{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:K5VCLWXLPBXDK37MDEZKDIKPLH","short_pith_number":"pith:K5VCLWXL","canonical_record":{"source":{"id":"1907.08258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-18T19:27:35Z","cross_cats_sorted":["math-ph","math.MP","math.SP","nlin.SI"],"title_canon_sha256":"09d25037d575d6e8acd44809588d0f7a1ea7f97c668e834eb80b349957304f9e","abstract_canon_sha256":"a2613bd97c79129a58b811034cfa23c177d2913b09add1f74991a4c5264408b0"},"schema_version":"1.0"},"canonical_sha256":"576a25daeb786e356fec1932a1a14f59f86bf539331fcf819f88b2b1579ead9a","source":{"kind":"arxiv","id":"1907.08258","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08258","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08258v1","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08258","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"K5VCLWXLPBXD","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"K5VCLWXLPBXDK37M","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"K5VCLWXL","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:K5VCLWXLPBXDK37MDEZKDIKPLH","target":"record","payload":{"canonical_record":{"source":{"id":"1907.08258","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-18T19:27:35Z","cross_cats_sorted":["math-ph","math.MP","math.SP","nlin.SI"],"title_canon_sha256":"09d25037d575d6e8acd44809588d0f7a1ea7f97c668e834eb80b349957304f9e","abstract_canon_sha256":"a2613bd97c79129a58b811034cfa23c177d2913b09add1f74991a4c5264408b0"},"schema_version":"1.0"},"canonical_sha256":"576a25daeb786e356fec1932a1a14f59f86bf539331fcf819f88b2b1579ead9a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:10.409566Z","signature_b64":"UAvxeoqOosIRHss8KK+VoCl8vD/JtUIYSAz5RAID8oQNuQ4hWEfOAudLHAJ3j6IvU4Bo4ldIdNtIf0QcRq7YDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"576a25daeb786e356fec1932a1a14f59f86bf539331fcf819f88b2b1579ead9a","last_reissued_at":"2026-05-17T23:40:10.409108Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:10.409108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.08258","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":"2026-05-17T23:40:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QMYoFPj3YYKrzQ/+qNHjmrbCUlDrp2W1YJVjk0fEQjbgPbFkS0oHxU/M41VvjTS0eSQsGiB3byqwlouh//zoCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:03:56.358204Z"},"content_sha256":"82bd0d37b2e43660717e7f7ac0ef603aa84e2f1d388e63ca02cf4773265c2a69","schema_version":"1.0","event_id":"sha256:82bd0d37b2e43660717e7f7ac0ef603aa84e2f1d388e63ca02cf4773265c2a69"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:K5VCLWXLPBXDK37MDEZKDIKPLH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"GBDT and explicit solutions for the matrix coupled dispersionless equations (local and nonlocal cases)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SP","nlin.SI"],"primary_cat":"math.AP","authors_text":"Alexander Sakhnovich, Roman O. Popovych","submitted_at":"2019-07-18T19:27:35Z","abstract_excerpt":"We introduce matrix coupled (local and nonlocal) dispersionless equations, construct wide classes of explicit multipole solutions, give explicit expressions for the corresponding Darboux and wave matrix valued functions and consider their asymptotics in some interesting cases. We consider the scalar cases of coupled, complex coupled and nonlocal dispersionless equations as well."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08258","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":"2026-05-17T23:40:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VkUrWPdegnO+SgAdk+1Qeyck5+moIVsdI2+GmAPURWQ3ql8b5cens+0E1W6+sy2GJe8sn1384ZdMt4jcCfkyAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T08:03:56.358937Z"},"content_sha256":"fb7a50414505ca3af3d4833d93f420eb2ecb4d311119f5da8d32e87b3cb78dbd","schema_version":"1.0","event_id":"sha256:fb7a50414505ca3af3d4833d93f420eb2ecb4d311119f5da8d32e87b3cb78dbd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K5VCLWXLPBXDK37MDEZKDIKPLH/bundle.json","state_url":"https://pith.science/pith/K5VCLWXLPBXDK37MDEZKDIKPLH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K5VCLWXLPBXDK37MDEZKDIKPLH/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":"2026-05-27T08:03:56Z","links":{"resolver":"https://pith.science/pith/K5VCLWXLPBXDK37MDEZKDIKPLH","bundle":"https://pith.science/pith/K5VCLWXLPBXDK37MDEZKDIKPLH/bundle.json","state":"https://pith.science/pith/K5VCLWXLPBXDK37MDEZKDIKPLH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K5VCLWXLPBXDK37MDEZKDIKPLH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:K5VCLWXLPBXDK37MDEZKDIKPLH","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":"a2613bd97c79129a58b811034cfa23c177d2913b09add1f74991a4c5264408b0","cross_cats_sorted":["math-ph","math.MP","math.SP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-18T19:27:35Z","title_canon_sha256":"09d25037d575d6e8acd44809588d0f7a1ea7f97c668e834eb80b349957304f9e"},"schema_version":"1.0","source":{"id":"1907.08258","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.08258","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"1907.08258v1","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.08258","created_at":"2026-05-17T23:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"K5VCLWXLPBXD","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"K5VCLWXLPBXDK37M","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"K5VCLWXL","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:fb7a50414505ca3af3d4833d93f420eb2ecb4d311119f5da8d32e87b3cb78dbd","target":"graph","created_at":"2026-05-17T23:40:10Z","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 matrix coupled (local and nonlocal) dispersionless equations, construct wide classes of explicit multipole solutions, give explicit expressions for the corresponding Darboux and wave matrix valued functions and consider their asymptotics in some interesting cases. We consider the scalar cases of coupled, complex coupled and nonlocal dispersionless equations as well.","authors_text":"Alexander Sakhnovich, Roman O. Popovych","cross_cats":["math-ph","math.MP","math.SP","nlin.SI"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-18T19:27:35Z","title":"GBDT and explicit solutions for the matrix coupled dispersionless equations (local and nonlocal cases)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.08258","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":"sha256:82bd0d37b2e43660717e7f7ac0ef603aa84e2f1d388e63ca02cf4773265c2a69","target":"record","created_at":"2026-05-17T23:40:10Z","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":"a2613bd97c79129a58b811034cfa23c177d2913b09add1f74991a4c5264408b0","cross_cats_sorted":["math-ph","math.MP","math.SP","nlin.SI"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-07-18T19:27:35Z","title_canon_sha256":"09d25037d575d6e8acd44809588d0f7a1ea7f97c668e834eb80b349957304f9e"},"schema_version":"1.0","source":{"id":"1907.08258","kind":"arxiv","version":1}},"canonical_sha256":"576a25daeb786e356fec1932a1a14f59f86bf539331fcf819f88b2b1579ead9a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"576a25daeb786e356fec1932a1a14f59f86bf539331fcf819f88b2b1579ead9a","first_computed_at":"2026-05-17T23:40:10.409108Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:10.409108Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UAvxeoqOosIRHss8KK+VoCl8vD/JtUIYSAz5RAID8oQNuQ4hWEfOAudLHAJ3j6IvU4Bo4ldIdNtIf0QcRq7YDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:10.409566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.08258","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:82bd0d37b2e43660717e7f7ac0ef603aa84e2f1d388e63ca02cf4773265c2a69","sha256:fb7a50414505ca3af3d4833d93f420eb2ecb4d311119f5da8d32e87b3cb78dbd"],"state_sha256":"bf581666a064fd9fa913c7fc3e7ace4e937d5bc66c18d889f03c0e6b8deae280"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZNlOzLqU7+KoApfyHFfCcGsuCPYfx4lQpftyMsHkRq2fUUZfm8VN6MiUfPfXWPDDJoYFRT0AVoTuhWP+G/tRAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T08:03:56.362774Z","bundle_sha256":"832c0089c13cef41bace19965940a72e18538babeb6392d0da34d0e5ba85b9c3"}}