{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:EDV4YD4J47GCEIMGTIMTQ542KP","short_pith_number":"pith:EDV4YD4J","canonical_record":{"source":{"id":"1503.07317","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-25T09:56:37Z","cross_cats_sorted":[],"title_canon_sha256":"6ef3fce82743d9aa247791ad0e0cac26b104ada033fde16302eadced6bde7798","abstract_canon_sha256":"facb24acbdb3bb34e6566bec10b7b44dd79bced2e509855022c489379ffd2468"},"schema_version":"1.0"},"canonical_sha256":"20ebcc0f89e7cc2221869a1938779a53cfee6a05cb2d18680306fa0421f6559d","source":{"kind":"arxiv","id":"1503.07317","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07317","created_at":"2026-05-18T02:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07317v2","created_at":"2026-05-18T02:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07317","created_at":"2026-05-18T02:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"EDV4YD4J47GC","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EDV4YD4J47GCEIMG","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EDV4YD4J","created_at":"2026-05-18T12:29:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:EDV4YD4J47GCEIMGTIMTQ542KP","target":"record","payload":{"canonical_record":{"source":{"id":"1503.07317","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-25T09:56:37Z","cross_cats_sorted":[],"title_canon_sha256":"6ef3fce82743d9aa247791ad0e0cac26b104ada033fde16302eadced6bde7798","abstract_canon_sha256":"facb24acbdb3bb34e6566bec10b7b44dd79bced2e509855022c489379ffd2468"},"schema_version":"1.0"},"canonical_sha256":"20ebcc0f89e7cc2221869a1938779a53cfee6a05cb2d18680306fa0421f6559d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:00:02.053141Z","signature_b64":"TMlageoGyCuT4y+MXHWMQytQxu61Wp77yDIlpbbXSnfDD1jeV1DxBvSt2+g89aOSzFFpFqkQWyAKTYFkF3cZCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20ebcc0f89e7cc2221869a1938779a53cfee6a05cb2d18680306fa0421f6559d","last_reissued_at":"2026-05-18T02:00:02.052677Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:00:02.052677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.07317","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":"2026-05-18T02:00:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QIgdxfFXvsdGpApc9iNPjVKCa3x+08SNtNQJ8a/soQ3PzdRSG7xCKTSeNjyNM0xIHiNZXvLq5IjlKDICLDLBDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:48:31.857210Z"},"content_sha256":"f22d99f6653795a6107c5b902b2d25c04cbc944865274c158da1b63f6badac80","schema_version":"1.0","event_id":"sha256:f22d99f6653795a6107c5b902b2d25c04cbc944865274c158da1b63f6badac80"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:EDV4YD4J47GCEIMGTIMTQ542KP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variable exponent Hardy-type inequalities in $\\mathbb{R}^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Iwona Skrzypczak, Sylwia Dudek","submitted_at":"2015-03-25T09:56:37Z","abstract_excerpt":"In this paper, we investigate further the weighted $p(x)$-Hardy inequality with the additional term of the form \\[ \\int_\\Omega |\\xi|^{p(x)}\\mu_{1,\\beta} (dx) \\leqslant \\int_\\Omega |\\nabla \\xi|^{p(x)}\\mu_{2,\\beta} (dx)+\\int_\\Omega \\left|\\xi{\\log \\xi} \\right|^{p(x)} \\mu_{3,\\beta} (dx), \\] holding for Lipschitz functions compactly supported in $\\Omega\\subseteq\\mathbb{R}^n$. The involved measures depend on a certain solution to the partial differential inequality involving $p(x)$-Laplacian ${-}\\Delta_{p(x)} u\\geqslant \\Phi$, where $\\Phi$ is a given locally integrable function, and $u$ is defined o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07317","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":"2026-05-18T02:00:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A9KUboEuJgPLsU7EGe/JkUCfbYcImw7WwG2U0wIYHqWTmfynkMtWnjDcVY2eMFCeomGQjHLA4KPA9lAX91D6BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T02:48:31.857582Z"},"content_sha256":"b9fd00d408368e45c3d3f01e7669025d88d5bcd7e0d5742705d29682e3a26622","schema_version":"1.0","event_id":"sha256:b9fd00d408368e45c3d3f01e7669025d88d5bcd7e0d5742705d29682e3a26622"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EDV4YD4J47GCEIMGTIMTQ542KP/bundle.json","state_url":"https://