{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JCZ2O2OEJ346FGOQWS5EB3USWO","short_pith_number":"pith:JCZ2O2OE","canonical_record":{"source":{"id":"1501.06164","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-25T14:18:55Z","cross_cats_sorted":[],"title_canon_sha256":"93032a8d94e8df975759aa0e8e33e1187eaf9c2e5c310a7c79c2197d65e694e4","abstract_canon_sha256":"c3c9d4192dd3eb5b0b595b03713762c32f35429036cc30d682dd90be253f92f9"},"schema_version":"1.0"},"canonical_sha256":"48b3a769c44ef9e299d0b4ba40ee92b38721595cba6260efb09f0bd03c9708cd","source":{"kind":"arxiv","id":"1501.06164","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06164","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06164v8","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06164","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"pith_short_12","alias_value":"JCZ2O2OEJ346","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JCZ2O2OEJ346FGOQ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JCZ2O2OE","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JCZ2O2OEJ346FGOQWS5EB3USWO","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06164","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-25T14:18:55Z","cross_cats_sorted":[],"title_canon_sha256":"93032a8d94e8df975759aa0e8e33e1187eaf9c2e5c310a7c79c2197d65e694e4","abstract_canon_sha256":"c3c9d4192dd3eb5b0b595b03713762c32f35429036cc30d682dd90be253f92f9"},"schema_version":"1.0"},"canonical_sha256":"48b3a769c44ef9e299d0b4ba40ee92b38721595cba6260efb09f0bd03c9708cd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:50:29.982090Z","signature_b64":"vseip40ZSJEfuHthPz+BlbHN/djCgb7pRwnqHMntSfH6HrUUHVzrJ8X1wAPfoIO7NV3SdDwiFZkBKFb2XmVwCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"48b3a769c44ef9e299d0b4ba40ee92b38721595cba6260efb09f0bd03c9708cd","last_reissued_at":"2026-05-18T00:50:29.981357Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:50:29.981357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06164","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:50:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IbSgxmCSiw186XI/+AXYhjLrFZ6Xk9mbLorYWotOgL79faUFASinQkT+vD/G580FqdTPSLElmtwR5DEC5rY/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T08:52:32.159027Z"},"content_sha256":"58f15c061cae2251092d91a6313e91298cfa4e00f3f10caf96dc787003f3a7b3","schema_version":"1.0","event_id":"sha256:58f15c061cae2251092d91a6313e91298cfa4e00f3f10caf96dc787003f3a7b3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JCZ2O2OEJ346FGOQWS5EB3USWO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalised Solutions for Fully Nonlinear PDE Systems and Existence-Uniqueness Theorems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Nikos Katzourakis (Reading, UK)","submitted_at":"2015-01-25T14:18:55Z","abstract_excerpt":"We introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of Distributions to PDEs and is not based on either integration by parts or on the maximum principle. Instead, our starting point builds on the probabilistic representation of derivatives via limits of difference quotients in the Young measures over a toric compactification of the space of jets. After developing some basic theory, as a first application we consider"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06164","kind":"arxiv","version":8},"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":"2026-05-18T00:50:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Qkhm5tCocbFHagbXxXLXvI6GfEh2YZCvnSUrE5TjgCX3A46kYAcehbERqcUfAccoCg5DULcepzCYTSbCUZUDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T08:52:32.159387Z"},"content_sha256":"824df528d14d4b04cbf61a706eca942614d19c9acd93ad3ad15cf4da8c961859","schema_version":"1.0","event_id":"sha256:824df528d14d4b04cbf61a706eca942614d19c9acd93ad3ad15cf4da8c961859"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JCZ2O2OEJ346FGOQWS5EB3USWO/bundle.json","state_url":"https://pith.science/pith/JCZ2O2OEJ346FGOQWS5EB3USWO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JCZ2O2OEJ346FGOQWS5EB3USWO/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":"2026-06-22T08:52:32Z","links":{"resolver":"https://pith.science/pith/JCZ2O2OEJ346FGOQWS5EB3USWO","bundle":"https://pith.science/pith/JCZ2O2OEJ346FGOQWS5EB3USWO/bundle.json","state":"https://pith.science/pith/JCZ2O2OEJ346FGOQWS5EB3USWO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JCZ2O2OEJ346FGOQWS5EB3USWO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JCZ2O2OEJ346FGOQWS5EB3USWO","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":"c3c9d4192dd3eb5b0b595b03713762c32f35429036cc30d682dd90be253f92f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-25T14:18:55Z","title_canon_sha256":"93032a8d94e8df975759aa0e8e33e1187eaf9c2e5c310a7c79c2197d65e694e4"},"schema_version":"1.0","source":{"id":"1501.06164","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06164","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06164v8","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06164","created_at":"2026-05-18T00:50:29Z"},{"alias_kind":"pith_short_12","alias_value":"JCZ2O2OEJ346","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JCZ2O2OEJ346FGOQ","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JCZ2O2OE","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:824df528d14d4b04cbf61a706eca942614d19c9acd93ad3ad15cf4da8c961859","target":"graph","created_at":"2026-05-18T00:50:29Z","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 introduce a new theory of generalised solutions which applies to fully nonlinear PDE systems of any order and allows for merely measurable maps as solutions. This approach bypasses the standard problems arising by the application of Distributions to PDEs and is not based on either integration by parts or on the maximum principle. Instead, our starting point builds on the probabilistic representation of derivatives via limits of difference quotients in the Young measures over a toric compactification of the space of jets. After developing some basic theory, as a first application we consider","authors_text":"Nikos Katzourakis (Reading, UK)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-25T14:18:55Z","title":"Generalised Solutions for Fully Nonlinear PDE Systems and Existence-Uniqueness Theorems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06164","kind":"arxiv","version":8},"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":"sha256:58f15c061cae2251092d91a6313e91298cfa4e00f3f10caf96dc787003f3a7b3","target":"record","created_at":"2026-05-18T00:50:29Z","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":"c3c9d4192dd3eb5b0b595b03713762c32f35429036cc30d682dd90be253f92f9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-01-25T14:18:55Z","title_canon_sha256":"93032a8d94e8df975759aa0e8e33e1187eaf9c2e5c310a7c79c2197d65e694e4"},"schema_version":"1.0","source":{"id":"1501.06164","kind":"arxiv","version":8}},"canonical_sha256":"48b3a769c44ef9e299d0b4ba40ee92b38721595cba6260efb09f0bd03c9708cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"48b3a769c44ef9e299d0b4ba40ee92b38721595cba6260efb09f0bd03c9708cd","first_computed_at":"2026-05-18T00:50:29.981357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:29.981357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vseip40ZSJEfuHthPz+BlbHN/djCgb7pRwnqHMntSfH6HrUUHVzrJ8X1wAPfoIO7NV3SdDwiFZkBKFb2XmVwCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:29.982090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06164","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58f15c061cae2251092d91a6313e91298cfa4e00f3f10caf96dc787003f3a7b3","sha256:824df528d14d4b04cbf61a706eca942614d19c9acd93ad3ad15cf4da8c961859"],"state_sha256":"a64c06400b0dc45136594b35cca35f992ade92d037e44f8852a9460195a704d8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"psMmoAfmY2u48BA8dlO0vuJuYEdmICHDCbqekM5TVwhiBGCe5I8PEUXDf9Y1WW6Zb/CX+/bl565LcQ+anBfDAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T08:52:32.161301Z","bundle_sha256":"cfed572554a27bf94441fe4aea1d9ba0cc5d3a4b05d6b8a8fcba2f8dbb259f48"}}