{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:PWWBQIHXLEFSCY3IVDUBIV7U6W","short_pith_number":"pith:PWWBQIHX","canonical_record":{"source":{"id":"1103.0371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-02T09:27:13Z","cross_cats_sorted":[],"title_canon_sha256":"91e2bd12c011d6c644fb98c2c227d5133badd65981b43a1ceee3eacff9f90099","abstract_canon_sha256":"9801582966458beefe34ee35c01e8c579732db7495b1ac26db628244889a077c"},"schema_version":"1.0"},"canonical_sha256":"7dac1820f7590b216368a8e81457f4f58ca292b3aa43e6920bfba636fcc93855","source":{"kind":"arxiv","id":"1103.0371","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0371","created_at":"2026-05-18T04:27:35Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0371v1","created_at":"2026-05-18T04:27:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0371","created_at":"2026-05-18T04:27:35Z"},{"alias_kind":"pith_short_12","alias_value":"PWWBQIHXLEFS","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PWWBQIHXLEFSCY3I","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PWWBQIHX","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:PWWBQIHXLEFSCY3IVDUBIV7U6W","target":"record","payload":{"canonical_record":{"source":{"id":"1103.0371","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-02T09:27:13Z","cross_cats_sorted":[],"title_canon_sha256":"91e2bd12c011d6c644fb98c2c227d5133badd65981b43a1ceee3eacff9f90099","abstract_canon_sha256":"9801582966458beefe34ee35c01e8c579732db7495b1ac26db628244889a077c"},"schema_version":"1.0"},"canonical_sha256":"7dac1820f7590b216368a8e81457f4f58ca292b3aa43e6920bfba636fcc93855","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:35.096255Z","signature_b64":"dxdbwq+XXn6hWZzX0w2jYTvbi85GfWquDdFrGSLeKJihQ3K0SebalVcbDjYX84FRRHOXKLMZ9hOjr92/YDbUCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dac1820f7590b216368a8e81457f4f58ca292b3aa43e6920bfba636fcc93855","last_reissued_at":"2026-05-18T04:27:35.095572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:35.095572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.0371","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":"2026-05-18T04:27:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yq4OUKWizLU18ztjl8M6WoE7dQQzgummLBWTO4o4rFGCHYXYlQ+xWvb5x1OUyKeVBLDOTz4Cs0eBEivqavzJAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:19:50.315726Z"},"content_sha256":"6f6a95bf0b5b738017c39ba8b4f1d9afe378c11742d331c62882bee754a4f3c1","schema_version":"1.0","event_id":"sha256:6f6a95bf0b5b738017c39ba8b4f1d9afe378c11742d331c62882bee754a4f3c1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:PWWBQIHXLEFSCY3IVDUBIV7U6W","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalized fractional smoothness and $L_p$-variation of BSDEs with non-Lipschitz terminal condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christel Geiss, Emmanuel Gobet, Stefan Geiss","submitted_at":"2011-03-02T09:27:13Z","abstract_excerpt":"We relate the $L_p$-variation, $2\\le p < \\infty$, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in time."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0371","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":"2026-05-18T04:27:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bvj7PhE/+6rtuF6dSlUpAvRyaM1tr/TxKVq9eY8lnTGef279U62huUg3rFyO8Xe1bwDXKLQ4M4PxpqN/VDxxAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:19:50.316085Z"},"content_sha256":"b9a98585f84ae8aa99cb1d198efbdbc36667f5a09dafbfa7f18765e178867c34","schema_version":"1.0","event_id":"sha256:b9a98585f84ae8aa99cb1d198efbdbc36667f5a09dafbfa7f18765e178867c34"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PWWBQIHXLEFSCY3IVDUBIV7U6W/bundle.json","state_url":"https://pith.science/pith/PWWBQIHXLEFSCY3IVDUBIV7U6W/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PWWBQIHXLEFSCY3IVDUBIV7U6W/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":"2026-06-11T10:19:50Z","links":{"resolver":"https://pith.science/pith/PWWBQIHXLEFSCY3IVDUBIV7U6W","bundle":"https://pith.science/pith/PWWBQIHXLEFSCY3IVDUBIV7U6W/bundle.json","state":"https://pith.science/pith/PWWBQIHXLEFSCY3IVDUBIV7U6W/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PWWBQIHXLEFSCY3IVDUBIV7U6W/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:PWWBQIHXLEFSCY3IVDUBIV7U6W","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":"9801582966458beefe34ee35c01e8c579732db7495b1ac26db628244889a077c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-02T09:27:13Z","title_canon_sha256":"91e2bd12c011d6c644fb98c2c227d5133badd65981b43a1ceee3eacff9f90099"},"schema_version":"1.0","source":{"id":"1103.0371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0371","created_at":"2026-05-18T04:27:35Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0371v1","created_at":"2026-05-18T04:27:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0371","created_at":"2026-05-18T04:27:35Z"},{"alias_kind":"pith_short_12","alias_value":"PWWBQIHXLEFS","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"PWWBQIHXLEFSCY3I","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"PWWBQIHX","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:b9a98585f84ae8aa99cb1d198efbdbc36667f5a09dafbfa7f18765e178867c34","target":"graph","created_at":"2026-05-18T04:27:35Z","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 relate the $L_p$-variation, $2\\le p < \\infty$, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in time.","authors_text":"Christel Geiss, Emmanuel Gobet, Stefan Geiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-02T09:27:13Z","title":"Generalized fractional smoothness and $L_p$-variation of BSDEs with non-Lipschitz terminal condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0371","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":"sha256:6f6a95bf0b5b738017c39ba8b4f1d9afe378c11742d331c62882bee754a4f3c1","target":"record","created_at":"2026-05-18T04:27:35Z","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":"9801582966458beefe34ee35c01e8c579732db7495b1ac26db628244889a077c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-03-02T09:27:13Z","title_canon_sha256":"91e2bd12c011d6c644fb98c2c227d5133badd65981b43a1ceee3eacff9f90099"},"schema_version":"1.0","source":{"id":"1103.0371","kind":"arxiv","version":1}},"canonical_sha256":"7dac1820f7590b216368a8e81457f4f58ca292b3aa43e6920bfba636fcc93855","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dac1820f7590b216368a8e81457f4f58ca292b3aa43e6920bfba636fcc93855","first_computed_at":"2026-05-18T04:27:35.095572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:35.095572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dxdbwq+XXn6hWZzX0w2jYTvbi85GfWquDdFrGSLeKJihQ3K0SebalVcbDjYX84FRRHOXKLMZ9hOjr92/YDbUCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:35.096255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6f6a95bf0b5b738017c39ba8b4f1d9afe378c11742d331c62882bee754a4f3c1","sha256:b9a98585f84ae8aa99cb1d198efbdbc36667f5a09dafbfa7f18765e178867c34"],"state_sha256":"b430a74cbcbcc26f348cd6cbe87b44c1644ca82e1fb233be36d5092029f244ef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OSuSlvfdqxsd28ph9PSHQD8v7Zx6v78j9UCmTErfZXXg5RGrVVDKuSQuk7DexJr3DEG+/7V3yvvy8R6WRF0bAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T10:19:50.318221Z","bundle_sha256":"fbc36c1e1f9e39fb5d4a3af476adb8ee14500550b6eceee0f73203c67cc9bbed"}}