{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:4APDNBA53KOXW4DPF67Z74JVIV","short_pith_number":"pith:4APDNBA5","canonical_record":{"source":{"id":"1104.2197","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-12T12:55:22Z","cross_cats_sorted":[],"title_canon_sha256":"c5639584b998c7345990ffd4e1ba2fc625116ba911343366344cfe7fde90e98b","abstract_canon_sha256":"3fa474e3f154befdc952813702f1a57ac7ada61b40af9a0e574610e87ceb281f"},"schema_version":"1.0"},"canonical_sha256":"e01e36841dda9d7b706f2fbf9ff135455ba0af3327458fab2e24f54627712497","source":{"kind":"arxiv","id":"1104.2197","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2197","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2197v1","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2197","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"4APDNBA53KOX","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4APDNBA53KOXW4DP","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4APDNBA5","created_at":"2026-05-18T12:26:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:4APDNBA53KOXW4DPF67Z74JVIV","target":"record","payload":{"canonical_record":{"source":{"id":"1104.2197","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-12T12:55:22Z","cross_cats_sorted":[],"title_canon_sha256":"c5639584b998c7345990ffd4e1ba2fc625116ba911343366344cfe7fde90e98b","abstract_canon_sha256":"3fa474e3f154befdc952813702f1a57ac7ada61b40af9a0e574610e87ceb281f"},"schema_version":"1.0"},"canonical_sha256":"e01e36841dda9d7b706f2fbf9ff135455ba0af3327458fab2e24f54627712497","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:24:35.768737Z","signature_b64":"Q7tH/i4lbuYImH8gI1TyLkRVFO6OT4d9gB2aMN0XOpzA74zobLgYSs4DgcwZMWpuNx54/VKJTsiLN29uiVTrCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e01e36841dda9d7b706f2fbf9ff135455ba0af3327458fab2e24f54627712497","last_reissued_at":"2026-05-18T04:24:35.768342Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:24:35.768342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.2197","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":"2026-05-18T04:24:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hthDozaHT7ICkxXgipMTudgiUGxMQxZpjYD8uTjNDn6/H4XomjSu7UoIu3OiLB9kZ0ZtSoB//TINDj6C+cxtAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:50:00.253730Z"},"content_sha256":"3838ec5d2733ccd01bacf27ff197c42577fcf66925600ef6700025ed34a65495","schema_version":"1.0","event_id":"sha256:3838ec5d2733ccd01bacf27ff197c42577fcf66925600ef6700025ed34a65495"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:4APDNBA53KOXW4DPF67Z74JVIV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A new proof for the equivalence of weak and viscosity solutions for the $p$-Laplace equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Petri Juutinen, Vesa Julin","submitted_at":"2011-04-12T12:55:22Z","abstract_excerpt":"In this paper, we give a new proof for the fact that the distributional weak solutions and the viscosity solutions of the $p$-Laplace equation $-\\diver(\\abs{Du}^{p-2}Du)=0$ coincide. Our proof is more direct and transparent than the original one by Juutinen, Lindqvist and Manfredi \\cite{jlm}, which relied on the full uniqueness machinery of the theory of viscosity solutions. We establish a similar result also for the solutions of the non-homogeneous version of the $p$-Laplace equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2197","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":"2026-05-18T04:24:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MCEkWWt5DFQjWJqj62Ju7LXSBkHWXOxycUR0yRPU1+u0d1oqcXMzav7gFrbS7nGFfWAMbmhW8tcsLwyc+RznAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T02:50:00.254072Z"},"content_sha256":"0796494d36d62ddb473467400595cc7826e75b8b73968c86dd3d4b0dad695ca4","schema_version":"1.0","event_id":"sha256:0796494d36d62ddb473467400595cc7826e75b8b73968c86dd3d4b0dad695ca4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4APDNBA53KOXW4DPF67Z74JVIV/bundle.json","state_url":"https://pith.science/pith/4APDNBA53KOXW4DPF67Z74JVIV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4APDNBA53KOXW4DPF67Z74JVIV/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":"2026-05-31T02:50:00Z","links":{"resolver":"https://pith.science/pith/4APDNBA53KOXW4DPF67Z74JVIV","bundle":"https://pith.science/pith/4APDNBA53KOXW4DPF67Z74JVIV/bundle.json","state":"https://pith.science/pith/4APDNBA53KOXW4DPF67Z74JVIV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4APDNBA53KOXW4DPF67Z74JVIV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4APDNBA53KOXW4DPF67Z74JVIV","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":"3fa474e3f154befdc952813702f1a57ac7ada61b40af9a0e574610e87ceb281f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-12T12:55:22Z","title_canon_sha256":"c5639584b998c7345990ffd4e1ba2fc625116ba911343366344cfe7fde90e98b"},"schema_version":"1.0","source":{"id":"1104.2197","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.2197","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"arxiv_version","alias_value":"1104.2197v1","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.2197","created_at":"2026-05-18T04:24:35Z"},{"alias_kind":"pith_short_12","alias_value":"4APDNBA53KOX","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4APDNBA53KOXW4DP","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4APDNBA5","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:0796494d36d62ddb473467400595cc7826e75b8b73968c86dd3d4b0dad695ca4","target":"graph","created_at":"2026-05-18T04:24:35Z","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 give a new proof for the fact that the distributional weak solutions and the viscosity solutions of the $p$-Laplace equation $-\\diver(\\abs{Du}^{p-2}Du)=0$ coincide. Our proof is more direct and transparent than the original one by Juutinen, Lindqvist and Manfredi \\cite{jlm}, which relied on the full uniqueness machinery of the theory of viscosity solutions. We establish a similar result also for the solutions of the non-homogeneous version of the $p$-Laplace equation.","authors_text":"Petri Juutinen, Vesa Julin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-12T12:55:22Z","title":"A new proof for the equivalence of weak and viscosity solutions for the $p$-Laplace equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.2197","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":"sha256:3838ec5d2733ccd01bacf27ff197c42577fcf66925600ef6700025ed34a65495","target":"record","created_at":"2026-05-18T04:24:35Z","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":"3fa474e3f154befdc952813702f1a57ac7ada61b40af9a0e574610e87ceb281f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-04-12T12:55:22Z","title_canon_sha256":"c5639584b998c7345990ffd4e1ba2fc625116ba911343366344cfe7fde90e98b"},"schema_version":"1.0","source":{"id":"1104.2197","kind":"arxiv","version":1}},"canonical_sha256":"e01e36841dda9d7b706f2fbf9ff135455ba0af3327458fab2e24f54627712497","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e01e36841dda9d7b706f2fbf9ff135455ba0af3327458fab2e24f54627712497","first_computed_at":"2026-05-18T04:24:35.768342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:24:35.768342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Q7tH/i4lbuYImH8gI1TyLkRVFO6OT4d9gB2aMN0XOpzA74zobLgYSs4DgcwZMWpuNx54/VKJTsiLN29uiVTrCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:24:35.768737Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.2197","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3838ec5d2733ccd01bacf27ff197c42577fcf66925600ef6700025ed34a65495","sha256:0796494d36d62ddb473467400595cc7826e75b8b73968c86dd3d4b0dad695ca4"],"state_sha256":"9167ba5000b92a9b80414a1e1585177fda69198241d478a8aec533e735ab3881"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"amAR0JzmUs0gRv3pQvIMXjod0+gdT/HVG+LRmXemg5ZIXJ1HwjNbNOh1JdrG9aS41KJIQyRJrlgTyW9lqmhqBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T02:50:00.255931Z","bundle_sha256":"a11f23a7d15c6d679b9a6655246bc38dceb69a2024ccc8a7036dc950319ce31b"}}