{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:D6I64XGZVVA2SLWYNYMECANZ3X","short_pith_number":"pith:D6I64XGZ","canonical_record":{"source":{"id":"1906.04145","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-10T17:35:23Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"d26e680e1ae86a40c4ce6d117cd23f9ba10999f23f9bc0c428b7266ac11698c4","abstract_canon_sha256":"176ce3b5269fff34e455b2df095fefbb88bfcf4eb0a7d460b6adab6cb08c9a8a"},"schema_version":"1.0"},"canonical_sha256":"1f91ee5cd9ad41a92ed86e184101b9ddcc86cf2a68371c31f62d88a4900ccb73","source":{"kind":"arxiv","id":"1906.04145","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.04145","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"1906.04145v1","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04145","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"D6I64XGZVVA2","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"D6I64XGZVVA2SLWY","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"D6I64XGZ","created_at":"2026-05-18T12:33:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:D6I64XGZVVA2SLWYNYMECANZ3X","target":"record","payload":{"canonical_record":{"source":{"id":"1906.04145","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-10T17:35:23Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"d26e680e1ae86a40c4ce6d117cd23f9ba10999f23f9bc0c428b7266ac11698c4","abstract_canon_sha256":"176ce3b5269fff34e455b2df095fefbb88bfcf4eb0a7d460b6adab6cb08c9a8a"},"schema_version":"1.0"},"canonical_sha256":"1f91ee5cd9ad41a92ed86e184101b9ddcc86cf2a68371c31f62d88a4900ccb73","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:43:43.764370Z","signature_b64":"wDKA6EjImY85v5vilfjMARwkIYNNcDh9EWLLYc/n+XtXvPFFmp1eNsL2+iRfxEs26TJ5pNvG2NqWc36EnHQeCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1f91ee5cd9ad41a92ed86e184101b9ddcc86cf2a68371c31f62d88a4900ccb73","last_reissued_at":"2026-05-17T23:43:43.763530Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:43:43.763530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1906.04145","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":"2026-05-17T23:43:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fqs2uaUmNQrjATsRcV4N1xM4h908BrFcjWfx2jkk+wLPFRi7llsI1ktyMl3YdJu6B3+0C0+iY8S6F7Q0pir6Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:16:51.749151Z"},"content_sha256":"38758becc38113641febb6a395a9820be39042d4f35a2f0fffc6aef8b7b17e2b","schema_version":"1.0","event_id":"sha256:38758becc38113641febb6a395a9820be39042d4f35a2f0fffc6aef8b7b17e2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:D6I64XGZVVA2SLWYNYMECANZ3X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"First-order linear evolution equations with c\\`adl\\`ag-in-time solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Ricardo Carrizo Vergara","submitted_at":"2019-06-10T17:35:23Z","abstract_excerpt":"In this work we study first-order linear parabolic evolution PDEs over $\\mathbb{R}^{d}\\times\\mathbb{R}$ and $\\mathbb{R}^{d}\\times\\mathbb{R}^{+}$ comprising a spatial operator defined through a symbol function and a source term such that its spatial Fourier transform is a slow-growing measure over $\\mathbb{R}^{d}\\times\\mathbb{R}$. When the source term is required to has its support on $\\mathbb{R}^{d}\\times\\mathbb{R}^{+}$, it is shown that there exists a unique solution such that its spatial Fourier transform is a slow-growing measure with support in $\\mathbb{R}^{d}\\times\\mathbb{R}^{+}$, which i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04145","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":"2026-05-17T23:43:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hhg2ivsU55leDabxcZlrZ9rZW6YYdl7fLqeZXN6ck31Ab71Y7vvW9nW2U+qa6d3LIdiMB5eel/WaM8PUjxUUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T02:16:51.749516Z"},"content_sha256":"2da4694b3299e14d804e145e2d5c5c3c6d9979cba7e91e3b4cddae1a86450f91","schema_version":"1.0","event_id":"sha256:2da4694b3299e14d804e145e2d5c5c3c6d9979cba7e91e3b4cddae1a86450f91"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D6I64XGZVVA2SLWYNYMECANZ3X/bundle.json","state_url":"https://pith.science/pith