{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:VODJYRGP5YQED3NBJG44CADVOO","short_pith_number":"pith:VODJYRGP","canonical_record":{"source":{"id":"1512.04328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-14T14:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"ffb07490d4f76c65ae41a0bdd993c25219cc3c140e6baeffe00fcb8780e155b6","abstract_canon_sha256":"67e0ef946ce7b5e8dc640e807f84e0567b9e0f48540634c59737d1ad0abdba5a"},"schema_version":"1.0"},"canonical_sha256":"ab869c44cfee2041eda149b9c1007573b7db629724989f10d85de8ba3e85c747","source":{"kind":"arxiv","id":"1512.04328","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04328","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04328v1","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04328","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"pith_short_12","alias_value":"VODJYRGP5YQE","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VODJYRGP5YQED3NB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VODJYRGP","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:VODJYRGP5YQED3NBJG44CADVOO","target":"record","payload":{"canonical_record":{"source":{"id":"1512.04328","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-14T14:11:45Z","cross_cats_sorted":[],"title_canon_sha256":"ffb07490d4f76c65ae41a0bdd993c25219cc3c140e6baeffe00fcb8780e155b6","abstract_canon_sha256":"67e0ef946ce7b5e8dc640e807f84e0567b9e0f48540634c59737d1ad0abdba5a"},"schema_version":"1.0"},"canonical_sha256":"ab869c44cfee2041eda149b9c1007573b7db629724989f10d85de8ba3e85c747","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:22.515415Z","signature_b64":"+HkUVkyyKBkezSOzUUxdWjWz6fAX7S2hoYBntzPb9c+UGDbINSA8J3/5Ot8VulvB3w+ucUL3U42SoRPRtBLjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab869c44cfee2041eda149b9c1007573b7db629724989f10d85de8ba3e85c747","last_reissued_at":"2026-05-18T01:24:22.514648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:22.514648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.04328","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":"2026-05-18T01:24:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C9rmsytqsKkQxJBprliBGiWkOLvHYPKAoc/jUKO0XhVw6TuGzRGg09j+1I170vFCdz/8lg3Oxjl++hrufDtTAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:57:08.457939Z"},"content_sha256":"503f1dfee07af5ae18ea04913366816c3aab9e924394e991329e3c0dfe07d959","schema_version":"1.0","event_id":"sha256:503f1dfee07af5ae18ea04913366816c3aab9e924394e991329e3c0dfe07d959"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:VODJYRGP5YQED3NBJG44CADVOO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Patrick Winkert, Rico Zacher","submitted_at":"2015-12-14T14:11:45Z","abstract_excerpt":"In this paper we study a rather wide class of quasilinear parabolic problems with nonlinear boundary condition and nonstandard growth terms. It includes the important case of equations with a $p(t,x)$-Laplacian. By means of the localization method and De Giorgi's iteration technique we derive global a priori bounds for weak solutions of such problems. Our results seem to be new even in the constant exponent case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04328","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":"2026-05-18T01:24:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"weEyhZZscepcB4LCKZ0vIGjIv/YROSCgkFePJMOAvFRu3ovLWlBnAXOHM+eiMWRYuz9LNvZemxbCXVhe8laUDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T02:57:08.458287Z"},"content_sha256":"e344aa223f2b1e38ebca1caa6ac367644b4e5d5aef7bc5312aca9f68e8fbbf4e","schema_version":"1.0","event_id":"sha256:e344aa223f2b1e38ebca1caa6ac367644b4e5d5aef7bc5312aca9f68e8fbbf4e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VODJYRGP5YQED3NBJG44CADVOO/bundle.json","state_url":"https://pith.science/pith/VODJYRGP5YQED3NBJG44CADVOO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VODJYRGP5YQED3NBJG44CADVOO/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":"2026-06-23T02:57:08Z","links":{"resolver":"https://pith.science/pith/VODJYRGP5YQED3NBJG44CADVOO","bundle":"https://pith.science/pith/VODJYRGP5YQED3NBJG44CADVOO/bundle.json","state":"https://pith.science/pith/VODJYRGP5YQED3NBJG44CADVOO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VODJYRGP5YQED3NBJG44CADVOO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:VODJYRGP5YQED3NBJG44CADVOO","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":"67e0ef946ce7b5e8dc640e807f84e0567b9e0f48540634c59737d1ad0abdba5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-14T14:11:45Z","title_canon_sha256":"ffb07490d4f76c65ae41a0bdd993c25219cc3c140e6baeffe00fcb8780e155b6"},"schema_version":"1.0","source":{"id":"1512.04328","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04328","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04328v1","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04328","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"pith_short_12","alias_value":"VODJYRGP5YQE","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"VODJYRGP5YQED3NB","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"VODJYRGP","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:e344aa223f2b1e38ebca1caa6ac367644b4e5d5aef7bc5312aca9f68e8fbbf4e","target":"graph","created_at":"2026-05-18T01:24:22Z","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 study a rather wide class of quasilinear parabolic problems with nonlinear boundary condition and nonstandard growth terms. It includes the important case of equations with a $p(t,x)$-Laplacian. By means of the localization method and De Giorgi's iteration technique we derive global a priori bounds for weak solutions of such problems. Our results seem to be new even in the constant exponent case.","authors_text":"Patrick Winkert, Rico Zacher","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-14T14:11:45Z","title":"Global a priori bounds for weak solutions to quasilinear parabolic equations with nonstandard growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04328","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":"sha256:503f1dfee07af5ae18ea04913366816c3aab9e924394e991329e3c0dfe07d959","target":"record","created_at":"2026-05-18T01:24:22Z","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":"67e0ef946ce7b5e8dc640e807f84e0567b9e0f48540634c59737d1ad0abdba5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-12-14T14:11:45Z","title_canon_sha256":"ffb07490d4f76c65ae41a0bdd993c25219cc3c140e6baeffe00fcb8780e155b6"},"schema_version":"1.0","source":{"id":"1512.04328","kind":"arxiv","version":1}},"canonical_sha256":"ab869c44cfee2041eda149b9c1007573b7db629724989f10d85de8ba3e85c747","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab869c44cfee2041eda149b9c1007573b7db629724989f10d85de8ba3e85c747","first_computed_at":"2026-05-18T01:24:22.514648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:22.514648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+HkUVkyyKBkezSOzUUxdWjWz6fAX7S2hoYBntzPb9c+UGDbINSA8J3/5Ot8VulvB3w+ucUL3U42SoRPRtBLjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:22.515415Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04328","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:503f1dfee07af5ae18ea04913366816c3aab9e924394e991329e3c0dfe07d959","sha256:e344aa223f2b1e38ebca1caa6ac367644b4e5d5aef7bc5312aca9f68e8fbbf4e"],"state_sha256":"b095096db7b7c8eb9f22f29812d1e7d07f37c08778e0dbddb9c330dffe3bac67"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4EtqLinIAFPXHhdQlJ2HlciuKsIgW5snbyMHZ8ANv+XuIHU3xuxLagDRwC5klE+xnuUfPb0DDPyr2SeVEiOlBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T02:57:08.460203Z","bundle_sha256":"2371a80e25c1df9952006db526a53fb1539d04595d907a206b222d660f9e73da"}}