{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:T4RRHF3YI4BIOPSENS7BIFKMNI","short_pith_number":"pith:T4RRHF3Y","canonical_record":{"source":{"id":"1709.09253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-26T20:26:57Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI","quant-ph"],"title_canon_sha256":"af7f83579beaffadee9127bb1b98d06c8ea976baa5e2b3fa7669ffb7e8317042","abstract_canon_sha256":"1157ffd65afbfa23ccd66f8adc73f2a32e0bc9ef7a1670fd62bf731a57bf0f61"},"schema_version":"1.0"},"canonical_sha256":"9f231397784702873e446cbe14154c6a1d02882789262310ea74121ac8c3f358","source":{"kind":"arxiv","id":"1709.09253","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09253","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09253v2","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09253","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"T4RRHF3YI4BI","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T4RRHF3YI4BIOPSE","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T4RRHF3Y","created_at":"2026-05-18T12:31:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:T4RRHF3YI4BIOPSENS7BIFKMNI","target":"record","payload":{"canonical_record":{"source":{"id":"1709.09253","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-26T20:26:57Z","cross_cats_sorted":["math-ph","math.MP","nlin.SI","quant-ph"],"title_canon_sha256":"af7f83579beaffadee9127bb1b98d06c8ea976baa5e2b3fa7669ffb7e8317042","abstract_canon_sha256":"1157ffd65afbfa23ccd66f8adc73f2a32e0bc9ef7a1670fd62bf731a57bf0f61"},"schema_version":"1.0"},"canonical_sha256":"9f231397784702873e446cbe14154c6a1d02882789262310ea74121ac8c3f358","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:31.217437Z","signature_b64":"D2hyyh9hWfolj/fir8mnPYvfQsKxNWxw//ATgVHOx45RTvnDkBdsDucHdzjVx/+AbDkKH6PAS4BigXJKDDffDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9f231397784702873e446cbe14154c6a1d02882789262310ea74121ac8c3f358","last_reissued_at":"2026-05-18T00:16:31.216951Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:31.216951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.09253","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":"2026-05-18T00:16:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hptROmm4aTKxefcIsQYfA8TGkDn2+MIROAipIpx0XQcl6HU1oh6jJiv5MP+YkvQjkD4HG/bzy3ih+/Ok3enaBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:09:04.147702Z"},"content_sha256":"97259155c320357f7b136f6659a50b7ed52ef75173d6f56f4e46b1e783fb81b2","schema_version":"1.0","event_id":"sha256:97259155c320357f7b136f6659a50b7ed52ef75173d6f56f4e46b1e783fb81b2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:T4RRHF3YI4BIOPSENS7BIFKMNI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Partial differential systems with nonlocal nonlinearities: Generation and solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI","quant-ph"],"primary_cat":"math.AP","authors_text":"Anastasia Doikou, Ioannis Stylianidis, Margaret Beck, Simon J.A. Malham","submitted_at":"2017-09-26T20:26:57Z","abstract_excerpt":"We develop a method for generating solutions to large classes of evolutionary partial differential systems with nonlocal nonlinearities. For arbitrary initial data, the solutions are generated from the corresponding linearized equations. The key is a Fredholm integral equation relating the linearized flow to an auxiliary linear flow. It is analogous to the Marchenko integral equation in integrable systems. We show explicitly how this can be achieved through several examples including reaction-diffusion systems with nonlocal quadratic nonlinearities and the nonlinear Schrodinger equation with a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09253","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":"2026-05-18T00:16:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WLPkyzRUQEE8CW7+DjnF9Z1MgFZq5hDsubU1q5jsGXMC3eRV8tpB9K9iL8iEbpgMYYLOC52AIh4stmX9QwTkCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T22:09:04.148402Z"},"content_sha256":"6131911e8bab46a0dd2c64557d70d6788e1877781d03818bf27854428b685246","schema_version":"1.0","event_id":"sha256:6131911e8bab46a0dd2c64557d70d6788e1877781d03818bf27854428b685246"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/T4RRHF3YI4BIOPSENS7BIFKMNI/bundle.json","state_url":"https://pith.science/pith/T4RRHF3YI4BIOPSENS7BIFKMNI