/D6I64XGZVVA2SLWYNYMECANZ3X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D6I64XGZVVA2SLWYNYMECANZ3X/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":"2026-06-27T02:16:51Z","links":{"resolver":"https://pith.science/pith/D6I64XGZVVA2SLWYNYMECANZ3X","bundle":"https://pith.science/pith/D6I64XGZVVA2SLWYNYMECANZ3X/bundle.json","state":"https://pith.science/pith/D6I64XGZVVA2SLWYNYMECANZ3X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D6I64XGZVVA2SLWYNYMECANZ3X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:D6I64XGZVVA2SLWYNYMECANZ3X","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":"176ce3b5269fff34e455b2df095fefbb88bfcf4eb0a7d460b6adab6cb08c9a8a","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-10T17:35:23Z","title_canon_sha256":"d26e680e1ae86a40c4ce6d117cd23f9ba10999f23f9bc0c428b7266ac11698c4"},"schema_version":"1.0","source":{"id":"1906.04145","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.04145","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"arxiv_version","alias_value":"1906.04145v1","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.04145","created_at":"2026-05-17T23:43:43Z"},{"alias_kind":"pith_short_12","alias_value":"D6I64XGZVVA2","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"D6I64XGZVVA2SLWY","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"D6I64XGZ","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:2da4694b3299e14d804e145e2d5c5c3c6d9979cba7e91e3b4cddae1a86450f91","target":"graph","created_at":"2026-05-17T23:43:43Z","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 work we study first-order linear parabolic evolution PDEs over $\\mathbb{R}^{d}\\times\\mathbb{R}$ and $\\mathbb{R}^{d}\\times\\mathbb{R}^{+}$ comprising a spatial operator defined through a symbol function and a source term such that its spatial Fourier transform is a slow-growing measure over $\\mathbb{R}^{d}\\times\\mathbb{R}$. When the source term is required to has its support on $\\mathbb{R}^{d}\\times\\mathbb{R}^{+}$, it is shown that there exists a unique solution such that its spatial Fourier transform is a slow-growing measure with support in $\\mathbb{R}^{d}\\times\\mathbb{R}^{+}$, which i","authors_text":"Ricardo Carrizo Vergara","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-10T17:35:23Z","title":"First-order linear evolution equations with c\\`adl\\`ag-in-time solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.04145","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":"sha256:38758becc38113641febb6a395a9820be39042d4f35a2f0fffc6aef8b7b17e2b","target":"record","created_at":"2026-05-17T23:43:43Z","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":"176ce3b5269fff34e455b2df095fefbb88bfcf4eb0a7d460b6adab6cb08c9a8a","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-06-10T17:35:23Z","title_canon_sha256":"d26e680e1ae86a40c4ce6d117cd23f9ba10999f23f9bc0c428b7266ac11698c4"},"schema_version":"1.0","source":{"id":"1906.04145","kind":"arxiv","version":1}},"canonical_sha256":"1f91ee5cd9ad41a92ed86e184101b9ddcc86cf2a68371c31f62d88a4900ccb73","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1f91ee5cd9ad41a92ed86e184101b9ddcc86cf2a68371c31f62d88a4900ccb73","first_computed_at":"2026-05-17T23:43:43.763530Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:43.763530Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wDKA6EjImY85v5vilfjMARwkIYNNcDh9EWLLYc/n+XtXvPFFmp1eNsL2+iRfxEs26TJ5pNvG2NqWc36EnHQeCA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:43.764370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.04145","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38758becc38113641febb6a395a9820be39042d4f35a2f0fffc6aef8b7b17e2b","sha256:2da4694b3299e14d804e145e2d5c5c3c6d9979cba7e91e3b4cddae1a86450f91"],"state_sha256":"de1d4c8dea769293c2bd6b615cc5bff60a7ce0e6b9aac6d62931bdbddc7f362f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ZKfPshupP9g/GD6szALfLLmnWMSsmoniO0RG2saL5cuYBLtw0j4UXm2bSgz37SUHD2WPB9jUa/I5Ib7vsBMDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T02:16:51.751408Z","bundle_sha256":"3baa87b6b526157629691fd4badc3f090c4e3ffc975039d7f3b56a5b4d2fd115"}}