6H5YQZVC3IPT7OYPHRE4W.json","graph_json":"https://pith.science/api/pith-number/MPM5C6H5YQZVC3IPT7OYPHRE4W/graph.json","events_json":"https://pith.science/api/pith-number/MPM5C6H5YQZVC3IPT7OYPHRE4W/events.json","paper":"https://pith.science/paper/MPM5C6H5"},"agent_actions":{"view_html":"https://pith.science/pith/MPM5C6H5YQZVC3IPT7OYPHRE4W","download_json":"https://pith.science/pith/MPM5C6H5YQZVC3IPT7OYPHRE4W.json","view_paper":"https://pith.science/paper/MPM5C6H5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.02348&json=true","fetch_graph":"https://pith.science/api/pith-number/MPM5C6H5YQZVC3IPT7OYPHRE4W/graph.json","fetch_events":"https://pith.science/api/pith-number/MPM5C6H5YQZVC3IPT7OYPHRE4W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MPM5C6H5YQZVC3IPT7OYPHRE4W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MPM5C6H5YQZVC3IPT7OYPHRE4W/action/storage_attestation","attest_author":"https://pith.science/pith/MPM5C6H5YQZVC3IPT7OYPHRE4W/action/author_attestation","sign_citation":"https://pith.science/pith/MPM5C6H5YQZVC3IPT7OYPHRE4W/action/citation_signature","submit_replication":"https://pith.science/pith/MPM5C6H5YQZVC3IPT7OYPHRE4W/action/replication_record"}},"created_at":"2026-07-03T01:17:49.095897+00:00","updated_at":"2026-07-03T01:17:49.095897+00:00"}