{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:532HATK7QF7JT6UOPMB2NUNK74","short_pith_number":"pith:532HATK7","canonical_record":{"source":{"id":"1202.3094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-14T17:23:07Z","cross_cats_sorted":["math.AP","math.NA"],"title_canon_sha256":"4c5a1b72d93d5ccea2b29f1d3a4b6e00e8ef56b2b15ac280ae6f29daad57a511","abstract_canon_sha256":"44fd3a46e7280c5c0e93552b31b8ce751cd2a6f24d30b1026335382e144064c2"},"schema_version":"1.0"},"canonical_sha256":"eef4704d5f817e99fa8e7b03a6d1aaff1b0ffbb6d96e12ab5e65cd1e3a851eb4","source":{"kind":"arxiv","id":"1202.3094","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3094","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3094v2","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3094","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"532HATK7QF7J","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"532HATK7QF7JT6UO","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"532HATK7","created_at":"2026-05-18T12:26:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:532HATK7QF7JT6UOPMB2NUNK74","target":"record","payload":{"canonical_record":{"source":{"id":"1202.3094","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-14T17:23:07Z","cross_cats_sorted":["math.AP","math.NA"],"title_canon_sha256":"4c5a1b72d93d5ccea2b29f1d3a4b6e00e8ef56b2b15ac280ae6f29daad57a511","abstract_canon_sha256":"44fd3a46e7280c5c0e93552b31b8ce751cd2a6f24d30b1026335382e144064c2"},"schema_version":"1.0"},"canonical_sha256":"eef4704d5f817e99fa8e7b03a6d1aaff1b0ffbb6d96e12ab5e65cd1e3a851eb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:10.088606Z","signature_b64":"pee0TnbopGu4iYxo6Gijm8tz40QwZ9UzB3nbpo1uvIwsCjvCYcY+jpCdLXLgoelvdOUoQ0gmU/bn0lq+I/JODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eef4704d5f817e99fa8e7b03a6d1aaff1b0ffbb6d96e12ab5e65cd1e3a851eb4","last_reissued_at":"2026-05-18T01:13:10.088189Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:10.088189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.3094","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":"2026-05-18T01:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NHioZmT0wW6u/zfP8yniVklgy0UwpOV+FEqJerfsuPsATmTYRgDMawEP96nZgoLtGp0dM9qw6NW3WZ+UF69EAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:28:44.886569Z"},"content_sha256":"b563a59f7a45392df96e13cf48e6f4811f214a285fece6d1e9ac7487fcf81a09","schema_version":"1.0","event_id":"sha256:b563a59f7a45392df96e13cf48e6f4811f214a285fece6d1e9ac7487fcf81a09"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:532HATK7QF7JT6UOPMB2NUNK74","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximating rough stochastic PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.NA"],"primary_cat":"math.PR","authors_text":"Hendrik Weber, Jan Maas, Martin Hairer","submitted_at":"2012-02-14T17:23:07Z","abstract_excerpt":"We study approximations to a class of vector-valued equations of Burgers type driven by a multiplicative space-time white noise. A solution theory for this class of equations has been developed recently in [Hairer, Weber, Probab. Theory Related Fields, to appear]. The key idea was to use the theory of controlled rough paths to give definitions of weak / mild solutions and to set up a Picard iteration argument.\n  In this article the limiting behaviour of a rather large class of (spatial) approximations to these equations is studied. These approximations are shown to converge and convergence rat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3094","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":"2026-05-18T01:13:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QLCGmFBQoN+smN4A3RmS0R26Yr03bUn42/Nf7zRDpn6+B38zVAwVnN6r2WEhOz78nm0pNha4e3FN5i80EOgZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T07:28:44.886925Z"},"content_sha256":"d8801995aaf75f9bc3fc856b0e9b4f81c181af52ed96f74700f5ac36fcb43375","schema_version":"1.0","event_id":"sha256:d8801995aaf75f9bc3fc856b0e9b4f81c181af52ed96f74700f5ac36fcb43375"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/532HATK7QF7JT6UOPMB2NUNK74/bundle.json","state_url":"https://pith.science/pith/532HATK7QF7JT6UOPMB2NUNK74/