{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:PWMEWOTG5MYYF64HKKS5INTIDF","short_pith_number":"pith:PWMEWOTG","schema_version":"1.0","canonical_sha256":"7d984b3a66eb3182fb8752a5d436681953ee5efe65743e874fbcaf486880ce52","source":{"kind":"arxiv","id":"2509.01194","version":2},"attestation_state":"computed","paper":{"title":"On infinity thick quasiconvexity and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Miguel Garc\\'ia-Bravo, Toni Ikonen, Zheng Zhu","submitted_at":"2025-09-01T07:24:40Z","abstract_excerpt":"We investigate geometric properties of a metric measure space where every function in the Newton--Sobolev space $N^{1,\\infty}(Z)$ has a Lipschitz representative. We prove that when the metric space is locally complete and the reference measure is infinitesimally doubling, the above property is equivalent to the space being very $\\infty$-thick quasiconvex up to a scale. That is, up to some scale, every pair of points can be joined by a family of quasiconvex curves that is not negligible for the $\\infty$-modulus.\n  As a first application, we prove a local-to-global improvement for the weak $(1,\\"},"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":"2509.01194","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.MG","submitted_at":"2025-09-01T07:24:40Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"3b417dcbe76c97218db5bab5a7108c10e15cc42593e5d6ba238887ce2395de38","abstract_canon_sha256":"1d8b75ff805ed27f701b50e48ce18c541cd9b1f80d18b8cad0cb2af8b7d28b5d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-01T02:03:26.067863Z","signature_b64":"f0ovVoRogpEyQH+QmeKvl3Xa090wf20eznhf1elg2pQnYNfvJaw3FpQzVXNxAQUBe35XnoQjy1dEJ6sP8YY0BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7d984b3a66eb3182fb8752a5d436681953ee5efe65743e874fbcaf486880ce52","last_reissued_at":"2026-06-01T02:03:26.066688Z","signature_status":"signed_v1","first_computed_at":"2026-06-01T02:03:26.066688Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On infinity thick quasiconvexity and applications","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Miguel Garc\\'ia-Bravo, Toni Ikonen, Zheng Zhu","submitted_at":"2025-09-01T07:24:40Z","abstract_excerpt":"We investigate geometric properties of a metric measure space where every function in the Newton--Sobolev space $N^{1,\\infty}(Z)$ has a Lipschitz representative. We prove that when the metric space is locally complete and the reference measure is infinitesimally doubling, the above property is equivalent to the space being very $\\infty$-thick quasiconvex up to a scale. That is, up to some scale, every pair of points can be joined by a family of quasiconvex curves that is not negligible for the $\\infty$-modulus.\n  As a first application, we prove a local-to-global improvement for the weak $(1,\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.01194","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.01194/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":"2509.01194","created_at":"2026-06-01T02:03:26.066856+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.01194v2","created_at":"2026-06-01T02:03:26.066856+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.01194","created_at":"2026-06-01T02:03:26.066856+00:00"},{"alias_kind":"pith_short_12","alias_value":"PWMEWOTG5MYY","created_at":"2026-06-01T02:03:26.066856+00:00"},{"alias_kind":"pith_short_16","alias_value":"PWMEWOTG5MYYF64H","created_at":"2026-06-01T02:03:26.066856+00:00"},{"alias_kind":"pith_short_8","alias_value":"PWMEWOTG","created_at":"2026-06-01T02:03:26.066856+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.22674","citing_title":"Quasicontinuity of $N^{1,\\infty}$ functions and the Vitali-Carath\\'eodory property on general metric spaces","ref_index":3,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PWMEWOTG5MYYF64HKKS5INTIDF","json":"https://pith.science/pith/PWMEWOTG5MYYF64HKKS5INTIDF.json","graph_json":"https://pith.science/api/pith-number/PWMEWOTG5MYYF64HKKS5INTIDF/graph.json","events_json":"https://pith.science/api/pith-number/PWMEWOTG5MYYF64HKKS5INTIDF/events.json","paper":"https://pith.science/paper/PWMEWOTG"},"agent_actions":{"view_html":"https://pith.science/pith/PWMEWOTG5MYYF64HKKS5INTIDF","download_json":"https://pith.science/pith/PWMEWOTG5MYYF64HKKS5INTIDF.json","view_paper":"https://pith.science/paper/PWMEWOTG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.01194&json=true","fetch_graph":"https://pith.science/api/pith-number/PWMEWOTG5MYYF64HKKS5INTIDF/graph.json","fetch_events":"https://pith.science/api/pith-number/PWMEWOTG5MYYF64HKKS5INTIDF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PWMEWOTG5MYYF64HKKS5INTIDF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PWMEWOTG5MYYF64HKKS5INTIDF/action/storage_attestation","attest_author":"https://pith.science/pith/PWMEWOTG5MYYF64HKKS5INTIDF/action/author_attestation","sign_citation":"https://pith.science/pith/PWMEWOTG5MYYF64HKKS5INTIDF/action/citation_signature","submit_replication":"https://pith.science/pith/PWMEWOTG5MYYF64HKKS5INTIDF/action/replication_record"}},"created_at":"2026-06-01T02:03:26.066856+00:00","updated_at":"2026-06-01T02:03:26.066856+00:00"}