{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:67VF4H242F44S3V4PFXRFL43HZ","short_pith_number":"pith:67VF4H24","canonical_record":{"source":{"id":"1803.01744","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-05T15:53:33Z","cross_cats_sorted":[],"title_canon_sha256":"5b6908cf1b8e661de18564be32629eaef3c94af09fa1f3931854c8fe0fe00e81","abstract_canon_sha256":"de953652564f16b36ca4ece2ed568d25bf13313ae20a7c6b93bb55b4bf29013c"},"schema_version":"1.0"},"canonical_sha256":"f7ea5e1f5cd179c96ebc796f12af9b3e6a62a0b549d338273b10d12133c16c2b","source":{"kind":"arxiv","id":"1803.01744","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01744","created_at":"2026-07-05T07:54:45Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01744v3","created_at":"2026-07-05T07:54:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01744","created_at":"2026-07-05T07:54:45Z"},{"alias_kind":"pith_short_12","alias_value":"67VF4H242F44","created_at":"2026-07-05T07:54:45Z"},{"alias_kind":"pith_short_16","alias_value":"67VF4H242F44S3V4","created_at":"2026-07-05T07:54:45Z"},{"alias_kind":"pith_short_8","alias_value":"67VF4H24","created_at":"2026-07-05T07:54:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:67VF4H242F44S3V4PFXRFL43HZ","target":"record","payload":{"canonical_record":{"source":{"id":"1803.01744","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-05T15:53:33Z","cross_cats_sorted":[],"title_canon_sha256":"5b6908cf1b8e661de18564be32629eaef3c94af09fa1f3931854c8fe0fe00e81","abstract_canon_sha256":"de953652564f16b36ca4ece2ed568d25bf13313ae20a7c6b93bb55b4bf29013c"},"schema_version":"1.0"},"canonical_sha256":"f7ea5e1f5cd179c96ebc796f12af9b3e6a62a0b549d338273b10d12133c16c2b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:54:45.614212Z","signature_b64":"86ODvMDnVNafzky8C3DKjLrQRz8VRlpTTxHcfXHDrMnwj12YSLlMECDBtu06SYOc/FFVVBe3ORzyPgle0ZFrAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f7ea5e1f5cd179c96ebc796f12af9b3e6a62a0b549d338273b10d12133c16c2b","last_reissued_at":"2026-07-05T07:54:45.613578Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:54:45.613578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.01744","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T07:54:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gABnYRU+GS5KFb/4UmfQLnJlQGyDJX94ES/lGn528aa86V1ydaOfYUS8yUsDiUtHxL+jYDfpyOFtkjXPxR70Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:10:48.430464Z"},"content_sha256":"80ae8726e35132202d3def96af1a66438bdd7bb0ccdfdbc00ef19c225a204b0a","schema_version":"1.0","event_id":"sha256:80ae8726e35132202d3def96af1a66438bdd7bb0ccdfdbc00ef19c225a204b0a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:67VF4H242F44S3V4PFXRFL43HZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An It\\^o type formula for the additive stochastic heat equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Carlo Bellingeri","submitted_at":"2018-03-05T15:53:33Z","abstract_excerpt":"We use the theory of regularity structures to develop an It\\^o formula for $u$, the solution of the one dimensional stochastic heat equation driven by space-time white noise with periodic boundary conditions. In particular for any smooth enough function $\\varphi$ we can express the random distribution $(\\partial_t-\\partial_{xx})\\varphi(u)$ and the random field $\\varphi(u)$ in terms of the reconstruction of some modelled distributions. The resulting objects are then identified with some classical constructions of stochastic calculus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01744","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1803.01744/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T07:54:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oHjrYmML5pbGRBhZ6m34LJmR6Ephf4P9MmY7WMnQzesJRVJqPHl/xa4Q62o7Ld9yrnmY6L5l3k5axVj1Zph1Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T13:10:48.430953Z"},"content_sha256":"9240db2cdccefc5ce824eefb385db1b1d70854b3b25324bf35dccc96d8081b0f","schema_version":"1.0","event_id":"sha256:9240db2cdccefc5ce824eefb385db1b1d70854b3b25324bf35dccc96d8081b0f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/67VF4H242F44S3V4PFXRFL43HZ/bundle.json","state_url":"https://pith.science/pith/67VF4H242F44S3V4PFXRFL43HZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/67VF4H242F44S3V4PFXRFL43HZ/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":"2026-08-16T13:10:48Z","links":{"resolver":"https://pith.science/pith/67VF4H242F44S3V4PFXRFL43HZ","bundle":"https://pith.science/pith/67VF4H242F44S3V4PFXRFL43HZ/bundle.json","state":"https://pith.science/pith/67VF4H242F44S3V4PFXRFL43HZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/67VF4H242F44S3V4PFXRFL43HZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:67VF4H242F44S3V4PFXRFL43HZ","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":"de953652564f16b36ca4ece2ed568d25bf13313ae20a7c6b93bb55b4bf29013c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-05T15:53:33Z","title_canon_sha256":"5b6908cf1b8e661de18564be32629eaef3c94af09fa1f3931854c8fe0fe00e81"},"schema_version":"1.0","source":{"id":"1803.01744","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.01744","created_at":"2026-07-05T07:54:45Z"},{"alias_kind":"arxiv_version","alias_value":"1803.01744v3","created_at":"2026-07-05T07:54:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.01744","created_at":"2026-07-05T07:54:45Z"},{"alias_kind":"pith_short_12","alias_value":"67VF4H242F44","created_at":"2026-07-05T07:54:45Z"},{"alias_kind":"pith_short_16","alias_value":"67VF4H242F44S3V4","created_at":"2026-07-05T07:54:45Z"},{"alias_kind":"pith_short_8","alias_value":"67VF4H24","created_at":"2026-07-05T07:54:45Z"}],"graph_snapshots":[{"event_id":"sha256:9240db2cdccefc5ce824eefb385db1b1d70854b3b25324bf35dccc96d8081b0f","target":"graph","created_at":"2026-07-05T07:54:45Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1803.01744/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We use the theory of regularity structures to develop an It\\^o formula for $u$, the solution of the one dimensional stochastic heat equation driven by space-time white noise with periodic boundary conditions. In particular for any smooth enough function $\\varphi$ we can express the random distribution $(\\partial_t-\\partial_{xx})\\varphi(u)$ and the random field $\\varphi(u)$ in terms of the reconstruction of some modelled distributions. The resulting objects are then identified with some classical constructions of stochastic calculus.","authors_text":"Carlo Bellingeri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-05T15:53:33Z","title":"An It\\^o type formula for the additive stochastic heat equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01744","kind":"arxiv","version":3},"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":"sha256:80ae8726e35132202d3def96af1a66438bdd7bb0ccdfdbc00ef19c225a204b0a","target":"record","created_at":"2026-07-05T07:54:45Z","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":"de953652564f16b36ca4ece2ed568d25bf13313ae20a7c6b93bb55b4bf29013c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-03-05T15:53:33Z","title_canon_sha256":"5b6908cf1b8e661de18564be32629eaef3c94af09fa1f3931854c8fe0fe00e81"},"schema_version":"1.0","source":{"id":"1803.01744","kind":"arxiv","version":3}},"canonical_sha256":"f7ea5e1f5cd179c96ebc796f12af9b3e6a62a0b549d338273b10d12133c16c2b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f7ea5e1f5cd179c96ebc796f12af9b3e6a62a0b549d338273b10d12133c16c2b","first_computed_at":"2026-07-05T07:54:45.613578Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:54:45.613578Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"86ODvMDnVNafzky8C3DKjLrQRz8VRlpTTxHcfXHDrMnwj12YSLlMECDBtu06SYOc/FFVVBe3ORzyPgle0ZFrAA==","signature_status":"signed_v1","signed_at":"2026-07-05T07:54:45.614212Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.01744","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:80ae8726e35132202d3def96af1a66438bdd7bb0ccdfdbc00ef19c225a204b0a","sha256:9240db2cdccefc5ce824eefb385db1b1d70854b3b25324bf35dccc96d8081b0f"],"state_sha256":"1dda971915294690db8adb551678f73f74ded111fa436c473d24a979204d7c9f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dw4BSfivM6w/mazsLBE4o3CFGUADCf//hcfdQeFyXBl6QzsUhp9+WKRu987WfNpx80MgoTWhYXjYw8bTXZQtCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T13:10:48.435667Z","bundle_sha256":"f0216e6d5fb359fff3d3027d2a20537fa4395064b3c7bd1128162bfaee60af23"}}