{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:FYUOKVSLGE5P5NSMRVVVRAA3P4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ebf91de02bbaf113db002cb3a508655bea444396763f229ce09ac17efe3888d6","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-04-18T13:20:28Z","title_canon_sha256":"52e6917d70cee9ff671ff47ded2361ab91fb3761cedea2295806e9c87f9c5145"},"schema_version":"1.0","source":{"id":"1104.3475","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3475","created_at":"2026-05-18T04:00:59Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3475v2","created_at":"2026-05-18T04:00:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3475","created_at":"2026-05-18T04:00:59Z"},{"alias_kind":"pith_short_12","alias_value":"FYUOKVSLGE5P","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"FYUOKVSLGE5P5NSM","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"FYUOKVSL","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:6fe5f9f066c7ca2a66e383c7a2c5ef473f08ed96268b9d502de2650b92fcbe35","target":"graph","created_at":"2026-05-18T04:00:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper studies Newtonian Sobolev-Lorentz spaces. We prove that these spaces are Banach. We also study the global p,q-capacity and the p,q-modulus of families of rectifiable curves. Under some additional assumptions (that is, the space carries a doubling measure and a weak Poincare inequality) and some restrictions on q, we show that the Lipschitz functions are dense in those spaces. Moreover, in the same setting we show that the p,q-capacity is Choquet provided that q is strictly greater than 1. We also provide a counterexample to the density result of Lipschitz functions in the Euclidean ","authors_text":"Michele Miranda Jr, Serban Costea","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-04-18T13:20:28Z","title":"Newtonian Lorentz Metric Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3475","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:d99b8bcd23f04e6b71bfc9134d07932655321c2fd9f42ed30a250c94c7d1be28","target":"record","created_at":"2026-05-18T04:00:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ebf91de02bbaf113db002cb3a508655bea444396763f229ce09ac17efe3888d6","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2011-04-18T13:20:28Z","title_canon_sha256":"52e6917d70cee9ff671ff47ded2361ab91fb3761cedea2295806e9c87f9c5145"},"schema_version":"1.0","source":{"id":"1104.3475","kind":"arxiv","version":2}},"canonical_sha256":"2e28e5564b313afeb64c8d6b58801b7f27259c46ee58bcae8cb8f99597e7d4f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e28e5564b313afeb64c8d6b58801b7f27259c46ee58bcae8cb8f99597e7d4f8","first_computed_at":"2026-05-18T04:00:59.765727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:00:59.765727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"edzk24Y0ZVUKILj7/KR91TM5yGYXYBvl3e9hWv40A18IwsFmPKSNduHIPlHefDAZB+yQhbOdF2spnuphyNfPCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:00:59.766418Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3475","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d99b8bcd23f04e6b71bfc9134d07932655321c2fd9f42ed30a250c94c7d1be28","sha256:6fe5f9f066c7ca2a66e383c7a2c5ef473f08ed96268b9d502de2650b92fcbe35"],"state_sha256":"a1e0cbaea12f3d5963c48a131c7b5fea6e52b75a49f9a054094e023f8e3ff5bb"}