{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:B6OMJLHEKCV26JTIIT7LOSSUL7","short_pith_number":"pith:B6OMJLHE","canonical_record":{"source":{"id":"1309.6604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-25T18:39:49Z","cross_cats_sorted":[],"title_canon_sha256":"516b0269919db2b9bcff1d34d11347236543341554be47441a948af7fb2a1e85","abstract_canon_sha256":"97ed58c5be0627cb68b10fbb9dfe3db5ce6d7c7948ee14a85f1f474f352f6d46"},"schema_version":"1.0"},"canonical_sha256":"0f9cc4ace450abaf266844feb74a545ff989afca3678ac50918cd7ba0190557e","source":{"kind":"arxiv","id":"1309.6604","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6604","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6604v1","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6604","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"B6OMJLHEKCV2","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"B6OMJLHEKCV26JTI","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"B6OMJLHE","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:B6OMJLHEKCV26JTIIT7LOSSUL7","target":"record","payload":{"canonical_record":{"source":{"id":"1309.6604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-25T18:39:49Z","cross_cats_sorted":[],"title_canon_sha256":"516b0269919db2b9bcff1d34d11347236543341554be47441a948af7fb2a1e85","abstract_canon_sha256":"97ed58c5be0627cb68b10fbb9dfe3db5ce6d7c7948ee14a85f1f474f352f6d46"},"schema_version":"1.0"},"canonical_sha256":"0f9cc4ace450abaf266844feb74a545ff989afca3678ac50918cd7ba0190557e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:12:20.561037Z","signature_b64":"JmLSJnqCj2PLDpPlk3eWn9V6sUc4B+4t02j7t9Y/X29FGgdTorDi2HpIO4Y88AiGZohFJWDjeoQdowKw2bn9Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f9cc4ace450abaf266844feb74a545ff989afca3678ac50918cd7ba0190557e","last_reissued_at":"2026-05-18T03:12:20.560242Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:12:20.560242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1309.6604","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":"2026-05-18T03:12:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xKGXJJxhkQeIdtx8TazdNRFeqy9Vyn9UxSy4ZAN7VJBGfZXqAjgGgFWXvKsT2ub9iGWy6fGidfyefOiKKFmJCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:54:38.762775Z"},"content_sha256":"59bc05a3c9e298caec5d386cd55478b7b4ddf314b4bda89caf4b1e9286ab81ad","schema_version":"1.0","event_id":"sha256:59bc05a3c9e298caec5d386cd55478b7b4ddf314b4bda89caf4b1e9286ab81ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:B6OMJLHEKCV26JTIIT7LOSSUL7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Skorohod and Stratonovich integration in the plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"INRIA Nancy - Grand Est / IECN), Khalil Chouk (CEREMADE), Samy Tindel (IECL","submitted_at":"2013-09-25T18:39:49Z","abstract_excerpt":"This article gives an account on various aspects of stochastic calculus in the plane. Specifically, our aim is 3-fold: (i) Derive a pathwise change of variable formula for a path indexed by a square, satisfying some H\\\"older regularity conditions with a H\\\"older exponent greater than 1/3. (ii) Get some Skorohod change of variable formulas for a large class of Gaussian processes defined on the suqare. (iii) Compare the bidimensional integrals obtained with those two methods, computing explicit correction terms whenever possible. As a byproduct, we also give explicit forms of corrections in the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6604","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":"2026-05-18T03:12:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GVzTh3hKiVUo2leNi/akpuX/QNgtQ0MG7KtnDHCzCSMzsfITQNHskgMDFT22CYz+y9Wzofh1CaeOxsEawDrFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:54:38.763116Z"},"content_sha256":"f05710cf5eac1d6fd40b7ff83e4f1d2cd5b513894cc8488610f44f467dab161d","schema_version":"1.0","event_id":"sha256:f05710cf5eac1d6fd40b7ff83e4f1d2cd5b513894cc8488610f44f467dab161d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B6OMJLHEKCV26JTIIT7LOSSUL7/bundle.json","state_url":"https://pith.science/pith/B6OMJLHEKCV26JTIIT7LOSSUL7