{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:I2KJXE2JKF254KU7XHEYPF7VS5","short_pith_number":"pith:I2KJXE2J","canonical_record":{"source":{"id":"1608.03766","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-12T12:08:21Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"444df325fcd97698746fd6e450a4676637cc47026df3621b8347c63450d960cc","abstract_canon_sha256":"0a2183bb30035c5d536779ffdd0a5856d546394a6733af5ee316df15d4c29232"},"schema_version":"1.0"},"canonical_sha256":"46949b93495175de2a9fb9c98797f59749ea0af1fd54d6dbe6c88e2ad25d52a0","source":{"kind":"arxiv","id":"1608.03766","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03766","created_at":"2026-05-17T23:57:33Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03766v1","created_at":"2026-05-17T23:57:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03766","created_at":"2026-05-17T23:57:33Z"},{"alias_kind":"pith_short_12","alias_value":"I2KJXE2JKF25","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I2KJXE2JKF254KU7","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I2KJXE2J","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:I2KJXE2JKF254KU7XHEYPF7VS5","target":"record","payload":{"canonical_record":{"source":{"id":"1608.03766","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-12T12:08:21Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"444df325fcd97698746fd6e450a4676637cc47026df3621b8347c63450d960cc","abstract_canon_sha256":"0a2183bb30035c5d536779ffdd0a5856d546394a6733af5ee316df15d4c29232"},"schema_version":"1.0"},"canonical_sha256":"46949b93495175de2a9fb9c98797f59749ea0af1fd54d6dbe6c88e2ad25d52a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:33.128858Z","signature_b64":"jC5S5IEzkT9SwLXsMBk3bj0IOmwQF9zTUiRXO09jN2aOmVhXLfa2ymrQdLiC/YG8uf61OKrGofVOwa1MS4/vBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46949b93495175de2a9fb9c98797f59749ea0af1fd54d6dbe6c88e2ad25d52a0","last_reissued_at":"2026-05-17T23:57:33.128464Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:33.128464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.03766","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":"2026-05-17T23:57:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5iqBZEKy0TBWkYuzciF3HwADecM2p99p5b5Yx1pal0L6emIbC5ou5CzKwTw6HXI8RJWCnot4cXaLIzVbXHPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:23:13.207978Z"},"content_sha256":"a065b56235d12c33044d27ae4e3c5eae1d48261b98cd712c6caa6b7372436751","schema_version":"1.0","event_id":"sha256:a065b56235d12c33044d27ae4e3c5eae1d48261b98cd712c6caa6b7372436751"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:I2KJXE2JKF254KU7XHEYPF7VS5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of a surface integral under local Malliavin assumption and integration by parts formulae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Giuseppe Da Prato, Luciano Tubaro, Stefano Bonaccorsi","submitted_at":"2016-08-12T12:08:21Z","abstract_excerpt":"In this paper, we consider convex sets $K_r = \\{g \\ge r\\}$ in an infinite dimensional Hilbert space, where $g$ is suitably related to a reference Gaussian measure $\\mu$ in $H$. We first show how to define a surface measure on the level sets $\\{g = r\\}$ that is related to $\\mu$. This allows to introduce an integration-by-parts formula in $H$. This formula can be applied in several important constructions, as for instance the case where $\\mu$ is the law of a (Gaussian) stochastic process and $H$ is the space of its trajectories"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03766","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":"2026-05-17T23:57:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"15wjPUFcxOEYJIowWrYAL1bdIN5WqA7X9V/O85S1r2i2gZ9EVZlQ1VsWMFpRuPmEY39BynaMq0uZZtcZ/takBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:23:13.208337Z"},"content_sha256":"dc3a3cae2e931fa7db2ad2204f70584a5a100c49bead047d8d9376c75c03fa43","schema_version":"1.0","event_id":"sha256:dc3a3cae2e931fa7db2ad2204f70584a5a100c49bead047d8d9376c75c03fa43"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5/bundle.json","state_url":