{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:KE44EGXMSAG5FWSKJNC3F2SW5U","short_pith_number":"pith:KE44EGXM","canonical_record":{"source":{"id":"1810.04097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-09T16:04:26Z","cross_cats_sorted":[],"title_canon_sha256":"b0acfec9fb99c3dababa28174de16531e219eb6b51ce202d6649d3be58e80b15","abstract_canon_sha256":"8552d7ed4e5b765806afced3266fdf4be5a3210fea6968a98a5cc2ad05556561"},"schema_version":"1.0"},"canonical_sha256":"5139c21aec900dd2da4a4b45b2ea56ed0e9615a6ddb44ad73f1dc1e571867c5d","source":{"kind":"arxiv","id":"1810.04097","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04097","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04097v1","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04097","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"pith_short_12","alias_value":"KE44EGXMSAG5","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KE44EGXMSAG5FWSK","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KE44EGXM","created_at":"2026-05-18T12:32:33Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:KE44EGXMSAG5FWSKJNC3F2SW5U","target":"record","payload":{"canonical_record":{"source":{"id":"1810.04097","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-09T16:04:26Z","cross_cats_sorted":[],"title_canon_sha256":"b0acfec9fb99c3dababa28174de16531e219eb6b51ce202d6649d3be58e80b15","abstract_canon_sha256":"8552d7ed4e5b765806afced3266fdf4be5a3210fea6968a98a5cc2ad05556561"},"schema_version":"1.0"},"canonical_sha256":"5139c21aec900dd2da4a4b45b2ea56ed0e9615a6ddb44ad73f1dc1e571867c5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:42.283527Z","signature_b64":"BdstYBS9G4s15dldAbKu+RpfngVMObaGZ8ToCEt8vgfBLpQzRnrxOQwd9PQYdkhmpaRT6GoN/fIHKdt5WvjUCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5139c21aec900dd2da4a4b45b2ea56ed0e9615a6ddb44ad73f1dc1e571867c5d","last_reissued_at":"2026-05-18T00:03:42.282965Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:42.282965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.04097","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":"2026-05-18T00:03:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s7cC7Ym7VT7sGj7xVSzsovdOLGK+5ELs5C8OSQtZY/M7sw6sHBBMH+0AF1v1IFZt1i2C+S6cPMTX8TWYT713CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:50:32.532480Z"},"content_sha256":"2160782dccac82998078a73396b05dfeb8ad6afb1715acedacbdcd29d9c83dd7","schema_version":"1.0","event_id":"sha256:2160782dccac82998078a73396b05dfeb8ad6afb1715acedacbdcd29d9c83dd7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:KE44EGXMSAG5FWSKJNC3F2SW5U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On coupled systems of PDEs with unbounded coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luca Lorenzi, Luciana Angiuli","submitted_at":"2018-10-09T16:04:26Z","abstract_excerpt":"We study the Cauchy problem associated to parabolic systems of the form $D_t\\boldsymbol{u}=\\boldsymbol{\\mathcal A}(t)\\boldsymbol u$ in $C_b(\\mathbb{R}^d;\\mathbb{R}^m)$, the space of continuous and bounded functions $\\boldsymbol{f}:\\mathbb{R}^d\\to\\mathbb{R}^m$. Here $\\boldsymbol{\\mathcal A}(t)$ is a weakly coupled elliptic operator acting on vector-valued functions, having diffusion and drift coefficients which change from equation to equation. We prove existence and uniqueness of the evolution operator $\\boldsymbol{G}(t,s)$ which governs the problem in $C_b(\\mathbb{R}^d;\\mathbb{R}^m)$ proving "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04097","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":"2026-05-18T00:03:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yeh1n+wmyIg33dshgzFVsJIVDFZCw+Cs7MDJBvRazzFNEdpE8X/5uqmvTj8qOhPnNcOMPKzw4Qu/MomrBxltBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T00:50:32.532824Z"},"content_sha256":"eb5a0e0a0080c2ec1e7ad87e50994ad6c29a58aed357fd0beb1ec04e536ce3d7","schema_version":"1.0","event_id":"sha256:eb5a0e0a0080c2ec1e7ad87e50994ad6c29a58aed357fd0beb1ec04e536ce3d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KE44EGXMSAG5FWSKJNC3F2SW5U/bundle.json","state_url":"https://pith.science/pith/KE44EGXMSAG5FWSKJNC3F2SW5U