{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LIZFUJCCSPH5K4TA2RHU3SBA2P","short_pith_number":"pith:LIZFUJCC","canonical_record":{"source":{"id":"1409.4250","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-15T13:27:56Z","cross_cats_sorted":[],"title_canon_sha256":"05fabce4881fabe5f4d3a8804f74369c113103d5407d06cc8399f0e0090a8724","abstract_canon_sha256":"107ee1e0c0319a50065e0f38c74875ce6f0e18c3104cc8df203ee9f2e9dcbccd"},"schema_version":"1.0"},"canonical_sha256":"5a325a244293cfd57260d44f4dc820d3e30bb5fe6ce59418dc5cebb68c5389de","source":{"kind":"arxiv","id":"1409.4250","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4250","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4250v3","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4250","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"pith_short_12","alias_value":"LIZFUJCCSPH5","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LIZFUJCCSPH5K4TA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LIZFUJCC","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LIZFUJCCSPH5K4TA2RHU3SBA2P","target":"record","payload":{"canonical_record":{"source":{"id":"1409.4250","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-15T13:27:56Z","cross_cats_sorted":[],"title_canon_sha256":"05fabce4881fabe5f4d3a8804f74369c113103d5407d06cc8399f0e0090a8724","abstract_canon_sha256":"107ee1e0c0319a50065e0f38c74875ce6f0e18c3104cc8df203ee9f2e9dcbccd"},"schema_version":"1.0"},"canonical_sha256":"5a325a244293cfd57260d44f4dc820d3e30bb5fe6ce59418dc5cebb68c5389de","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:20.420113Z","signature_b64":"fScDdu7FlmRU9f5M+pMgOIZm9vxZwGe3vlS7R/BCqbPMxcvQXB484dLF0na9zOzt1qjy11tMODXPovBbmP9FBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5a325a244293cfd57260d44f4dc820d3e30bb5fe6ce59418dc5cebb68c5389de","last_reissued_at":"2026-05-18T01:00:20.419478Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:20.419478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.4250","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":"2026-05-18T01:00:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HxD2auguzObpHIpTfGlfk2zG1JoX22efWo58mzeyJ6rRwjuJ6pGdc6w1w3H29KiDYQnFpwpS5O5RX/hkajXoDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:13:30.882626Z"},"content_sha256":"4aa199d7c56075f2a851b9b6993193755a27c4f9cba28810b45bb5c654d4cdfc","schema_version":"1.0","event_id":"sha256:4aa199d7c56075f2a851b9b6993193755a27c4f9cba28810b45bb5c654d4cdfc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LIZFUJCCSPH5K4TA2RHU3SBA2P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Support theorem for a singular semilinear stochastic partial differential equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"K. Chouk, P.K. Friz","submitted_at":"2014-09-15T13:27:56Z","abstract_excerpt":"We consider the generalized parabolic Anderson equation (gPAM) in 2 dimensions with periodic boundary. This is an example of a singular semilinear stochastic partial differential equations, solutions of which require renormalization and have only be understood recently via Hairer's regularity structures and, in some cases equivalently, paracontrollled distributions due to Gubinelli, Imkeller and Perkowski. In the present paper we describe the law of gPAM, by establishing a Stroock{Varadhan type support theorem in suitable Holder{Besov spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4250","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":""},"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":"2026-05-18T01:00:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CKnYxU/3izWNtnvE5AU4Yb9yMQAFfLovSSgFuM1yt+OUOrU71Hc2nEERapLFUqC/gJQ0Jgvqqg4KCU/VrCVBBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T17:13:30.883174Z"},"content_sha256":"fe634e7661534ccbf47299ee11fe542475806f3965a754d72cc3db5c700c4967","schema_version":"1.0","event_id":"sha256:fe634e7661534ccbf47299ee11fe542475806f3965a754d72cc3db5c700c4967"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LIZFUJCCSPH5K4TA2RHU3SBA2P/bundle.json","state_url":"https://pith