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/T4RRHF3YI4BIOPSENS7BIFKMNI/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":"2026-06-11T22:09:04Z","links":{"resolver":"https://pith.science/pith/T4RRHF3YI4BIOPSENS7BIFKMNI","bundle":"https://pith.science/pith/T4RRHF3YI4BIOPSENS7BIFKMNI/bundle.json","state":"https://pith.science/pith/T4RRHF3YI4BIOPSENS7BIFKMNI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/T4RRHF3YI4BIOPSENS7BIFKMNI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:T4RRHF3YI4BIOPSENS7BIFKMNI","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":"1157ffd65afbfa23ccd66f8adc73f2a32e0bc9ef7a1670fd62bf731a57bf0f61","cross_cats_sorted":["math-ph","math.MP","nlin.SI","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-26T20:26:57Z","title_canon_sha256":"af7f83579beaffadee9127bb1b98d06c8ea976baa5e2b3fa7669ffb7e8317042"},"schema_version":"1.0","source":{"id":"1709.09253","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.09253","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1709.09253v2","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.09253","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"T4RRHF3YI4BI","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_16","alias_value":"T4RRHF3YI4BIOPSE","created_at":"2026-05-18T12:31:43Z"},{"alias_kind":"pith_short_8","alias_value":"T4RRHF3Y","created_at":"2026-05-18T12:31:43Z"}],"graph_snapshots":[{"event_id":"sha256:6131911e8bab46a0dd2c64557d70d6788e1877781d03818bf27854428b685246","target":"graph","created_at":"2026-05-18T00:16:31Z","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 develop a method for generating solutions to large classes of evolutionary partial differential systems with nonlocal nonlinearities. For arbitrary initial data, the solutions are generated from the corresponding linearized equations. The key is a Fredholm integral equation relating the linearized flow to an auxiliary linear flow. It is analogous to the Marchenko integral equation in integrable systems. We show explicitly how this can be achieved through several examples including reaction-diffusion systems with nonlocal quadratic nonlinearities and the nonlinear Schrodinger equation with a","authors_text":"Anastasia Doikou, Ioannis Stylianidis, Margaret Beck, Simon J.A. Malham","cross_cats":["math-ph","math.MP","nlin.SI","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-26T20:26:57Z","title":"Partial differential systems with nonlocal nonlinearities: Generation and solutions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09253","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":"sha256:97259155c320357f7b136f6659a50b7ed52ef75173d6f56f4e46b1e783fb81b2","target":"record","created_at":"2026-05-18T00:16:31Z","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":"1157ffd65afbfa23ccd66f8adc73f2a32e0bc9ef7a1670fd62bf731a57bf0f61","cross_cats_sorted":["math-ph","math.MP","nlin.SI","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-26T20:26:57Z","title_canon_sha256":"af7f83579beaffadee9127bb1b98d06c8ea976baa5e2b3fa7669ffb7e8317042"},"schema_version":"1.0","source":{"id":"1709.09253","kind":"arxiv","version":2}},"canonical_sha256":"9f231397784702873e446cbe14154c6a1d02882789262310ea74121ac8c3f358","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9f231397784702873e446cbe14154c6a1d02882789262310ea74121ac8c3f358","first_computed_at":"2026-05-18T00:16:31.216951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:31.216951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D2hyyh9hWfolj/fir8mnPYvfQsKxNWxw//ATgVHOx45RTvnDkBdsDucHdzjVx/+AbDkKH6PAS4BigXJKDDffDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:31.217437Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.09253","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97259155c320357f7b136f6659a50b7ed52ef75173d6f56f4e46b1e783fb81b2","sha256:6131911e8bab46a0dd2c64557d70d6788e1877781d03818bf27854428b685246"],"state_sha256":"991cf28bfdd904fd44339668fc8a4d44f0a4cc00a96cde9d808c322e90cdd257"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9gU2L7ptdaP8dN644ED2h3n+1vjGuT20rjO9gE0SC3lRe15BzjlAh0JNRknMLR45XygoTnnkfvkFJIoS8U5XBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T22:09:04.152297Z","bundle_sha256":"e6d2c4646a78ebe43c5f08c7998a583f28962c84f440c74859a4b38916efe9ed"}}