{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:DEKZDGKY6AYO3WMZMBXJKK4WZ5","short_pith_number":"pith:DEKZDGKY","canonical_record":{"source":{"id":"1107.6016","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-29T16:44:16Z","cross_cats_sorted":[],"title_canon_sha256":"91107b2a70b85909ff4f2240c8ad9a20244feaadb494c55e5bcd9cd3c9e5db45","abstract_canon_sha256":"b13a8bb423e5dfc35d419bcd2b60c06d60897d4778ffb9ea03e5a23d3266b278"},"schema_version":"1.0"},"canonical_sha256":"1915919958f030edd999606e952b96cf604c0b331280152c059bec8a6bcc451d","source":{"kind":"arxiv","id":"1107.6016","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.6016","created_at":"2026-05-18T03:14:50Z"},{"alias_kind":"arxiv_version","alias_value":"1107.6016v2","created_at":"2026-05-18T03:14:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.6016","created_at":"2026-05-18T03:14:50Z"},{"alias_kind":"pith_short_12","alias_value":"DEKZDGKY6AYO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DEKZDGKY6AYO3WMZ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DEKZDGKY","created_at":"2026-05-18T12:26:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:DEKZDGKY6AYO3WMZMBXJKK4WZ5","target":"record","payload":{"canonical_record":{"source":{"id":"1107.6016","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-29T16:44:16Z","cross_cats_sorted":[],"title_canon_sha256":"91107b2a70b85909ff4f2240c8ad9a20244feaadb494c55e5bcd9cd3c9e5db45","abstract_canon_sha256":"b13a8bb423e5dfc35d419bcd2b60c06d60897d4778ffb9ea03e5a23d3266b278"},"schema_version":"1.0"},"canonical_sha256":"1915919958f030edd999606e952b96cf604c0b331280152c059bec8a6bcc451d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:14:50.416822Z","signature_b64":"vsgA6u2FOXwdzCnuQBflUvbO8DdYx2y321GCWVGSQtA4qr9BcMlNlZ/KPARcpEEO1AvbYec+IKdKMKmMjktcDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1915919958f030edd999606e952b96cf604c0b331280152c059bec8a6bcc451d","last_reissued_at":"2026-05-18T03:14:50.415509Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:14:50.415509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1107.6016","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":"2026-05-18T03:14:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WipoprjHJTyCVfjISvwEy6poFq85HHiud6hFHb2aRIuBzuOpdQnLRhxP2dLlZfHDcnB1ohBFFuzY/BBZFeK2DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:35:24.210976Z"},"content_sha256":"cddd31c88aa8cee993db01bbee940a9a696b2a5332c1fa93becbb1425ca5df60","schema_version":"1.0","event_id":"sha256:cddd31c88aa8cee993db01bbee940a9a696b2a5332c1fa93becbb1425ca5df60"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:DEKZDGKY6AYO3WMZMBXJKK4WZ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"2-microlocal analysis of martingales and stochastic integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erick Herbin, Paul Balan\\c{c}a","submitted_at":"2011-07-29T16:44:16Z","abstract_excerpt":"Recently, a new approach in the fine analysis of stochastic processes sample paths has been developed to predict the evolution of the local regularity under (pseudo-)differential operators. In this paper, we study the sample paths of continuous martingales and stochastic integrals. We proved that the almost sure 2-microlocal frontier of a martingale can be obtained through the local regularity of its quadratic variation. It allows to link the H\\\"older regularity of a stochastic integral to the regularity of the integrand and integrator processes. These results provide a methodology to predict "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.6016","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":"2026-05-18T03:14:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YfZCy28pIVUsT7cZGKZHU3/PkNJYB+JIYTGYNBkxyOm3iXFNUjNv3cufpb5IQUeRsUn1Pv5XIwF6E6gmWVZVBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T18:35:24.211339Z"},"content_sha256":"2ea52e4d2514cad4e2d9d843c9c6bc243b32a096f65717804c96b6962f8d5803","schema_version":"1.0","event_id":"sha256:2ea52e4d2514cad4e2d9d843c9c6bc243b32a096f65717804c96b6962f8d5803"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DEKZDGKY6AYO3WMZMBXJKK4WZ5/bundle.json","state_url":"https://pith.science/pith/DEKZDGKY6AYO3WMZMBXJKK4WZ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DEKZDGKY6AYO3WMZMBXJKK4WZ5/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":"2026-06-05T18:35:24Z","links":{"resolver":"https://pith.science/pith/DEKZDGKY6AYO3WMZMBXJKK4WZ5","bundle":"https://pith.science/pith/DEKZDGKY6AYO3WMZMBXJKK4WZ5/bundle.json","state":"https://pith.science/pith/DEKZDGKY6AYO3WMZMBXJKK4WZ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DEKZDGKY6AYO3WMZMBXJKK4WZ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:DEKZDGKY6AYO3WMZMBXJKK4WZ5","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":"b13a8bb423e5dfc35d419bcd2b60c06d60897d4778ffb9ea03e5a23d3266b278","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-29T16:44:16Z","title_canon_sha256":"91107b2a70b85909ff4f2240c8ad9a20244feaadb494c55e5bcd9cd3c9e5db45"},"schema_version":"1.0","source":{"id":"1107.6016","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.6016","created_at":"2026-05-18T03:14:50Z"},{"alias_kind":"arxiv_version","alias_value":"1107.6016v2","created_at":"2026-05-18T03:14:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.6016","created_at":"2026-05-18T03:14:50Z"},{"alias_kind":"pith_short_12","alias_value":"DEKZDGKY6AYO","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_16","alias_value":"DEKZDGKY6AYO3WMZ","created_at":"2026-05-18T12:26:26Z"},{"alias_kind":"pith_short_8","alias_value":"DEKZDGKY","created_at":"2026-05-18T12:26:26Z"}],"graph_snapshots":[{"event_id":"sha256:2ea52e4d2514cad4e2d9d843c9c6bc243b32a096f65717804c96b6962f8d5803","target":"graph","created_at":"2026-05-18T03:14:50Z","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":"Recently, a new approach in the fine analysis of stochastic processes sample paths has been developed to predict the evolution of the local regularity under (pseudo-)differential operators. In this paper, we study the sample paths of continuous martingales and stochastic integrals. We proved that the almost sure 2-microlocal frontier of a martingale can be obtained through the local regularity of its quadratic variation. It allows to link the H\\\"older regularity of a stochastic integral to the regularity of the integrand and integrator processes. These results provide a methodology to predict ","authors_text":"Erick Herbin, Paul Balan\\c{c}a","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-29T16:44:16Z","title":"2-microlocal analysis of martingales and stochastic integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.6016","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:cddd31c88aa8cee993db01bbee940a9a696b2a5332c1fa93becbb1425ca5df60","target":"record","created_at":"2026-05-18T03:14:50Z","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":"b13a8bb423e5dfc35d419bcd2b60c06d60897d4778ffb9ea03e5a23d3266b278","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-29T16:44:16Z","title_canon_sha256":"91107b2a70b85909ff4f2240c8ad9a20244feaadb494c55e5bcd9cd3c9e5db45"},"schema_version":"1.0","source":{"id":"1107.6016","kind":"arxiv","version":2}},"canonical_sha256":"1915919958f030edd999606e952b96cf604c0b331280152c059bec8a6bcc451d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1915919958f030edd999606e952b96cf604c0b331280152c059bec8a6bcc451d","first_computed_at":"2026-05-18T03:14:50.415509Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:14:50.415509Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vsgA6u2FOXwdzCnuQBflUvbO8DdYx2y321GCWVGSQtA4qr9BcMlNlZ/KPARcpEEO1AvbYec+IKdKMKmMjktcDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:14:50.416822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.6016","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cddd31c88aa8cee993db01bbee940a9a696b2a5332c1fa93becbb1425ca5df60","sha256:2ea52e4d2514cad4e2d9d843c9c6bc243b32a096f65717804c96b6962f8d5803"],"state_sha256":"cde8309f50e325131cafb55c47f27a813419b12c66a544111879b057e2b95570"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VnguoF2j2my9nfgyM7TWMXn+bbGCMUoUmD9NfLRHzs4ClmaUCQwyitkWKnLXstBZA1feYUNWj8oX+NuiNPZdAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T18:35:24.213226Z","bundle_sha256":"8e0eb381b3e2c7ef60e49e7abe203a4aeeb6a5881576e7cb155c083747d11686"}}