{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:T7QPIIYXWVARZJKJK7BZLWQYBJ","short_pith_number":"pith:T7QPIIYX","canonical_record":{"source":{"id":"1410.3100","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-12T15:22:36Z","cross_cats_sorted":[],"title_canon_sha256":"2339b58403e4b425045f1517be122f58e09c487a19e3e1743bbcad371a67d666","abstract_canon_sha256":"252935f2b5afabd0eaaf0099dca6b1cdd34295e66428cda352a75c2523243732"},"schema_version":"1.0"},"canonical_sha256":"9fe0f42317b5411ca54957c395da180a417b0006b02c814e03cc95c59e37299c","source":{"kind":"arxiv","id":"1410.3100","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3100","created_at":"2026-05-18T01:36:31Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3100v2","created_at":"2026-05-18T01:36:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3100","created_at":"2026-05-18T01:36:31Z"},{"alias_kind":"pith_short_12","alias_value":"T7QPIIYXWVAR","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T7QPIIYXWVARZJKJ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T7QPIIYX","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:T7QPIIYXWVARZJKJK7BZLWQYBJ","target":"record","payload":{"canonical_record":{"source":{"id":"1410.3100","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-12T15:22:36Z","cross_cats_sorted":[],"title_canon_sha256":"2339b58403e4b425045f1517be122f58e09c487a19e3e1743bbcad371a67d666","abstract_canon_sha256":"252935f2b5afabd0eaaf0099dca6b1cdd34295e66428cda352a75c2523243732"},"schema_version":"1.0"},"canonical_sha256":"9fe0f42317b5411ca54957c395da180a417b0006b02c814e03cc95c59e37299c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:31.391105Z","signature_b64":"S+KaTyB+7Hb97CUUvBBp9wiaVeJ5JxjvLaFAySjAUWiBSHz+uJ6HvNA1YzysfTH3bq04En/JOuPURLJRBAuABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9fe0f42317b5411ca54957c395da180a417b0006b02c814e03cc95c59e37299c","last_reissued_at":"2026-05-18T01:36:31.390582Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:31.390582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.3100","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:36:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mslFfYl4UfzZ+vPEjglfbFfXDBO/XKXYuu+Zf46/n2OTc/8IX9fLN+w0z5KlqGu/4NdpTzYzBDqc/UDEgWsrAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:46:33.149058Z"},"content_sha256":"18306151028d7d49e888b5680e32c893a32804562f31d45c5b9cfc8842b3b8de","schema_version":"1.0","event_id":"sha256:18306151028d7d49e888b5680e32c893a32804562f31d45c5b9cfc8842b3b8de"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:T7QPIIYXWVARZJKJK7BZLWQYBJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On planar Sobolev $L^m_p$-extension domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Nahum Zobin, Pavel Shvartsman","submitted_at":"2014-10-12T15:22:36Z","abstract_excerpt":"For each $m\\ge 1$ and $p>2$ we characterize bounded simply connected Sobolev $L^m_p$-extension domains $\\Omega\\subset R^2$. Our criterion is expressed in terms of certain intrinsic subhyperbolic metrics in $\\Omega$. Its proof is based on a series of results related to the existence of special chains of squares joining given points $x$ and $y$ in $\\Omega$.\n  An important geometrical ingredient for obtaining these results is a new \"Square Separation Theorem\". It states that under certain natural assumptions on the relative positions of a point $x$ and a square $S\\subset\\Omega$ there exists a sim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3100","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":""},"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":"2026-05-18T01:36:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c5tcTJ8m0qHlmaui+xEeq7PjYj6LKFjXiVIXaLqRJhnRMC0A4tYjsCwvekq977+P/y/oekMj+s14dsu3CQxCCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T22:46:33.149438Z"},"content_sha256":"cf9a2e74e4fb8a2112675a93e328fae53ab35ed18fe6a3562969e7c3eef4dd21","schema_version":"1.0","event_id":"sha256:cf9a2e74e4fb8a2112675a93e328fae53ab35ed18fe6a3562969e7c3eef4dd21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T7QPIIYXWVARZJKJK7BZLWQYBJ/bundle.json","state_url":"https