{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:G7MYF4RIPUTU2JLHQEGLJJ74JU","short_pith_number":"pith:G7MYF4RI","canonical_record":{"source":{"id":"1402.6596","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-26T16:32:21Z","cross_cats_sorted":[],"title_canon_sha256":"21e3b74e6a5e80c48644bbc7ac26bba81db3d3a74773363ec311b0f4629d4645","abstract_canon_sha256":"2d8fa796377629ac8250f8dfbf5a288906f042ffb63bc9445d016f8f4d05eba1"},"schema_version":"1.0"},"canonical_sha256":"37d982f2287d274d2567810cb4a7fc4d060a8cab545eb1dc9134e871f39ca1e0","source":{"kind":"arxiv","id":"1402.6596","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6596","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6596v2","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6596","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"pith_short_12","alias_value":"G7MYF4RIPUTU","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G7MYF4RIPUTU2JLH","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G7MYF4RI","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:G7MYF4RIPUTU2JLHQEGLJJ74JU","target":"record","payload":{"canonical_record":{"source":{"id":"1402.6596","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-26T16:32:21Z","cross_cats_sorted":[],"title_canon_sha256":"21e3b74e6a5e80c48644bbc7ac26bba81db3d3a74773363ec311b0f4629d4645","abstract_canon_sha256":"2d8fa796377629ac8250f8dfbf5a288906f042ffb63bc9445d016f8f4d05eba1"},"schema_version":"1.0"},"canonical_sha256":"37d982f2287d274d2567810cb4a7fc4d060a8cab545eb1dc9134e871f39ca1e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:44.325170Z","signature_b64":"2/icegPANOZ9185xPcD+aOzwpN51LUjgIzhqYhWJzjgaFv9Drysug+KsfI/Fh9U7jTRDFYevBGniY1YBG2tLDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"37d982f2287d274d2567810cb4a7fc4d060a8cab545eb1dc9134e871f39ca1e0","last_reissued_at":"2026-05-18T02:47:44.324432Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:44.324432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1402.6596","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":"2026-05-18T02:47:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Quyzf+cop8rN0GGjU0QzCs6EJM5/nBft/FVtEvMXJOggOHXb+8AYz0RfFFgWzCrzt1Z48v6ZjuDTrggHtQVLCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T07:15:55.818454Z"},"content_sha256":"70092b7636a3adf5c18a919ffc313d3a002ee22db9b9eff84c8715e5d9e07a1c","schema_version":"1.0","event_id":"sha256:70092b7636a3adf5c18a919ffc313d3a002ee22db9b9eff84c8715e5d9e07a1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:G7MYF4RIPUTU2JLHQEGLJJ74JU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quadratic BSDEs with $\\mathbb{L}^2$--terminal data Existence results, Krylov's estimate and It\\^o--Krylov's formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Khaled Bahlali, M'hamed Eddahbi, Youssef Ouknine","submitted_at":"2014-02-26T16:32:21Z","abstract_excerpt":"In a first step, we establish the existence (and sometimes the uniqueness) of solutions for a large class of quadratic backward stochastic differential equations (QBSDEs) with continuous generator and a merely square integrable terminal condition. Our approach is different from those existing in the literature. Although we are focused on QBSDEs, our existence result also covers the BSDEs with linear growth, keeping $\\xi$ square integrable in both cases. As byproduct, the existence of viscosity solutions is established for a class of quadratic partial differential equations (QPDEs) with a squar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6596","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":"2026-05-18T02:47:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cgJzav8DF5KuuSDHImZcG6PdL/7ksVICAV3A5v91tu10Y5ei/yCDZzRDg2OuIsomSnK31n9/5lKv/l4v8HU2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T07:15:55.818801Z"},"content_sha256":"3947ccd3fa85c01d91f492df2e7f5a5477e0530380dc87a380b299b92f7438d9","schema_version":"1.0","event_id":"sha256:3947ccd3fa85c01d91f492df2e7f5a5477e0530380dc87a380b299b92f7438d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G7MYF4RIPUTU2JLHQEGLJJ74JU/bundle.json","state_url":"https://pith.science/pith/G7MYF4RIPUTU2JLHQEGLJJ74JU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G7MYF4RIPUTU2JLHQEGLJJ74JU/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":"2026-06-30T07:15:55Z","links":{"resolver":"https://pith.science/pith/G7MYF4RIPUTU2JLHQEGLJJ74JU","bundle":"https://pith.science/pith/G7MYF4RIPUTU2JLHQEGLJJ74JU/bundle.json","state":"https://pith.science/pith/G7MYF4RIPUTU2JLHQEGLJJ74JU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G7MYF4RIPUTU2JLHQEGLJJ74JU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:G7MYF4RIPUTU2JLHQEGLJJ74JU","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":"2d8fa796377629ac8250f8dfbf5a288906f042ffb63bc9445d016f8f4d05eba1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-26T16:32:21Z","title_canon_sha256":"21e3b74e6a5e80c48644bbc7ac26bba81db3d3a74773363ec311b0f4629d4645"},"schema_version":"1.0","source":{"id":"1402.6596","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.6596","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"arxiv_version","alias_value":"1402.6596v2","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.6596","created_at":"2026-05-18T02:47:44Z"},{"alias_kind":"pith_short_12","alias_value":"G7MYF4RIPUTU","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G7MYF4RIPUTU2JLH","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G7MYF4RI","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:3947ccd3fa85c01d91f492df2e7f5a5477e0530380dc87a380b299b92f7438d9","target":"graph","created_at":"2026-05-18T02:47:44Z","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 a first step, we establish the existence (and sometimes the uniqueness) of solutions for a large class of quadratic backward stochastic differential equations (QBSDEs) with continuous generator and a merely square integrable terminal condition. Our approach is different from those existing in the literature. Although we are focused on QBSDEs, our existence result also covers the BSDEs with linear growth, keeping $\\xi$ square integrable in both cases. As byproduct, the existence of viscosity solutions is established for a class of quadratic partial differential equations (QPDEs) with a squar","authors_text":"Khaled Bahlali, M'hamed Eddahbi, Youssef Ouknine","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-26T16:32:21Z","title":"Quadratic BSDEs with $\\mathbb{L}^2$--terminal data Existence results, Krylov's estimate and It\\^o--Krylov's formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6596","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":"sha256:70092b7636a3adf5c18a919ffc313d3a002ee22db9b9eff84c8715e5d9e07a1c","target":"record","created_at":"2026-05-18T02:47:44Z","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":"2d8fa796377629ac8250f8dfbf5a288906f042ffb63bc9445d016f8f4d05eba1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-26T16:32:21Z","title_canon_sha256":"21e3b74e6a5e80c48644bbc7ac26bba81db3d3a74773363ec311b0f4629d4645"},"schema_version":"1.0","source":{"id":"1402.6596","kind":"arxiv","version":2}},"canonical_sha256":"37d982f2287d274d2567810cb4a7fc4d060a8cab545eb1dc9134e871f39ca1e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"37d982f2287d274d2567810cb4a7fc4d060a8cab545eb1dc9134e871f39ca1e0","first_computed_at":"2026-05-18T02:47:44.324432Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:47:44.324432Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2/icegPANOZ9185xPcD+aOzwpN51LUjgIzhqYhWJzjgaFv9Drysug+KsfI/Fh9U7jTRDFYevBGniY1YBG2tLDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:47:44.325170Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.6596","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70092b7636a3adf5c18a919ffc313d3a002ee22db9b9eff84c8715e5d9e07a1c","sha256:3947ccd3fa85c01d91f492df2e7f5a5477e0530380dc87a380b299b92f7438d9"],"state_sha256":"5f34619545a0607bad7512b7e84cddad77bc6ffb079234f845fdc645d142bfc5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t6kPDz8yxKH6AYbXJ4Uro/3qNi7C0uZXq7FFKrQHR45AMmurT2m5y+gpHI44blpRn5Zm3Av7jeAO2NtOc8sNBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T07:15:55.821039Z","bundle_sha256":"c59e6a00a20096a541e5c2087fd3065e322f5258f1875cea9158dcaf2700b27c"}}