{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:2HPOIFP3GNV5V7REZOZNYBVOE3","short_pith_number":"pith:2HPOIFP3","schema_version":"1.0","canonical_sha256":"d1dee415fb336bdafe24cbb2dc06ae26d997af962c94e827894969fa5de08328","source":{"kind":"arxiv","id":"1103.1315","version":3},"attestation_state":"computed","paper":{"title":"On finitely Lipschitz space mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ruslan Salimov","submitted_at":"2011-03-07T16:29:56Z","abstract_excerpt":"It is established that a ring $Q$-homeomorphism with respect to $p$-modulus in ${\\Bbb R}^n$, $n\\geqslant2,$ is finitely Lipschitz if $n-1<p<n$ and if the mean integral value of $Q(x)$ over infinitisimial balls $B(x_0,\\epsilon)$ is finite everywhere."},"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":"1103.1315","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2011-03-07T16:29:56Z","cross_cats_sorted":[],"title_canon_sha256":"5d0afcf3c56ceb21a210142cb10899473560e34f4446807709a2f3534ad6bc19","abstract_canon_sha256":"18543939dfb1c47a3475ad2360eba34a9797819ad31ebe853993da2a4d263050"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:51.500915Z","signature_b64":"AXT60KlA5A2RN+aGZRu/0cVhm5VKjB1EV63PRJ15p8QdTnQCAInWwJ9ivzSvm6qVz/ncqJesOfG/JVUeg9UVDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1dee415fb336bdafe24cbb2dc06ae26d997af962c94e827894969fa5de08328","last_reissued_at":"2026-05-18T04:21:51.500332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:51.500332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On finitely Lipschitz space mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Ruslan Salimov","submitted_at":"2011-03-07T16:29:56Z","abstract_excerpt":"It is established that a ring $Q$-homeomorphism with respect to $p$-modulus in ${\\Bbb R}^n$, $n\\geqslant2,$ is finitely Lipschitz if $n-1<p<n$ and if the mean integral value of $Q(x)$ over infinitisimial balls $B(x_0,\\epsilon)$ is finite everywhere."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.1315","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1103.1315","created_at":"2026-05-18T04:21:51.500416+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.1315v3","created_at":"2026-05-18T04:21:51.500416+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.1315","created_at":"2026-05-18T04:21:51.500416+00:00"},{"alias_kind":"pith_short_12","alias_value":"2HPOIFP3GNV5","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_16","alias_value":"2HPOIFP3GNV5V7RE","created_at":"2026-05-18T12:26:18.847500+00:00"},{"alias_kind":"pith_short_8","alias_value":"2HPOIFP3","created_at":"2026-05-18T12:26:18.847500+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/2HPOIFP3GNV5V7REZOZNYBVOE3","json":"https://pith.science/pith/2HPOIFP3GNV5V7REZOZNYBVOE3.json","graph_json":"https://pith.science/api/pith-number/2HPOIFP3GNV5V7REZOZNYBVOE3/graph.json","events_json":"https://pith.science/api/pith-number/2HPOIFP3GNV5V7REZOZNYBVOE3/events.json","paper":"https://pith.science/paper/2HPOIFP3"},"agent_actions":{"view_html":"https://pith.science/pith/2HPOIFP3GNV5V7REZOZNYBVOE3","download_json":"https://pith.science/pith/2HPOIFP3GNV5V7REZOZNYBVOE3.json","view_paper":"https://pith.science/paper/2HPOIFP3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.1315&json=true","fetch_graph":"https://pith.science/api/pith-number/2HPOIFP3GNV5V7REZOZNYBVOE3/graph.json","fetch_events":"https://pith.science/api/pith-number/2HPOIFP3GNV5V7REZOZNYBVOE3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2HPOIFP3GNV5V7REZOZNYBVOE3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2HPOIFP3GNV5V7REZOZNYBVOE3/action/storage_attestation","attest_author":"https://pith.science/pith/2HPOIFP3GNV5V7REZOZNYBVOE3/action/author_attestation","sign_citation":"https://pith.science/pith/2HPOIFP3GNV5V7REZOZNYBVOE3/action/citation_signature","submit_replication":"https://pith.science/pith/2HPOIFP3GNV5V7REZOZNYBVOE3/action/replication_record"}},"created_at":"2026-05-18T04:21:51.500416+00:00","updated_at":"2026-05-18T04:21:51.500416+00:00"}