{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:RW4XXMXKRQKW4DHH5KNMXJI3HD","short_pith_number":"pith:RW4XXMXK","canonical_record":{"source":{"id":"2410.13292","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-17T07:42:05Z","cross_cats_sorted":[],"title_canon_sha256":"5a6a6c31ea1fa1cb0ceea6e161ee03eccf4d23d16083ec54974df83da6fb74a6","abstract_canon_sha256":"efec528847ad649fd1b4089de0e64faa6d0488c890ce70848a24a9dbf0f9df83"},"schema_version":"1.0"},"canonical_sha256":"8db97bb2ea8c156e0ce7ea9acba51b38f8b0febf29b534c3122d0505ccdf0313","source":{"kind":"arxiv","id":"2410.13292","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.13292","created_at":"2026-07-05T11:33:16Z"},{"alias_kind":"arxiv_version","alias_value":"2410.13292v2","created_at":"2026-07-05T11:33:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.13292","created_at":"2026-07-05T11:33:16Z"},{"alias_kind":"pith_short_12","alias_value":"RW4XXMXKRQKW","created_at":"2026-07-05T11:33:16Z"},{"alias_kind":"pith_short_16","alias_value":"RW4XXMXKRQKW4DHH","created_at":"2026-07-05T11:33:16Z"},{"alias_kind":"pith_short_8","alias_value":"RW4XXMXK","created_at":"2026-07-05T11:33:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:RW4XXMXKRQKW4DHH5KNMXJI3HD","target":"record","payload":{"canonical_record":{"source":{"id":"2410.13292","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-17T07:42:05Z","cross_cats_sorted":[],"title_canon_sha256":"5a6a6c31ea1fa1cb0ceea6e161ee03eccf4d23d16083ec54974df83da6fb74a6","abstract_canon_sha256":"efec528847ad649fd1b4089de0e64faa6d0488c890ce70848a24a9dbf0f9df83"},"schema_version":"1.0"},"canonical_sha256":"8db97bb2ea8c156e0ce7ea9acba51b38f8b0febf29b534c3122d0505ccdf0313","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:33:16.683997Z","signature_b64":"W1i0hGLroO398lrMTCuUtDCUTDCeHrkuBArd61Xjbk6PFIFx48ju6qCIJ31EfJKzO03fn7DSypCfPDNClW1qBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8db97bb2ea8c156e0ce7ea9acba51b38f8b0febf29b534c3122d0505ccdf0313","last_reissued_at":"2026-07-05T11:33:16.683357Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:33:16.683357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2410.13292","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":"2026-07-05T11:33:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"utDVhN7FzibxhxB43cANv7fGBZDEg9Z32Ru6iWb+YuKUMedhD8oEUQ/CZKqlKuMarDin/DIzWVMLs9nd2WW8DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T21:56:14.629178Z"},"content_sha256":"fd9b6f8fabe9103108390d966b6f009e88fdd18d8eb611fe371125087139b293","schema_version":"1.0","event_id":"sha256:fd9b6f8fabe9103108390d966b6f009e88fdd18d8eb611fe371125087139b293"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:RW4XXMXKRQKW4DHH5KNMXJI3HD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Singularities of solutions of nonlocal nonlinear equations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Minhyun Kim, Se-Chan Lee","submitted_at":"2024-10-17T07:42:05Z","abstract_excerpt":"We study the local behavior of weak solutions, with possible singularities, of nonlocal nonlinear equations. We first prove that sets of capacity zero are removable for weak solutions under certain integrability conditions. We then characterize the asymptotic behavior of singular solutions near an isolated singularity in terms of the fundamental solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.13292","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.13292/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:33:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OMEBj7VkGx1dUSiJky0tm8li7xXwvcUvr7dbcBZIu/EqMfgb6moD9j571TrUAMTcpswxCGlgmGeAqci3j32JDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-19T21:56:14.629987Z"},"content_sha256":"2f9bd84f82de61cd4415fb47594a374e8609a01ae067350f82f9bf75a0b71384","schema_version":"1.0","event_id":"sha256:2f9bd84f82de61cd4415fb47594a374e8609a01ae067350f82f9bf75a0b71384"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RW4XXMXKRQKW4DHH5KNMXJI3HD/bundle.json","state_url":"https://pith.science/