.science/pith/LIZFUJCCSPH5K4TA2RHU3SBA2P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LIZFUJCCSPH5K4TA2RHU3SBA2P/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":"2026-06-26T17:13:30Z","links":{"resolver":"https://pith.science/pith/LIZFUJCCSPH5K4TA2RHU3SBA2P","bundle":"https://pith.science/pith/LIZFUJCCSPH5K4TA2RHU3SBA2P/bundle.json","state":"https://pith.science/pith/LIZFUJCCSPH5K4TA2RHU3SBA2P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LIZFUJCCSPH5K4TA2RHU3SBA2P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LIZFUJCCSPH5K4TA2RHU3SBA2P","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":"107ee1e0c0319a50065e0f38c74875ce6f0e18c3104cc8df203ee9f2e9dcbccd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-15T13:27:56Z","title_canon_sha256":"05fabce4881fabe5f4d3a8804f74369c113103d5407d06cc8399f0e0090a8724"},"schema_version":"1.0","source":{"id":"1409.4250","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.4250","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"arxiv_version","alias_value":"1409.4250v3","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.4250","created_at":"2026-05-18T01:00:20Z"},{"alias_kind":"pith_short_12","alias_value":"LIZFUJCCSPH5","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LIZFUJCCSPH5K4TA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LIZFUJCC","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:fe634e7661534ccbf47299ee11fe542475806f3965a754d72cc3db5c700c4967","target":"graph","created_at":"2026-05-18T01:00:20Z","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":"We consider the generalized parabolic Anderson equation (gPAM) in 2 dimensions with periodic boundary. This is an example of a singular semilinear stochastic partial differential equations, solutions of which require renormalization and have only be understood recently via Hairer's regularity structures and, in some cases equivalently, paracontrollled distributions due to Gubinelli, Imkeller and Perkowski. In the present paper we describe the law of gPAM, by establishing a Stroock{Varadhan type support theorem in suitable Holder{Besov spaces.","authors_text":"K. Chouk, P.K. Friz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-15T13:27:56Z","title":"Support theorem for a singular semilinear stochastic partial differential equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4250","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":"sha256:4aa199d7c56075f2a851b9b6993193755a27c4f9cba28810b45bb5c654d4cdfc","target":"record","created_at":"2026-05-18T01:00:20Z","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":"107ee1e0c0319a50065e0f38c74875ce6f0e18c3104cc8df203ee9f2e9dcbccd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-09-15T13:27:56Z","title_canon_sha256":"05fabce4881fabe5f4d3a8804f74369c113103d5407d06cc8399f0e0090a8724"},"schema_version":"1.0","source":{"id":"1409.4250","kind":"arxiv","version":3}},"canonical_sha256":"5a325a244293cfd57260d44f4dc820d3e30bb5fe6ce59418dc5cebb68c5389de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5a325a244293cfd57260d44f4dc820d3e30bb5fe6ce59418dc5cebb68c5389de","first_computed_at":"2026-05-18T01:00:20.419478Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:00:20.419478Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fScDdu7FlmRU9f5M+pMgOIZm9vxZwGe3vlS7R/BCqbPMxcvQXB484dLF0na9zOzt1qjy11tMODXPovBbmP9FBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:00:20.420113Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.4250","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4aa199d7c56075f2a851b9b6993193755a27c4f9cba28810b45bb5c654d4cdfc","sha256:fe634e7661534ccbf47299ee11fe542475806f3965a754d72cc3db5c700c4967"],"state_sha256":"89e2adcdac303d513d94ee7d02cd51a83f17030cc61c47f122bbc927e981397e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qXUyDPzkBoYTixSjOQkJMfRNRXqQIRuKiO6q/U1uqNi55111uEmyF8tBzCzG2vEyfe9/7teeHkMok/kXjYs4Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T17:13:30.885965Z","bundle_sha256":"c66ce61924507fcf37627692656ab7591ebdd814235394bcf6fa4dc1655828f1"}}