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/532HATK7QF7JT6UOPMB2NUNK74/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":"2026-05-28T07:28:44Z","links":{"resolver":"https://pith.science/pith/532HATK7QF7JT6UOPMB2NUNK74","bundle":"https://pith.science/pith/532HATK7QF7JT6UOPMB2NUNK74/bundle.json","state":"https://pith.science/pith/532HATK7QF7JT6UOPMB2NUNK74/state.json","well_known_bundle":"https://pith.science/.well-known/pith/532HATK7QF7JT6UOPMB2NUNK74/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:532HATK7QF7JT6UOPMB2NUNK74","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":"44fd3a46e7280c5c0e93552b31b8ce751cd2a6f24d30b1026335382e144064c2","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-14T17:23:07Z","title_canon_sha256":"4c5a1b72d93d5ccea2b29f1d3a4b6e00e8ef56b2b15ac280ae6f29daad57a511"},"schema_version":"1.0","source":{"id":"1202.3094","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.3094","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"arxiv_version","alias_value":"1202.3094v2","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.3094","created_at":"2026-05-18T01:13:10Z"},{"alias_kind":"pith_short_12","alias_value":"532HATK7QF7J","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_16","alias_value":"532HATK7QF7JT6UO","created_at":"2026-05-18T12:26:53Z"},{"alias_kind":"pith_short_8","alias_value":"532HATK7","created_at":"2026-05-18T12:26:53Z"}],"graph_snapshots":[{"event_id":"sha256:d8801995aaf75f9bc3fc856b0e9b4f81c181af52ed96f74700f5ac36fcb43375","target":"graph","created_at":"2026-05-18T01:13:10Z","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 study approximations to a class of vector-valued equations of Burgers type driven by a multiplicative space-time white noise. A solution theory for this class of equations has been developed recently in [Hairer, Weber, Probab. Theory Related Fields, to appear]. The key idea was to use the theory of controlled rough paths to give definitions of weak / mild solutions and to set up a Picard iteration argument.\n  In this article the limiting behaviour of a rather large class of (spatial) approximations to these equations is studied. These approximations are shown to converge and convergence rat","authors_text":"Hendrik Weber, Jan Maas, Martin Hairer","cross_cats":["math.AP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-14T17:23:07Z","title":"Approximating rough stochastic PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.3094","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:b563a59f7a45392df96e13cf48e6f4811f214a285fece6d1e9ac7487fcf81a09","target":"record","created_at":"2026-05-18T01:13:10Z","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":"44fd3a46e7280c5c0e93552b31b8ce751cd2a6f24d30b1026335382e144064c2","cross_cats_sorted":["math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-14T17:23:07Z","title_canon_sha256":"4c5a1b72d93d5ccea2b29f1d3a4b6e00e8ef56b2b15ac280ae6f29daad57a511"},"schema_version":"1.0","source":{"id":"1202.3094","kind":"arxiv","version":2}},"canonical_sha256":"eef4704d5f817e99fa8e7b03a6d1aaff1b0ffbb6d96e12ab5e65cd1e3a851eb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eef4704d5f817e99fa8e7b03a6d1aaff1b0ffbb6d96e12ab5e65cd1e3a851eb4","first_computed_at":"2026-05-18T01:13:10.088189Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:10.088189Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pee0TnbopGu4iYxo6Gijm8tz40QwZ9UzB3nbpo1uvIwsCjvCYcY+jpCdLXLgoelvdOUoQ0gmU/bn0lq+I/JODg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:10.088606Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.3094","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b563a59f7a45392df96e13cf48e6f4811f214a285fece6d1e9ac7487fcf81a09","sha256:d8801995aaf75f9bc3fc856b0e9b4f81c181af52ed96f74700f5ac36fcb43375"],"state_sha256":"5783f377398e05063544f0a74d43f9d95a25ff6a091fae63f9506bfaf8769041"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QWm1HhRvGuNhtXqk3K+fPYVlEXBNQpZCLiJkVDEoyskhZUw3OtktxPFljp/U7vKrHxFlqqsgRlZP6MVsj5oRBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T07:28:44.889066Z","bundle_sha256":"b765a007dadd8d943cb6073661bcf54c95ae1ffb188e24688365f34c7679989c"}}