://pith.science/pith/T7QPIIYXWVARZJKJK7BZLWQYBJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T7QPIIYXWVARZJKJK7BZLWQYBJ/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":"2026-06-22T22:46:33Z","links":{"resolver":"https://pith.science/pith/T7QPIIYXWVARZJKJK7BZLWQYBJ","bundle":"https://pith.science/pith/T7QPIIYXWVARZJKJK7BZLWQYBJ/bundle.json","state":"https://pith.science/pith/T7QPIIYXWVARZJKJK7BZLWQYBJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T7QPIIYXWVARZJKJK7BZLWQYBJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:T7QPIIYXWVARZJKJK7BZLWQYBJ","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":"252935f2b5afabd0eaaf0099dca6b1cdd34295e66428cda352a75c2523243732","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-12T15:22:36Z","title_canon_sha256":"2339b58403e4b425045f1517be122f58e09c487a19e3e1743bbcad371a67d666"},"schema_version":"1.0","source":{"id":"1410.3100","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3100","created_at":"2026-05-18T01:36:31Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3100v2","created_at":"2026-05-18T01:36:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3100","created_at":"2026-05-18T01:36:31Z"},{"alias_kind":"pith_short_12","alias_value":"T7QPIIYXWVAR","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"T7QPIIYXWVARZJKJ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"T7QPIIYX","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:cf9a2e74e4fb8a2112675a93e328fae53ab35ed18fe6a3562969e7c3eef4dd21","target":"graph","created_at":"2026-05-18T01:36:31Z","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":"For each $m\\ge 1$ and $p>2$ we characterize bounded simply connected Sobolev $L^m_p$-extension domains $\\Omega\\subset R^2$. Our criterion is expressed in terms of certain intrinsic subhyperbolic metrics in $\\Omega$. Its proof is based on a series of results related to the existence of special chains of squares joining given points $x$ and $y$ in $\\Omega$.\n  An important geometrical ingredient for obtaining these results is a new \"Square Separation Theorem\". It states that under certain natural assumptions on the relative positions of a point $x$ and a square $S\\subset\\Omega$ there exists a sim","authors_text":"Nahum Zobin, Pavel Shvartsman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-12T15:22:36Z","title":"On planar Sobolev $L^m_p$-extension domains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3100","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":"sha256:18306151028d7d49e888b5680e32c893a32804562f31d45c5b9cfc8842b3b8de","target":"record","created_at":"2026-05-18T01:36:31Z","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":"252935f2b5afabd0eaaf0099dca6b1cdd34295e66428cda352a75c2523243732","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-10-12T15:22:36Z","title_canon_sha256":"2339b58403e4b425045f1517be122f58e09c487a19e3e1743bbcad371a67d666"},"schema_version":"1.0","source":{"id":"1410.3100","kind":"arxiv","version":2}},"canonical_sha256":"9fe0f42317b5411ca54957c395da180a417b0006b02c814e03cc95c59e37299c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fe0f42317b5411ca54957c395da180a417b0006b02c814e03cc95c59e37299c","first_computed_at":"2026-05-18T01:36:31.390582Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:31.390582Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"S+KaTyB+7Hb97CUUvBBp9wiaVeJ5JxjvLaFAySjAUWiBSHz+uJ6HvNA1YzysfTH3bq04En/JOuPURLJRBAuABg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:31.391105Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3100","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18306151028d7d49e888b5680e32c893a32804562f31d45c5b9cfc8842b3b8de","sha256:cf9a2e74e4fb8a2112675a93e328fae53ab35ed18fe6a3562969e7c3eef4dd21"],"state_sha256":"5348aab3fbd249c0829de2edc1e7cc5794f9bd976c2b0126daa2623ca737f721"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BEKOJujAh5HAh0j4HvMLd1Goo5g819MN54xpR1sbPuFcX+vZ6OovcQpHb1knHBunBkcf9D38b7tf/uPidmY0Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T22:46:33.151419Z","bundle_sha256":"37112041fd2eb349fc9884abc7671e8c4178c76c4097e08b38cd06709a1a8494"}}