pith.science/pith/EDV4YD4J47GCEIMGTIMTQ542KP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EDV4YD4J47GCEIMGTIMTQ542KP/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":"2026-06-04T02:48:31Z","links":{"resolver":"https://pith.science/pith/EDV4YD4J47GCEIMGTIMTQ542KP","bundle":"https://pith.science/pith/EDV4YD4J47GCEIMGTIMTQ542KP/bundle.json","state":"https://pith.science/pith/EDV4YD4J47GCEIMGTIMTQ542KP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EDV4YD4J47GCEIMGTIMTQ542KP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:EDV4YD4J47GCEIMGTIMTQ542KP","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":"facb24acbdb3bb34e6566bec10b7b44dd79bced2e509855022c489379ffd2468","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-25T09:56:37Z","title_canon_sha256":"6ef3fce82743d9aa247791ad0e0cac26b104ada033fde16302eadced6bde7798"},"schema_version":"1.0","source":{"id":"1503.07317","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07317","created_at":"2026-05-18T02:00:02Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07317v2","created_at":"2026-05-18T02:00:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07317","created_at":"2026-05-18T02:00:02Z"},{"alias_kind":"pith_short_12","alias_value":"EDV4YD4J47GC","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"EDV4YD4J47GCEIMG","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"EDV4YD4J","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:b9fd00d408368e45c3d3f01e7669025d88d5bcd7e0d5742705d29682e3a26622","target":"graph","created_at":"2026-05-18T02:00:02Z","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":"In this paper, we investigate further the weighted $p(x)$-Hardy inequality with the additional term of the form \\[ \\int_\\Omega |\\xi|^{p(x)}\\mu_{1,\\beta} (dx) \\leqslant \\int_\\Omega |\\nabla \\xi|^{p(x)}\\mu_{2,\\beta} (dx)+\\int_\\Omega \\left|\\xi{\\log \\xi} \\right|^{p(x)} \\mu_{3,\\beta} (dx), \\] holding for Lipschitz functions compactly supported in $\\Omega\\subseteq\\mathbb{R}^n$. The involved measures depend on a certain solution to the partial differential inequality involving $p(x)$-Laplacian ${-}\\Delta_{p(x)} u\\geqslant \\Phi$, where $\\Phi$ is a given locally integrable function, and $u$ is defined o","authors_text":"Iwona Skrzypczak, Sylwia Dudek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-25T09:56:37Z","title":"Variable exponent Hardy-type inequalities in $\\mathbb{R}^n$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07317","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:f22d99f6653795a6107c5b902b2d25c04cbc944865274c158da1b63f6badac80","target":"record","created_at":"2026-05-18T02:00:02Z","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":"facb24acbdb3bb34e6566bec10b7b44dd79bced2e509855022c489379ffd2468","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-25T09:56:37Z","title_canon_sha256":"6ef3fce82743d9aa247791ad0e0cac26b104ada033fde16302eadced6bde7798"},"schema_version":"1.0","source":{"id":"1503.07317","kind":"arxiv","version":2}},"canonical_sha256":"20ebcc0f89e7cc2221869a1938779a53cfee6a05cb2d18680306fa0421f6559d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20ebcc0f89e7cc2221869a1938779a53cfee6a05cb2d18680306fa0421f6559d","first_computed_at":"2026-05-18T02:00:02.052677Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:00:02.052677Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TMlageoGyCuT4y+MXHWMQytQxu61Wp77yDIlpbbXSnfDD1jeV1DxBvSt2+g89aOSzFFpFqkQWyAKTYFkF3cZCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:00:02.053141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07317","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f22d99f6653795a6107c5b902b2d25c04cbc944865274c158da1b63f6badac80","sha256:b9fd00d408368e45c3d3f01e7669025d88d5bcd7e0d5742705d29682e3a26622"],"state_sha256":"e2b8707e3073ff475e464dce6daa3bf5a5c86bbf3b7508d837ee6632478f39f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"574P9A9AxtPemVd8WKkPQJXj1gsq1XP3m8PahJshVGIxNwSnGWnyhzxny5WnfXNidgGtTqRQ9WZpce+Rx6OVDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T02:48:31.859563Z","bundle_sha256":"ccf1a1cc81f3ee12562ed9f0958c3eb2f1094d5c5e0545af217722a9b7a8c5ff"}}