{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YWY2NCUTCSEVKHZHPKDIVAFORL","short_pith_number":"pith:YWY2NCUT","canonical_record":{"source":{"id":"1302.4054","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-17T10:49:24Z","cross_cats_sorted":[],"title_canon_sha256":"e07b65e498bbb8cc0a2b2a0fbad6c8246f9b4888fdcc5274ce20b436f2214337","abstract_canon_sha256":"ce3541cc51d04995638091fcf0b4d7d32270ac590d6bed505788bba8cbc204a3"},"schema_version":"1.0"},"canonical_sha256":"c5b1a68a931489551f277a868a80ae8af49f9aa3725ef4f1b4233f908bb5bf1f","source":{"kind":"arxiv","id":"1302.4054","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4054","created_at":"2026-05-18T03:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4054v3","created_at":"2026-05-18T03:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4054","created_at":"2026-05-18T03:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"YWY2NCUTCSEV","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YWY2NCUTCSEVKHZH","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YWY2NCUT","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YWY2NCUTCSEVKHZHPKDIVAFORL","target":"record","payload":{"canonical_record":{"source":{"id":"1302.4054","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-17T10:49:24Z","cross_cats_sorted":[],"title_canon_sha256":"e07b65e498bbb8cc0a2b2a0fbad6c8246f9b4888fdcc5274ce20b436f2214337","abstract_canon_sha256":"ce3541cc51d04995638091fcf0b4d7d32270ac590d6bed505788bba8cbc204a3"},"schema_version":"1.0"},"canonical_sha256":"c5b1a68a931489551f277a868a80ae8af49f9aa3725ef4f1b4233f908bb5bf1f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:25:25.152596Z","signature_b64":"n8fRIE6smGbgk3qwA8bqbUbaq4NPPHYH+L3XsOnum6V3I8U0AZ0kW+QKzr15doRfKssjhh0FI7icCjkpuaDIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5b1a68a931489551f277a868a80ae8af49f9aa3725ef4f1b4233f908bb5bf1f","last_reissued_at":"2026-05-18T03:25:25.151918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:25:25.151918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.4054","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:25:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zShLzU1D6Tvp96FE074YN18LpBbvEior5p4I6AqrwuESHQz/TJT/N7KjAEqNRA+jErgXQ+ljLCh/rzr1NeVbDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:22:46.085437Z"},"content_sha256":"a02ca36e876ea104a20f0d2cb232d2e9b6627d0f4aebf85a29bf5ff27b61e07a","schema_version":"1.0","event_id":"sha256:a02ca36e876ea104a20f0d2cb232d2e9b6627d0f4aebf85a29bf5ff27b61e07a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YWY2NCUTCSEVKHZHPKDIVAFORL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universal conformal weights on Sobolev spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A.Ukhlov, V.Gol'dshtein","submitted_at":"2013-02-17T10:49:24Z","abstract_excerpt":"The Riemann Mapping Theorem states existence of a conformal homeomorphism $\\varphi$ of a simply connected plane domain $\\Omega\\subset\\mathbb C$ with non-empty boundary onto the unit disc $\\mathbb D\\subset \\mathbb C$. In the first part of the paper we study embeddings of Sobolev spaces $\\overset{\\circ}{W_{p}^{1}}(\\Omega)$ into weighted Lebesgue spaces $L_{q}(\\Omega,h)$ with an {}\"universal\" weight that is Jacobian of $\\varphi$ i.e. $h(z):=J(z,\\varphi)=| \\varphi'(z)|^2$. Weighted Lebesgue spaces with such weights depend only on a conformal structure of $\\Omega$. By this reason we call the weight"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4054","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:25:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eyyvr+KQOZwdcWnwYBfb4VjRBNfSkittMJK1AYoHHLFMU0xSeTW5rxkSjWaW3ESgtAG78s++vG0m9H3CeRSwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T19:22:46.086652Z"},"content_sha256":"031137babc749257a0cd8ef9b305f1ed84b96d9775faeb2fce77e68d82165bfd","schema_version":"1.0","event_id":"sha256:031137babc749257a0cd8ef9b305f1ed84b96d9775faeb2fce77e68d82165bfd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YWY2NCUTCSEVKHZHPKDIVAFORL/bundle.json","state_url":"https://pith.science/pith/YWY2NCUTCSEVKHZHPKDIVAFORL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YWY2NCUTCSEVKHZHPKDIVAFORL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T19:22:46Z","links":{"resolver":"https://pith.science/pith/YWY2NCUTCSEVKHZHPKDIVAFORL","bundle":"https://pith.science/pith/YWY2NCUTCSEVKHZHPKDIVAFORL/bundle.json","state":"https://pith.science/pith/YWY2NCUTCSEVKHZHPKDIVAFORL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YWY2NCUTCSEVKHZHPKDIVAFORL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YWY2NCUTCSEVKHZHPKDIVAFORL","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":"ce3541cc51d04995638091fcf0b4d7d32270ac590d6bed505788bba8cbc204a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-17T10:49:24Z","title_canon_sha256":"e07b65e498bbb8cc0a2b2a0fbad6c8246f9b4888fdcc5274ce20b436f2214337"},"schema_version":"1.0","source":{"id":"1302.4054","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.4054","created_at":"2026-05-18T03:25:25Z"},{"alias_kind":"arxiv_version","alias_value":"1302.4054v3","created_at":"2026-05-18T03:25:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.4054","created_at":"2026-05-18T03:25:25Z"},{"alias_kind":"pith_short_12","alias_value":"YWY2NCUTCSEV","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"YWY2NCUTCSEVKHZH","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"YWY2NCUT","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:031137babc749257a0cd8ef9b305f1ed84b96d9775faeb2fce77e68d82165bfd","target":"graph","created_at":"2026-05-18T03:25:25Z","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":"The Riemann Mapping Theorem states existence of a conformal homeomorphism $\\varphi$ of a simply connected plane domain $\\Omega\\subset\\mathbb C$ with non-empty boundary onto the unit disc $\\mathbb D\\subset \\mathbb C$. In the first part of the paper we study embeddings of Sobolev spaces $\\overset{\\circ}{W_{p}^{1}}(\\Omega)$ into weighted Lebesgue spaces $L_{q}(\\Omega,h)$ with an {}\"universal\" weight that is Jacobian of $\\varphi$ i.e. $h(z):=J(z,\\varphi)=| \\varphi'(z)|^2$. Weighted Lebesgue spaces with such weights depend only on a conformal structure of $\\Omega$. By this reason we call the weight","authors_text":"A.Ukhlov, V.Gol'dshtein","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-17T10:49:24Z","title":"Universal conformal weights on Sobolev spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4054","kind":"arxiv","version":3},"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:a02ca36e876ea104a20f0d2cb232d2e9b6627d0f4aebf85a29bf5ff27b61e07a","target":"record","created_at":"2026-05-18T03:25:25Z","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":"ce3541cc51d04995638091fcf0b4d7d32270ac590d6bed505788bba8cbc204a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-02-17T10:49:24Z","title_canon_sha256":"e07b65e498bbb8cc0a2b2a0fbad6c8246f9b4888fdcc5274ce20b436f2214337"},"schema_version":"1.0","source":{"id":"1302.4054","kind":"arxiv","version":3}},"canonical_sha256":"c5b1a68a931489551f277a868a80ae8af49f9aa3725ef4f1b4233f908bb5bf1f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5b1a68a931489551f277a868a80ae8af49f9aa3725ef4f1b4233f908bb5bf1f","first_computed_at":"2026-05-18T03:25:25.151918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:25.151918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n8fRIE6smGbgk3qwA8bqbUbaq4NPPHYH+L3XsOnum6V3I8U0AZ0kW+QKzr15doRfKssjhh0FI7icCjkpuaDIAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:25.152596Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.4054","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a02ca36e876ea104a20f0d2cb232d2e9b6627d0f4aebf85a29bf5ff27b61e07a","sha256:031137babc749257a0cd8ef9b305f1ed84b96d9775faeb2fce77e68d82165bfd"],"state_sha256":"0535f4615fe0d070fa04c84042b2b86f11ad29e84117b90e66db97961471e486"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FhdNVP3A/o9WcTcb4U27M/P0P9e9T/h1z4ugYaMzCYcl4QFlESGqgDpat1MJe161gOIgzPtTgntzMk3iPP6fBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T19:22:46.090312Z","bundle_sha256":"3fc0cde16b30ae4fa9132f13812533ba00e7ee090e3f961499afee67618e1e11"}}