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I2KJXE2JKF254KU7XHEYPF7VS5/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":"2026-06-27T10:23:13Z","links":{"resolver":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5","bundle":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5/bundle.json","state":"https://pith.science/pith/I2KJXE2JKF254KU7XHEYPF7VS5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I2KJXE2JKF254KU7XHEYPF7VS5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I2KJXE2JKF254KU7XHEYPF7VS5","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":"0a2183bb30035c5d536779ffdd0a5856d546394a6733af5ee316df15d4c29232","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-12T12:08:21Z","title_canon_sha256":"444df325fcd97698746fd6e450a4676637cc47026df3621b8347c63450d960cc"},"schema_version":"1.0","source":{"id":"1608.03766","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.03766","created_at":"2026-05-17T23:57:33Z"},{"alias_kind":"arxiv_version","alias_value":"1608.03766v1","created_at":"2026-05-17T23:57:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.03766","created_at":"2026-05-17T23:57:33Z"},{"alias_kind":"pith_short_12","alias_value":"I2KJXE2JKF25","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I2KJXE2JKF254KU7","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I2KJXE2J","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:dc3a3cae2e931fa7db2ad2204f70584a5a100c49bead047d8d9376c75c03fa43","target":"graph","created_at":"2026-05-17T23:57:33Z","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 this paper, we consider convex sets $K_r = \\{g \\ge r\\}$ in an infinite dimensional Hilbert space, where $g$ is suitably related to a reference Gaussian measure $\\mu$ in $H$. We first show how to define a surface measure on the level sets $\\{g = r\\}$ that is related to $\\mu$. This allows to introduce an integration-by-parts formula in $H$. This formula can be applied in several important constructions, as for instance the case where $\\mu$ is the law of a (Gaussian) stochastic process and $H$ is the space of its trajectories","authors_text":"Giuseppe Da Prato, Luciano Tubaro, Stefano Bonaccorsi","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-12T12:08:21Z","title":"Construction of a surface integral under local Malliavin assumption and integration by parts formulae"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.03766","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:a065b56235d12c33044d27ae4e3c5eae1d48261b98cd712c6caa6b7372436751","target":"record","created_at":"2026-05-17T23:57:33Z","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":"0a2183bb30035c5d536779ffdd0a5856d546394a6733af5ee316df15d4c29232","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-08-12T12:08:21Z","title_canon_sha256":"444df325fcd97698746fd6e450a4676637cc47026df3621b8347c63450d960cc"},"schema_version":"1.0","source":{"id":"1608.03766","kind":"arxiv","version":1}},"canonical_sha256":"46949b93495175de2a9fb9c98797f59749ea0af1fd54d6dbe6c88e2ad25d52a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46949b93495175de2a9fb9c98797f59749ea0af1fd54d6dbe6c88e2ad25d52a0","first_computed_at":"2026-05-17T23:57:33.128464Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:33.128464Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jC5S5IEzkT9SwLXsMBk3bj0IOmwQF9zTUiRXO09jN2aOmVhXLfa2ymrQdLiC/YG8uf61OKrGofVOwa1MS4/vBA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:33.128858Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.03766","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a065b56235d12c33044d27ae4e3c5eae1d48261b98cd712c6caa6b7372436751","sha256:dc3a3cae2e931fa7db2ad2204f70584a5a100c49bead047d8d9376c75c03fa43"],"state_sha256":"35d9e9f962edd2211e7d281280ffb7650bc26a26ea1dc53ea56a665eeaeecadd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yOmu68nBMcoGinUKjVyfug4jKmDbxbJikYu/xDU+cbYahWMmOBUU0Y4xB8/aXEq5vGFLpOyflThh51W95VWdDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T10:23:13.210148Z","bundle_sha256":"108b03a674a6e384fe1a56b1d90aaf7f1c22f44c200f9a080b51c31d839624a4"}}