{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZXMT46QC5U5KWBESH2KKQ44SQD","short_pith_number":"pith:ZXMT46QC","canonical_record":{"source":{"id":"1610.06726","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-21T10:05:28Z","cross_cats_sorted":[],"title_canon_sha256":"65014a919699ba97abc71c76ef0371486a81d9b3072a6dee5ee7c3ee9e30c5dd","abstract_canon_sha256":"8b1e60ef11860b9e32a098bd7e6b9ff452634080a83461a38d001e9d04b3206a"},"schema_version":"1.0"},"canonical_sha256":"cdd93e7a02ed3aab04923e94a8739280ebd85cdbc2899ba954591a9f055e336a","source":{"kind":"arxiv","id":"1610.06726","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06726","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06726v2","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06726","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZXMT46QC5U5K","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZXMT46QC5U5KWBES","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZXMT46QC","created_at":"2026-05-18T12:30:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZXMT46QC5U5KWBESH2KKQ44SQD","target":"record","payload":{"canonical_record":{"source":{"id":"1610.06726","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-21T10:05:28Z","cross_cats_sorted":[],"title_canon_sha256":"65014a919699ba97abc71c76ef0371486a81d9b3072a6dee5ee7c3ee9e30c5dd","abstract_canon_sha256":"8b1e60ef11860b9e32a098bd7e6b9ff452634080a83461a38d001e9d04b3206a"},"schema_version":"1.0"},"canonical_sha256":"cdd93e7a02ed3aab04923e94a8739280ebd85cdbc2899ba954591a9f055e336a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:45.308447Z","signature_b64":"NB1rgrxDgX86hBD9MK9OMOp9YxjhEMxlk5kvMfXJQd0LFG993+WivxSgNTZO66z3dWYAdql8cK+jnjhRtJZtDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cdd93e7a02ed3aab04923e94a8739280ebd85cdbc2899ba954591a9f055e336a","last_reissued_at":"2026-05-18T00:56:45.307649Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:45.307649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1610.06726","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":"2026-05-18T00:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ysSQGB2tJagks3LX3zfYn1rWTuFiGh6FkuW7MS+pBFSsSh4/+s1EKK3Z25z0Ab/rbqOUo+vmnm0TPTyAn2OTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:15:05.981047Z"},"content_sha256":"65c97f5205f6d368a907f20ac431604b7e57335e0dc9b7923c13468b8b2ddb83","schema_version":"1.0","event_id":"sha256:65c97f5205f6d368a907f20ac431604b7e57335e0dc9b7923c13468b8b2ddb83"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZXMT46QC5U5KWBESH2KKQ44SQD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasilinear generalized parabolic Anderson model equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Arnaud Debussche, Ismael Bailleul, Martina Hofmanova","submitted_at":"2016-10-21T10:05:28Z","abstract_excerpt":"We present in this note a local in time well-posedness result for the singular $2$-dimensional quasilinear generalized parabolic Anderson model equation $$ \\partial_t u - a(u)\\Delta u = g(u)\\xi $$ The key idea of our approach is a simple transformation of the equation which allows to treat the problem as a semilinear problem. The analysis is done within the elementary setting of paracontrolled calculus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06726","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":"2026-05-18T00:56:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eDf/Sd8daxL0xLPb2sIwvQmAiarXtJIPTdvfbwSfW+7B42JNEzpRzTOroBpmQl0ZAnNcBONrJTqNkUxGLAm4Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T12:15:05.981661Z"},"content_sha256":"316fec39c1799771894a400f15dd16a3ac3573032ed2ad9d24d9c8cb5e312d93","schema_version":"1.0","event_id":"sha256:316fec39c1799771894a400f15dd16a3ac3573032ed2ad9d24d9c8cb5e312d93"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZXMT46QC5U5KWBESH2KKQ44SQD/bundle.json","state_url":"https://pith.science/pith/ZXMT46QC5U5KWBESH2KKQ44SQD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZXMT46QC5U5KWBESH2KKQ44SQD/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":"2026-05-27T12:15:05Z","links":{"resolver":"https://pith.science/pith/ZXMT46QC5U5KWBESH2KKQ44SQD","bundle":"https://pith.science/pith/ZXMT46QC5U5KWBESH2KKQ44SQD/bundle.json","state":"https://pith.science/pith/ZXMT46QC5U5KWBESH2KKQ44SQD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZXMT46QC5U5KWBESH2KKQ44SQD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZXMT46QC5U5KWBESH2KKQ44SQD","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":"8b1e60ef11860b9e32a098bd7e6b9ff452634080a83461a38d001e9d04b3206a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-21T10:05:28Z","title_canon_sha256":"65014a919699ba97abc71c76ef0371486a81d9b3072a6dee5ee7c3ee9e30c5dd"},"schema_version":"1.0","source":{"id":"1610.06726","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1610.06726","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"arxiv_version","alias_value":"1610.06726v2","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06726","created_at":"2026-05-18T00:56:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZXMT46QC5U5K","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_16","alias_value":"ZXMT46QC5U5KWBES","created_at":"2026-05-18T12:30:55Z"},{"alias_kind":"pith_short_8","alias_value":"ZXMT46QC","created_at":"2026-05-18T12:30:55Z"}],"graph_snapshots":[{"event_id":"sha256:316fec39c1799771894a400f15dd16a3ac3573032ed2ad9d24d9c8cb5e312d93","target":"graph","created_at":"2026-05-18T00:56:45Z","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 present in this note a local in time well-posedness result for the singular $2$-dimensional quasilinear generalized parabolic Anderson model equation $$ \\partial_t u - a(u)\\Delta u = g(u)\\xi $$ The key idea of our approach is a simple transformation of the equation which allows to treat the problem as a semilinear problem. The analysis is done within the elementary setting of paracontrolled calculus.","authors_text":"Arnaud Debussche, Ismael Bailleul, Martina Hofmanova","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-21T10:05:28Z","title":"Quasilinear generalized parabolic Anderson model equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06726","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":"sha256:65c97f5205f6d368a907f20ac431604b7e57335e0dc9b7923c13468b8b2ddb83","target":"record","created_at":"2026-05-18T00:56:45Z","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":"8b1e60ef11860b9e32a098bd7e6b9ff452634080a83461a38d001e9d04b3206a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-10-21T10:05:28Z","title_canon_sha256":"65014a919699ba97abc71c76ef0371486a81d9b3072a6dee5ee7c3ee9e30c5dd"},"schema_version":"1.0","source":{"id":"1610.06726","kind":"arxiv","version":2}},"canonical_sha256":"cdd93e7a02ed3aab04923e94a8739280ebd85cdbc2899ba954591a9f055e336a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cdd93e7a02ed3aab04923e94a8739280ebd85cdbc2899ba954591a9f055e336a","first_computed_at":"2026-05-18T00:56:45.307649Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:45.307649Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NB1rgrxDgX86hBD9MK9OMOp9YxjhEMxlk5kvMfXJQd0LFG993+WivxSgNTZO66z3dWYAdql8cK+jnjhRtJZtDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:45.308447Z","signed_message":"canonical_sha256_bytes"},"source_id":"1610.06726","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:65c97f5205f6d368a907f20ac431604b7e57335e0dc9b7923c13468b8b2ddb83","sha256:316fec39c1799771894a400f15dd16a3ac3573032ed2ad9d24d9c8cb5e312d93"],"state_sha256":"fde7a182356f31b9ad7574793310731633483ee565f1be7b9fd58ce565bccdf4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OcwqQf9C+8CgvlOiWhbNcFE4ZlTlfB04gW2y9vy7acC96owsOht9zHl2C8yg0gTjv4XWGQ4seAglK9uA07o/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T12:15:05.984894Z","bundle_sha256":"e5f84eaf6dbf21aa0b541b40a4bed662156933a2e3f0576ba6272df6399ba621"}}