{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:RXI4WOASYTBLERRZUJINKFZIYS","short_pith_number":"pith:RXI4WOAS","schema_version":"1.0","canonical_sha256":"8dd1cb3812c4c2b24639a250d51728c49c29918c05d6e41bfd973581d4959149","source":{"kind":"arxiv","id":"2607.09353","version":1},"attestation_state":"computed","paper":{"title":"A rescaling principle for quasiregular curves with applications to hyperbolicity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Jonathan Pim, Toni Ikonen","submitted_at":"2026-07-10T12:30:47Z","abstract_excerpt":"We prove a Miniowitz--Zalcman rescaling principle for quasiregular curves into calibrated manifolds. We have two main applications.\n  First, we introduce Brody hyperbolicity adapted to our setting and prove its equivalence to the normality of the family of quasiregular curves from the Euclidean unit ball into the target. When normality holds, we quantify the local modulus of continuity for quasiregular curves using an injectivity radius lower bound and a sectional curvature upper bound of the target.\n  Second, in the special case of conformal curves into closed calibrated manifolds, we prove t"},"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":"2607.09353","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2026-07-10T12:30:47Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"5e6a90cef0211029cf3f01b81bad71399300107c62936eac4544ff999a6a8d26","abstract_canon_sha256":"0fa38836d25d93820011104dfe3af9434650bbe525febc1c783a3ae6f8108b1a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-13T01:19:05.410419Z","signature_b64":"TZTOSMe7/MCkoGqSG/lcGMEUir48r5TZ1BfRZmaUcYpOef/WceKVbILmIi7+THx5KoaXPmrasdM5QTpKKoziDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8dd1cb3812c4c2b24639a250d51728c49c29918c05d6e41bfd973581d4959149","last_reissued_at":"2026-07-13T01:19:05.409466Z","signature_status":"signed_v1","first_computed_at":"2026-07-13T01:19:05.409466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A rescaling principle for quasiregular curves with applications to hyperbolicity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Jonathan Pim, Toni Ikonen","submitted_at":"2026-07-10T12:30:47Z","abstract_excerpt":"We prove a Miniowitz--Zalcman rescaling principle for quasiregular curves into calibrated manifolds. We have two main applications.\n  First, we introduce Brody hyperbolicity adapted to our setting and prove its equivalence to the normality of the family of quasiregular curves from the Euclidean unit ball into the target. When normality holds, we quantify the local modulus of continuity for quasiregular curves using an injectivity radius lower bound and a sectional curvature upper bound of the target.\n  Second, in the special case of conformal curves into closed calibrated manifolds, we prove t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.09353","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/2607.09353/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":"2607.09353","created_at":"2026-07-13T01:19:05.409959+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.09353v1","created_at":"2026-07-13T01:19:05.409959+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.09353","created_at":"2026-07-13T01:19:05.409959+00:00"},{"alias_kind":"pith_short_12","alias_value":"RXI4WOASYTBL","created_at":"2026-07-13T01:19:05.409959+00:00"},{"alias_kind":"pith_short_16","alias_value":"RXI4WOASYTBLERRZ","created_at":"2026-07-13T01:19:05.409959+00:00"},{"alias_kind":"pith_short_8","alias_value":"RXI4WOAS","created_at":"2026-07-13T01:19:05.409959+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/RXI4WOASYTBLERRZUJINKFZIYS","json":"https://pith.science/pith/RXI4WOASYTBLERRZUJINKFZIYS.json","graph_json":"https://pith.science/api/pith-number/RXI4WOASYTBLERRZUJINKFZIYS/graph.json","events_json":"https://pith.science/api/pith-number/RXI4WOASYTBLERRZUJINKFZIYS/events.json","paper":"https://pith.science/paper/RXI4WOAS"},"agent_actions":{"view_html":"https://pith.science/pith/RXI4WOASYTBLERRZUJINKFZIYS","download_json":"https://pith.science/pith/RXI4WOASYTBLERRZUJINKFZIYS.json","view_paper":"https://pith.science/paper/RXI4WOAS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.09353&json=true","fetch_graph":"https://pith.science/api/pith-number/RXI4WOASYTBLERRZUJINKFZIYS/graph.json","fetch_events":"https://pith.science/api/pith-number/RXI4WOASYTBLERRZUJINKFZIYS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/RXI4WOASYTBLERRZUJINKFZIYS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/RXI4WOASYTBLERRZUJINKFZIYS/action/storage_attestation","attest_author":"https://pith.science/pith/RXI4WOASYTBLERRZUJINKFZIYS/action/author_attestation","sign_citation":"https://pith.science/pith/RXI4WOASYTBLERRZUJINKFZIYS/action/citation_signature","submit_replication":"https://pith.science/pith/RXI4WOASYTBLERRZUJINKFZIYS/action/replication_record"}},"created_at":"2026-07-13T01:19:05.409959+00:00","updated_at":"2026-07-13T01:19:05.409959+00:00"}