{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GZ3IO5ONEBIZPNJFUBBJRNT76A","short_pith_number":"pith:GZ3IO5ON","canonical_record":{"source":{"id":"1605.05552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-18T12:35:04Z","cross_cats_sorted":[],"title_canon_sha256":"f9f22c469d7f4d1f6748774e86821c0a2513be8b077bc84df846b35b9f97fc97","abstract_canon_sha256":"c67695cbcf0d72bc5f310f61a47f46feaf89a2b6ee775f99e81eab4f7d4b3dbf"},"schema_version":"1.0"},"canonical_sha256":"36768775cd205197b525a04298b67ff03f1f79273bc46d90d0fa2dae63e14b39","source":{"kind":"arxiv","id":"1605.05552","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05552","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05552v1","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05552","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"pith_short_12","alias_value":"GZ3IO5ONEBIZ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GZ3IO5ONEBIZPNJF","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GZ3IO5ON","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GZ3IO5ONEBIZPNJFUBBJRNT76A","target":"record","payload":{"canonical_record":{"source":{"id":"1605.05552","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-18T12:35:04Z","cross_cats_sorted":[],"title_canon_sha256":"f9f22c469d7f4d1f6748774e86821c0a2513be8b077bc84df846b35b9f97fc97","abstract_canon_sha256":"c67695cbcf0d72bc5f310f61a47f46feaf89a2b6ee775f99e81eab4f7d4b3dbf"},"schema_version":"1.0"},"canonical_sha256":"36768775cd205197b525a04298b67ff03f1f79273bc46d90d0fa2dae63e14b39","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:34.620313Z","signature_b64":"RzJscDBDI1PjOUDmtvfzbKfl6J10mmvLInwv+SdgybJAeKq8V4VYP40Hfsgta3zbq8D6bmoaewsz13DXZ2hLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36768775cd205197b525a04298b67ff03f1f79273bc46d90d0fa2dae63e14b39","last_reissued_at":"2026-05-18T01:14:34.619739Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:34.619739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.05552","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":"2026-05-18T01:14:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eDpeiRRt7+0LA+fDiy0r7Ro4I+zTVi5MIg7Uh5AwM/y3dSHn6IbKer7jDrPDe4mXojkuYrkO9frBsDOZTOBjCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:50:45.102589Z"},"content_sha256":"3e6ad83a2e793139b74b9a5ab9c871f58e1f36d5579c57007a1a751a5ce688e2","schema_version":"1.0","event_id":"sha256:3e6ad83a2e793139b74b9a5ab9c871f58e1f36d5579c57007a1a751a5ce688e2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GZ3IO5ONEBIZPNJFUBBJRNT76A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Caccioppoli--type estimates and Hardy--type inequalities derived from degenerated $p$--harmonic problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Agnieszka Ka{\\l}amajska, Iwona Skrzypczak, Pavel Dr\\'abek","submitted_at":"2016-05-18T12:35:04Z","abstract_excerpt":"We obtain Caccioppoli--type estimates for nontrivial and nonnegative solutions to the anticoercive partial differential inequalities of elliptic type involving degenerated $p$--Laplacian: $-\\Delta_{p,a} u:= -\\mathrm{div}(a(x)|\\na u|^{p-2}\\na u)\\ge b(x)\\Phi (u)$, where $u$ is defined in a domain $\\Omega$. Using Caccioppoli--type estimates, we obtain several variants of Hardy--type inequalities in weighted Sobolev spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05552","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":"2026-05-18T01:14:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fHaVm44taEekxHbUU56AHmw8wg5Db0/UIjhLtt/elhvutjcxnRexJEDjUt1Z5qgP6rc/G8DVrddtRoM3tvQ2Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T08:50:45.102922Z"},"content_sha256":"cc0fa971fe70bd8bef437fe291610a636f97cf8e0d00871fdb0542b1f70d448e","schema_version":"1.0","event_id":"sha256:cc0fa971fe70bd8bef437fe291610a636f97cf8e0d00871fdb0542b1f70d448e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GZ3IO5ONEBIZPNJFUBBJRNT76A/bundle.json","state_url":"https://pith.science/pith/GZ3IO5ONEBIZPNJFUBBJRNT76A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GZ3IO5ONEBIZPNJFUBBJRNT76A/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":"2026-06-21T08:50:45Z","links":{"resolver":"https://pith.science/pith/GZ3IO5ONEBIZPNJFUBBJRNT76A","bundle":"https://pith.science/pith/GZ3IO5ONEBIZPNJFUBBJRNT76A/bundle.json","state":"https://pith.science/pith/GZ3IO5ONEBIZPNJFUBBJRNT76A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GZ3IO5ONEBIZPNJFUBBJRNT76A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GZ3IO5ONEBIZPNJFUBBJRNT76A","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":"c67695cbcf0d72bc5f310f61a47f46feaf89a2b6ee775f99e81eab4f7d4b3dbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-18T12:35:04Z","title_canon_sha256":"f9f22c469d7f4d1f6748774e86821c0a2513be8b077bc84df846b35b9f97fc97"},"schema_version":"1.0","source":{"id":"1605.05552","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.05552","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"arxiv_version","alias_value":"1605.05552v1","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05552","created_at":"2026-05-18T01:14:34Z"},{"alias_kind":"pith_short_12","alias_value":"GZ3IO5ONEBIZ","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GZ3IO5ONEBIZPNJF","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GZ3IO5ON","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:cc0fa971fe70bd8bef437fe291610a636f97cf8e0d00871fdb0542b1f70d448e","target":"graph","created_at":"2026-05-18T01:14:34Z","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 obtain Caccioppoli--type estimates for nontrivial and nonnegative solutions to the anticoercive partial differential inequalities of elliptic type involving degenerated $p$--Laplacian: $-\\Delta_{p,a} u:= -\\mathrm{div}(a(x)|\\na u|^{p-2}\\na u)\\ge b(x)\\Phi (u)$, where $u$ is defined in a domain $\\Omega$. Using Caccioppoli--type estimates, we obtain several variants of Hardy--type inequalities in weighted Sobolev spaces.","authors_text":"Agnieszka Ka{\\l}amajska, Iwona Skrzypczak, Pavel Dr\\'abek","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-18T12:35:04Z","title":"Caccioppoli--type estimates and Hardy--type inequalities derived from degenerated $p$--harmonic problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05552","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":"sha256:3e6ad83a2e793139b74b9a5ab9c871f58e1f36d5579c57007a1a751a5ce688e2","target":"record","created_at":"2026-05-18T01:14:34Z","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":"c67695cbcf0d72bc5f310f61a47f46feaf89a2b6ee775f99e81eab4f7d4b3dbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-05-18T12:35:04Z","title_canon_sha256":"f9f22c469d7f4d1f6748774e86821c0a2513be8b077bc84df846b35b9f97fc97"},"schema_version":"1.0","source":{"id":"1605.05552","kind":"arxiv","version":1}},"canonical_sha256":"36768775cd205197b525a04298b67ff03f1f79273bc46d90d0fa2dae63e14b39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36768775cd205197b525a04298b67ff03f1f79273bc46d90d0fa2dae63e14b39","first_computed_at":"2026-05-18T01:14:34.619739Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:34.619739Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RzJscDBDI1PjOUDmtvfzbKfl6J10mmvLInwv+SdgybJAeKq8V4VYP40Hfsgta3zbq8D6bmoaewsz13DXZ2hLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:34.620313Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.05552","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3e6ad83a2e793139b74b9a5ab9c871f58e1f36d5579c57007a1a751a5ce688e2","sha256:cc0fa971fe70bd8bef437fe291610a636f97cf8e0d00871fdb0542b1f70d448e"],"state_sha256":"18d2cf56694e249a62b93c6d805bd460214f62b630412cb424f5b30e50debef5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fq8C2N0hx6poO9a9yApY9MepOKe70+shRCmm5Zaa7zG1km0nLE/MJZdP6jbI48j9F3/3UHHd/3k2gCyAIRGjDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T08:50:45.104786Z","bundle_sha256":"085bf174d70a3fa8de792af43633c0485e9c1366ce986c7a524a701d0d70e37f"}}