{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:55HU42D74L72F4KFU7OM4R2QPO","short_pith_number":"pith:55HU42D7","canonical_record":{"source":{"id":"1504.05385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-21T11:00:58Z","cross_cats_sorted":[],"title_canon_sha256":"a908bcd9f0a5d83f4c4203b3b06bfa371a77b9c9d573e16493c1dfab216b9b35","abstract_canon_sha256":"915154c11edb7c7c6a1b0914508eddaf349ded76dc9134ff731f5ab463c015e9"},"schema_version":"1.0"},"canonical_sha256":"ef4f4e687fe2ffa2f145a7dcce47507b936040c4286e1e378d1fba9dbbac6608","source":{"kind":"arxiv","id":"1504.05385","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05385","created_at":"2026-05-18T02:18:14Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05385v1","created_at":"2026-05-18T02:18:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05385","created_at":"2026-05-18T02:18:14Z"},{"alias_kind":"pith_short_12","alias_value":"55HU42D74L72","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"55HU42D74L72F4KF","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"55HU42D7","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:55HU42D74L72F4KFU7OM4R2QPO","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05385","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-21T11:00:58Z","cross_cats_sorted":[],"title_canon_sha256":"a908bcd9f0a5d83f4c4203b3b06bfa371a77b9c9d573e16493c1dfab216b9b35","abstract_canon_sha256":"915154c11edb7c7c6a1b0914508eddaf349ded76dc9134ff731f5ab463c015e9"},"schema_version":"1.0"},"canonical_sha256":"ef4f4e687fe2ffa2f145a7dcce47507b936040c4286e1e378d1fba9dbbac6608","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:14.414474Z","signature_b64":"i1FioY8gGhKtMa+NqpMzWl/HixfBYOW7SPw/ADjT7rBRmyJeXXmboVZGNvUZ307wVLBQRr9Uo3NxV++PQoxIBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ef4f4e687fe2ffa2f145a7dcce47507b936040c4286e1e378d1fba9dbbac6608","last_reissued_at":"2026-05-18T02:18:14.414001Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:14.414001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05385","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:18:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e+j17Pia5E52LIBenywHbmAiI7gLNarojflmOjnfSNYSg9kMv/bR2HRk2ZXE4lcv//zf4lzpT3zF2jjC8pfuBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:44:41.220925Z"},"content_sha256":"8697d8af1ae372b254737cdf5e2c1a234a6b8d69e3b16c6d9d5420b000876e88","schema_version":"1.0","event_id":"sha256:8697d8af1ae372b254737cdf5e2c1a234a6b8d69e3b16c6d9d5420b000876e88"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:55HU42D74L72F4KFU7OM4R2QPO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Absolute continuity on paths of spatial open discrete mappings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Anatoly Golberg, Evgeny Sevost'yanov","submitted_at":"2015-04-21T11:00:58Z","abstract_excerpt":"We prove that open discrete mappings of Sobolev classes $W_{\\rm loc}^{1, p},$ $p>n-1,$ with locally integrable inner dilatations admit $ACP_p^{\\,-1}$-property, which means that these mappings are absolutely continuous on almost all preimage paths with respect to $p$-module. In particular, our results extend the well-known Poletski\\u\\i\\ lemma for quasiregular mappings. We also establish the upper bounds for $p$-module of such mappings in terms of integrals depending on the inner dilatations and arbitrary admissible functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05385","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":""},"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":"2026-05-18T02:18:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f+ymq5/5oMvVpAIWJhWLoKSVHxrg/XFEIemhSp1zP+1xWmzQXypXrYHttdsCYrvf3Wwmx+13a/2E5y9OzVviCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T02:44:41.221271Z"},"content_sha256":"7e04e994169d2de49e2469514bd6eb4df7b644671a1f3007ad46faa1610f7065","schema_version":"1.0","event_id":"sha256:7e04e994169d2de49e2469514bd6eb4df7b644671a1f3007ad46faa1610f7065"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/55HU42D74L72F4KFU7OM4R2QPO/bundle.json","state_url":"https://pith.science/