pith/RW4XXMXKRQKW4DHH5KNMXJI3HD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RW4XXMXKRQKW4DHH5KNMXJI3HD/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":"2026-08-19T21:56:14Z","links":{"resolver":"https://pith.science/pith/RW4XXMXKRQKW4DHH5KNMXJI3HD","bundle":"https://pith.science/pith/RW4XXMXKRQKW4DHH5KNMXJI3HD/bundle.json","state":"https://pith.science/pith/RW4XXMXKRQKW4DHH5KNMXJI3HD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RW4XXMXKRQKW4DHH5KNMXJI3HD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RW4XXMXKRQKW4DHH5KNMXJI3HD","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":"efec528847ad649fd1b4089de0e64faa6d0488c890ce70848a24a9dbf0f9df83","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-17T07:42:05Z","title_canon_sha256":"5a6a6c31ea1fa1cb0ceea6e161ee03eccf4d23d16083ec54974df83da6fb74a6"},"schema_version":"1.0","source":{"id":"2410.13292","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2410.13292","created_at":"2026-07-05T11:33:16Z"},{"alias_kind":"arxiv_version","alias_value":"2410.13292v2","created_at":"2026-07-05T11:33:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2410.13292","created_at":"2026-07-05T11:33:16Z"},{"alias_kind":"pith_short_12","alias_value":"RW4XXMXKRQKW","created_at":"2026-07-05T11:33:16Z"},{"alias_kind":"pith_short_16","alias_value":"RW4XXMXKRQKW4DHH","created_at":"2026-07-05T11:33:16Z"},{"alias_kind":"pith_short_8","alias_value":"RW4XXMXK","created_at":"2026-07-05T11:33:16Z"}],"graph_snapshots":[{"event_id":"sha256:2f9bd84f82de61cd4415fb47594a374e8609a01ae067350f82f9bf75a0b71384","target":"graph","created_at":"2026-07-05T11:33:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2410.13292/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the local behavior of weak solutions, with possible singularities, of nonlocal nonlinear equations. We first prove that sets of capacity zero are removable for weak solutions under certain integrability conditions. We then characterize the asymptotic behavior of singular solutions near an isolated singularity in terms of the fundamental solution.","authors_text":"Minhyun Kim, Se-Chan Lee","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-17T07:42:05Z","title":"Singularities of solutions of nonlocal nonlinear equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.13292","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:fd9b6f8fabe9103108390d966b6f009e88fdd18d8eb611fe371125087139b293","target":"record","created_at":"2026-07-05T11:33:16Z","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":"efec528847ad649fd1b4089de0e64faa6d0488c890ce70848a24a9dbf0f9df83","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2024-10-17T07:42:05Z","title_canon_sha256":"5a6a6c31ea1fa1cb0ceea6e161ee03eccf4d23d16083ec54974df83da6fb74a6"},"schema_version":"1.0","source":{"id":"2410.13292","kind":"arxiv","version":2}},"canonical_sha256":"8db97bb2ea8c156e0ce7ea9acba51b38f8b0febf29b534c3122d0505ccdf0313","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8db97bb2ea8c156e0ce7ea9acba51b38f8b0febf29b534c3122d0505ccdf0313","first_computed_at":"2026-07-05T11:33:16.683357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:33:16.683357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"W1i0hGLroO398lrMTCuUtDCUTDCeHrkuBArd61Xjbk6PFIFx48ju6qCIJ31EfJKzO03fn7DSypCfPDNClW1qBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:33:16.683997Z","signed_message":"canonical_sha256_bytes"},"source_id":"2410.13292","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd9b6f8fabe9103108390d966b6f009e88fdd18d8eb611fe371125087139b293","sha256:2f9bd84f82de61cd4415fb47594a374e8609a01ae067350f82f9bf75a0b71384"],"state_sha256":"acb537772c21a3c2d1f96e8f9f1c17cb2d0d01fd5cc5597a8e57d3f0b206a9df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/NJlXBAHwyLitBewhCKiYwJ9o7LTOL6sUbgKfdi3I1c52NTpAtLVCYS8vLfxuslPB6UBERkvxuNG2y5hurcTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-19T21:56:14.635616Z","bundle_sha256":"0e2dd13cf18d57858f4f8937deb6435b10d977473270b63e972dbd897ed7c79f"}}