{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:WLT4FLAO3VZNGLPHCEZT6A6PON","short_pith_number":"pith:WLT4FLAO","canonical_record":{"source":{"id":"1512.03992","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-13T02:58:27Z","cross_cats_sorted":[],"title_canon_sha256":"34ad5a87abbf486874164910d61562050a846387a4f7db780bd18bf355288a72","abstract_canon_sha256":"36c1692522155df3fce505e0f414d25b9b12fef3835aeeeb8d6e40f939eaebb2"},"schema_version":"1.0"},"canonical_sha256":"b2e7c2ac0edd72d32de711333f03cf736c81fe45f5f566169cc8719eaa7f3448","source":{"kind":"arxiv","id":"1512.03992","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03992","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03992v2","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03992","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"WLT4FLAO3VZN","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WLT4FLAO3VZNGLPH","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WLT4FLAO","created_at":"2026-05-18T12:29:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:WLT4FLAO3VZNGLPHCEZT6A6PON","target":"record","payload":{"canonical_record":{"source":{"id":"1512.03992","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-13T02:58:27Z","cross_cats_sorted":[],"title_canon_sha256":"34ad5a87abbf486874164910d61562050a846387a4f7db780bd18bf355288a72","abstract_canon_sha256":"36c1692522155df3fce505e0f414d25b9b12fef3835aeeeb8d6e40f939eaebb2"},"schema_version":"1.0"},"canonical_sha256":"b2e7c2ac0edd72d32de711333f03cf736c81fe45f5f566169cc8719eaa7f3448","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:24.187648Z","signature_b64":"7ALkdvB/3hZAxuCAyrDEe/FvlH9tMPohn4lXzsYTCDm6JT17vh6yNxdDMdk1LAkiNnUjY0+B2Vla5g8m8m6oCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b2e7c2ac0edd72d32de711333f03cf736c81fe45f5f566169cc8719eaa7f3448","last_reissued_at":"2026-05-18T00:08:24.187046Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:24.187046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.03992","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":"2026-05-18T00:08:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NK6Z2qj47fBxUfZ9RGbkKD2R6w1KOawksByW8qPXQJZao7Or+TOhZXxRB9DUyrgQA4fvADkJb4MYJTryYzMcCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:47:35.153324Z"},"content_sha256":"b98e7a739a8d244ca9f948cf7693a281623323f1ca4513c49d583d076278764f","schema_version":"1.0","event_id":"sha256:b98e7a739a8d244ca9f948cf7693a281623323f1ca4513c49d583d076278764f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:WLT4FLAO3VZNGLPHCEZT6A6PON","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integral representations of martingales for progressive enlargements of filtrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Aksamit, Marek Rutkowski, Monique Jeanblanc","submitted_at":"2015-12-13T02:58:27Z","abstract_excerpt":"We work in the setting of the progressive enlargement $\\mathbb G$ of a reference filtration $\\mathbb F$ through the observation of a random time $\\tau$. We study an integral representation property for some classes of $\\mathbb G$-martingales stopped at $\\tau$. In the first part, we focus on the case where $\\mathbb F$ is a Poisson filtration and we establish a predictable representation property with respect to three $\\mathbb G$-martingales. In the second part, we relax the assumption that $\\mathbb F$ is a Poisson filtration and we assume that $\\tau$ is an $\\mathbb F$-pseudo-stopping time. We e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03992","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":"2026-05-18T00:08:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yUaQe/EpSaWabCAmaI+TzHKlCZS3vgyX8T5N/mhYmYkThsCCyO3DGVzVC1QmQgfkJFIJ1UNLjwCcrooEIluJCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T05:47:35.153678Z"},"content_sha256":"cd4e66a5d80a329c09a6017df438f36678532b99da9a1e7f3c93005bc5d0c9d8","schema_version":"1.0","event_id":"sha256:cd4e66a5d80a329c09a6017df438f36678532b99da9a1e7f3c93005bc5d0c9d8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WLT4FLAO3VZNGLPHCEZT6A6PON/bundle.json","state_url":"https://pith.science/pith/WLT4FLAO3VZNGLPHCEZT6A6PON/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WLT4FLAO3VZNGLPHCEZT6A6PON/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":"2026-05-28T05:47:35Z","links":{"resolver":"https://pith.science/pith/WLT4FLAO3VZNGLPHCEZT6A6PON","bundle":"https://pith.science/pith/WLT4FLAO3VZNGLPHCEZT6A6PON/bundle.json","state":"https://pith.science/pith/WLT4FLAO3VZNGLPHCEZT6A6PON/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WLT4FLAO3VZNGLPHCEZT6A6PON/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WLT4FLAO3VZNGLPHCEZT6A6PON","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":"36c1692522155df3fce505e0f414d25b9b12fef3835aeeeb8d6e40f939eaebb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-13T02:58:27Z","title_canon_sha256":"34ad5a87abbf486874164910d61562050a846387a4f7db780bd18bf355288a72"},"schema_version":"1.0","source":{"id":"1512.03992","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.03992","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"arxiv_version","alias_value":"1512.03992v2","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.03992","created_at":"2026-05-18T00:08:24Z"},{"alias_kind":"pith_short_12","alias_value":"WLT4FLAO3VZN","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WLT4FLAO3VZNGLPH","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WLT4FLAO","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:cd4e66a5d80a329c09a6017df438f36678532b99da9a1e7f3c93005bc5d0c9d8","target":"graph","created_at":"2026-05-18T00:08:24Z","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 work in the setting of the progressive enlargement $\\mathbb G$ of a reference filtration $\\mathbb F$ through the observation of a random time $\\tau$. We study an integral representation property for some classes of $\\mathbb G$-martingales stopped at $\\tau$. In the first part, we focus on the case where $\\mathbb F$ is a Poisson filtration and we establish a predictable representation property with respect to three $\\mathbb G$-martingales. In the second part, we relax the assumption that $\\mathbb F$ is a Poisson filtration and we assume that $\\tau$ is an $\\mathbb F$-pseudo-stopping time. We e","authors_text":"Anna Aksamit, Marek Rutkowski, Monique Jeanblanc","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-13T02:58:27Z","title":"Integral representations of martingales for progressive enlargements of filtrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.03992","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:b98e7a739a8d244ca9f948cf7693a281623323f1ca4513c49d583d076278764f","target":"record","created_at":"2026-05-18T00:08:24Z","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":"36c1692522155df3fce505e0f414d25b9b12fef3835aeeeb8d6e40f939eaebb2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-13T02:58:27Z","title_canon_sha256":"34ad5a87abbf486874164910d61562050a846387a4f7db780bd18bf355288a72"},"schema_version":"1.0","source":{"id":"1512.03992","kind":"arxiv","version":2}},"canonical_sha256":"b2e7c2ac0edd72d32de711333f03cf736c81fe45f5f566169cc8719eaa7f3448","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b2e7c2ac0edd72d32de711333f03cf736c81fe45f5f566169cc8719eaa7f3448","first_computed_at":"2026-05-18T00:08:24.187046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:24.187046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ALkdvB/3hZAxuCAyrDEe/FvlH9tMPohn4lXzsYTCDm6JT17vh6yNxdDMdk1LAkiNnUjY0+B2Vla5g8m8m6oCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:24.187648Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.03992","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b98e7a739a8d244ca9f948cf7693a281623323f1ca4513c49d583d076278764f","sha256:cd4e66a5d80a329c09a6017df438f36678532b99da9a1e7f3c93005bc5d0c9d8"],"state_sha256":"ae70bd37c676542409ec73a3e90ebf2fdeea4b13b52a90641a32848d6562cc71"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VsNcZpTi2qvKzD1fleUzSW+PTGRrcr95GJ2lKcFhWzovXJeZGF+XTnFjGdopcl7GURubsznZkv5bXHGTLCzpDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T05:47:35.155649Z","bundle_sha256":"a326a83029002a35d857fe9df0320a1a1d33c9e2c1e24a63e8e479abdf4504df"}}