pith/55HU42D74L72F4KFU7OM4R2QPO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/55HU42D74L72F4KFU7OM4R2QPO/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":"2026-06-24T02:44:41Z","links":{"resolver":"https://pith.science/pith/55HU42D74L72F4KFU7OM4R2QPO","bundle":"https://pith.science/pith/55HU42D74L72F4KFU7OM4R2QPO/bundle.json","state":"https://pith.science/pith/55HU42D74L72F4KFU7OM4R2QPO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/55HU42D74L72F4KFU7OM4R2QPO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:55HU42D74L72F4KFU7OM4R2QPO","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":"915154c11edb7c7c6a1b0914508eddaf349ded76dc9134ff731f5ab463c015e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-21T11:00:58Z","title_canon_sha256":"a908bcd9f0a5d83f4c4203b3b06bfa371a77b9c9d573e16493c1dfab216b9b35"},"schema_version":"1.0","source":{"id":"1504.05385","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05385","created_at":"2026-05-18T02:18:14Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05385v1","created_at":"2026-05-18T02:18:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05385","created_at":"2026-05-18T02:18:14Z"},{"alias_kind":"pith_short_12","alias_value":"55HU42D74L72","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"55HU42D74L72F4KF","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"55HU42D7","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:7e04e994169d2de49e2469514bd6eb4df7b644671a1f3007ad46faa1610f7065","target":"graph","created_at":"2026-05-18T02:18:14Z","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":"We prove that open discrete mappings of Sobolev classes $W_{\\rm loc}^{1, p},$ $p>n-1,$ with locally integrable inner dilatations admit $ACP_p^{\\,-1}$-property, which means that these mappings are absolutely continuous on almost all preimage paths with respect to $p$-module. In particular, our results extend the well-known Poletski\\u\\i\\ lemma for quasiregular mappings. We also establish the upper bounds for $p$-module of such mappings in terms of integrals depending on the inner dilatations and arbitrary admissible functions.","authors_text":"Anatoly Golberg, Evgeny Sevost'yanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-21T11:00:58Z","title":"Absolute continuity on paths of spatial open discrete mappings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05385","kind":"arxiv","version":1},"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":"sha256:8697d8af1ae372b254737cdf5e2c1a234a6b8d69e3b16c6d9d5420b000876e88","target":"record","created_at":"2026-05-18T02:18:14Z","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":"915154c11edb7c7c6a1b0914508eddaf349ded76dc9134ff731f5ab463c015e9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-04-21T11:00:58Z","title_canon_sha256":"a908bcd9f0a5d83f4c4203b3b06bfa371a77b9c9d573e16493c1dfab216b9b35"},"schema_version":"1.0","source":{"id":"1504.05385","kind":"arxiv","version":1}},"canonical_sha256":"ef4f4e687fe2ffa2f145a7dcce47507b936040c4286e1e378d1fba9dbbac6608","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ef4f4e687fe2ffa2f145a7dcce47507b936040c4286e1e378d1fba9dbbac6608","first_computed_at":"2026-05-18T02:18:14.414001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:14.414001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i1FioY8gGhKtMa+NqpMzWl/HixfBYOW7SPw/ADjT7rBRmyJeXXmboVZGNvUZ307wVLBQRr9Uo3NxV++PQoxIBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:14.414474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05385","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8697d8af1ae372b254737cdf5e2c1a234a6b8d69e3b16c6d9d5420b000876e88","sha256:7e04e994169d2de49e2469514bd6eb4df7b644671a1f3007ad46faa1610f7065"],"state_sha256":"9ef278973985cb3b44c9526bf8371762b87b7d378397a7dbedf00dab4853a15c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1R3egJrdCgMmuNL2yZCGP2FSflUzBVH8g+5Oq3gAA8oetxCxXVtg1QC6Ah/8MrU3PJ1bVo//+k9lr650GcO3Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T02:44:41.223179Z","bundle_sha256":"a76da1f5ae5a9e78c650d445c7115d663e6d3385d62af25a86d9b325f43c93f2"}}