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B6OMJLHEKCV26JTIIT7LOSSUL7/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":"2026-06-24T04:54:38Z","links":{"resolver":"https://pith.science/pith/B6OMJLHEKCV26JTIIT7LOSSUL7","bundle":"https://pith.science/pith/B6OMJLHEKCV26JTIIT7LOSSUL7/bundle.json","state":"https://pith.science/pith/B6OMJLHEKCV26JTIIT7LOSSUL7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B6OMJLHEKCV26JTIIT7LOSSUL7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:B6OMJLHEKCV26JTIIT7LOSSUL7","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":"97ed58c5be0627cb68b10fbb9dfe3db5ce6d7c7948ee14a85f1f474f352f6d46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-25T18:39:49Z","title_canon_sha256":"516b0269919db2b9bcff1d34d11347236543341554be47441a948af7fb2a1e85"},"schema_version":"1.0","source":{"id":"1309.6604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1309.6604","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"arxiv_version","alias_value":"1309.6604v1","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1309.6604","created_at":"2026-05-18T03:12:20Z"},{"alias_kind":"pith_short_12","alias_value":"B6OMJLHEKCV2","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"B6OMJLHEKCV26JTI","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"B6OMJLHE","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:f05710cf5eac1d6fd40b7ff83e4f1d2cd5b513894cc8488610f44f467dab161d","target":"graph","created_at":"2026-05-18T03:12:20Z","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":"This article gives an account on various aspects of stochastic calculus in the plane. Specifically, our aim is 3-fold: (i) Derive a pathwise change of variable formula for a path indexed by a square, satisfying some H\\\"older regularity conditions with a H\\\"older exponent greater than 1/3. (ii) Get some Skorohod change of variable formulas for a large class of Gaussian processes defined on the suqare. (iii) Compare the bidimensional integrals obtained with those two methods, computing explicit correction terms whenever possible. As a byproduct, we also give explicit forms of corrections in the ","authors_text":"INRIA Nancy - Grand Est / IECN), Khalil Chouk (CEREMADE), Samy Tindel (IECL","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-25T18:39:49Z","title":"Skorohod and Stratonovich integration in the plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6604","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":"sha256:59bc05a3c9e298caec5d386cd55478b7b4ddf314b4bda89caf4b1e9286ab81ad","target":"record","created_at":"2026-05-18T03:12:20Z","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":"97ed58c5be0627cb68b10fbb9dfe3db5ce6d7c7948ee14a85f1f474f352f6d46","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-09-25T18:39:49Z","title_canon_sha256":"516b0269919db2b9bcff1d34d11347236543341554be47441a948af7fb2a1e85"},"schema_version":"1.0","source":{"id":"1309.6604","kind":"arxiv","version":1}},"canonical_sha256":"0f9cc4ace450abaf266844feb74a545ff989afca3678ac50918cd7ba0190557e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f9cc4ace450abaf266844feb74a545ff989afca3678ac50918cd7ba0190557e","first_computed_at":"2026-05-18T03:12:20.560242Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:20.560242Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JmLSJnqCj2PLDpPlk3eWn9V6sUc4B+4t02j7t9Y/X29FGgdTorDi2HpIO4Y88AiGZohFJWDjeoQdowKw2bn9Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:20.561037Z","signed_message":"canonical_sha256_bytes"},"source_id":"1309.6604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59bc05a3c9e298caec5d386cd55478b7b4ddf314b4bda89caf4b1e9286ab81ad","sha256:f05710cf5eac1d6fd40b7ff83e4f1d2cd5b513894cc8488610f44f467dab161d"],"state_sha256":"cd0ca6281eb8ecb8ebfd365a57ca77c3cf8212b3b360f6fdcca05efe5df8e33d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gcHOqIQ+Bk2TJDeP2s4Evshj20lQiEIdqJW3+/MaJYfGaKO/uET7nB4l5VzG7Zr8zOAR4lBDU6K07gXo6T7SDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:54:38.765023Z","bundle_sha256":"fdebfbf96055b73377cf140d67c1abfbc83b337446d1822509060e24177acdde"}}