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KE44EGXMSAG5FWSKJNC3F2SW5U/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":"2026-06-26T00:50:32Z","links":{"resolver":"https://pith.science/pith/KE44EGXMSAG5FWSKJNC3F2SW5U","bundle":"https://pith.science/pith/KE44EGXMSAG5FWSKJNC3F2SW5U/bundle.json","state":"https://pith.science/pith/KE44EGXMSAG5FWSKJNC3F2SW5U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KE44EGXMSAG5FWSKJNC3F2SW5U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:KE44EGXMSAG5FWSKJNC3F2SW5U","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":"8552d7ed4e5b765806afced3266fdf4be5a3210fea6968a98a5cc2ad05556561","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-09T16:04:26Z","title_canon_sha256":"b0acfec9fb99c3dababa28174de16531e219eb6b51ce202d6649d3be58e80b15"},"schema_version":"1.0","source":{"id":"1810.04097","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.04097","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"arxiv_version","alias_value":"1810.04097v1","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.04097","created_at":"2026-05-18T00:03:42Z"},{"alias_kind":"pith_short_12","alias_value":"KE44EGXMSAG5","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_16","alias_value":"KE44EGXMSAG5FWSK","created_at":"2026-05-18T12:32:33Z"},{"alias_kind":"pith_short_8","alias_value":"KE44EGXM","created_at":"2026-05-18T12:32:33Z"}],"graph_snapshots":[{"event_id":"sha256:eb5a0e0a0080c2ec1e7ad87e50994ad6c29a58aed357fd0beb1ec04e536ce3d7","target":"graph","created_at":"2026-05-18T00:03:42Z","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 study the Cauchy problem associated to parabolic systems of the form $D_t\\boldsymbol{u}=\\boldsymbol{\\mathcal A}(t)\\boldsymbol u$ in $C_b(\\mathbb{R}^d;\\mathbb{R}^m)$, the space of continuous and bounded functions $\\boldsymbol{f}:\\mathbb{R}^d\\to\\mathbb{R}^m$. Here $\\boldsymbol{\\mathcal A}(t)$ is a weakly coupled elliptic operator acting on vector-valued functions, having diffusion and drift coefficients which change from equation to equation. We prove existence and uniqueness of the evolution operator $\\boldsymbol{G}(t,s)$ which governs the problem in $C_b(\\mathbb{R}^d;\\mathbb{R}^m)$ proving ","authors_text":"Luca Lorenzi, Luciana Angiuli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-09T16:04:26Z","title":"On coupled systems of PDEs with unbounded coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.04097","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":"sha256:2160782dccac82998078a73396b05dfeb8ad6afb1715acedacbdcd29d9c83dd7","target":"record","created_at":"2026-05-18T00:03:42Z","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":"8552d7ed4e5b765806afced3266fdf4be5a3210fea6968a98a5cc2ad05556561","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2018-10-09T16:04:26Z","title_canon_sha256":"b0acfec9fb99c3dababa28174de16531e219eb6b51ce202d6649d3be58e80b15"},"schema_version":"1.0","source":{"id":"1810.04097","kind":"arxiv","version":1}},"canonical_sha256":"5139c21aec900dd2da4a4b45b2ea56ed0e9615a6ddb44ad73f1dc1e571867c5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5139c21aec900dd2da4a4b45b2ea56ed0e9615a6ddb44ad73f1dc1e571867c5d","first_computed_at":"2026-05-18T00:03:42.282965Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:42.282965Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BdstYBS9G4s15dldAbKu+RpfngVMObaGZ8ToCEt8vgfBLpQzRnrxOQwd9PQYdkhmpaRT6GoN/fIHKdt5WvjUCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:42.283527Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.04097","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2160782dccac82998078a73396b05dfeb8ad6afb1715acedacbdcd29d9c83dd7","sha256:eb5a0e0a0080c2ec1e7ad87e50994ad6c29a58aed357fd0beb1ec04e536ce3d7"],"state_sha256":"0b4a5fa68981ba6890c17dbb5abd60238a2c7ce7310de328a2766cb04aedf28b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dhbKvt5npbi7zldMtrQkxj9soQDQ/VzwK/1GtIAQBOUiIMvzSU/9l2JNrVLHqraCI4fLFnXsjo6xqgIYHuJ+Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T00:50:32.534670Z","bundle_sha256":"646e01599ee0cade5fa76f61c9fa5f8ab8ac9e6902a048f832976fd12a559758"}}