{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:RGINHPT45WCCHJAOD62OKLFKRR","short_pith_number":"pith:RGINHPT4","canonical_record":{"source":{"id":"2409.20451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-30T16:10:06Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"cf072bb4b32af213da0d169ab3a8d16308219e03191a41b7aabcbc447ffd9b25","abstract_canon_sha256":"0d487d92e15facbe69eb888959a6ef247f5ec0b02b154623648941a101e56dc1"},"schema_version":"1.0"},"canonical_sha256":"8990d3be7ced8423a40e1fb4e52caa8c77efa9357f6a08cccde2c47512e6ad38","source":{"kind":"arxiv","id":"2409.20451","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.20451","created_at":"2026-07-05T09:13:43Z"},{"alias_kind":"arxiv_version","alias_value":"2409.20451v1","created_at":"2026-07-05T09:13:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.20451","created_at":"2026-07-05T09:13:43Z"},{"alias_kind":"pith_short_12","alias_value":"RGINHPT45WCC","created_at":"2026-07-05T09:13:43Z"},{"alias_kind":"pith_short_16","alias_value":"RGINHPT45WCCHJAO","created_at":"2026-07-05T09:13:43Z"},{"alias_kind":"pith_short_8","alias_value":"RGINHPT4","created_at":"2026-07-05T09:13:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:RGINHPT45WCCHJAOD62OKLFKRR","target":"record","payload":{"canonical_record":{"source":{"id":"2409.20451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-30T16:10:06Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"cf072bb4b32af213da0d169ab3a8d16308219e03191a41b7aabcbc447ffd9b25","abstract_canon_sha256":"0d487d92e15facbe69eb888959a6ef247f5ec0b02b154623648941a101e56dc1"},"schema_version":"1.0"},"canonical_sha256":"8990d3be7ced8423a40e1fb4e52caa8c77efa9357f6a08cccde2c47512e6ad38","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:13:43.718645Z","signature_b64":"SH4w0b13XSj1o3U5J9Gd4tYEwTaMIyVwAqKcBFfT7eBCIJPYqZyE+T3NUFT2baOY5utuZrPDpxeGE+ZKvpKfAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8990d3be7ced8423a40e1fb4e52caa8c77efa9357f6a08cccde2c47512e6ad38","last_reissued_at":"2026-07-05T09:13:43.717963Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:13:43.717963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.20451","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":"2026-07-05T09:13:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QU4wlyDRDWzRulrAYUewFY4lrr5S1hZ4RuoWNM83tbNtHpqKhm/xa1+Jtg94Q/wQjVaxkPn1BTyzY8X8CZj2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T19:15:18.119468Z"},"content_sha256":"d0b1a0ee967dc2e0c895e7ed394ac3dbf5aac0755f014e91b1501820262075f9","schema_version":"1.0","event_id":"sha256:d0b1a0ee967dc2e0c895e7ed394ac3dbf5aac0755f014e91b1501820262075f9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:RGINHPT45WCCHJAOD62OKLFKRR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Justin Forlano, Leonardo Tolomeo","submitted_at":"2024-09-30T16:10:06Z","abstract_excerpt":"We consider the stochastic damped nonlinear wave equation $\\partial_t^{2}u+\\partial_t u+u-\\Delta u +u^{3} = \\sqrt{2} {\\langle{\\nabla}\\rangle^{-s}} \\xi$ on the two-dimensional torus $\\mathbb T^2$, where $\\xi$ denotes a space-time white noise and $s>0$. We show that the measure $\\vec{\\mu}_s$ corresponding to the unique invariant measure for the flow of the associated linear equation is quasi-invariant under the nonlinear stochastic flow."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.20451","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.20451/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":"2026-07-05T09:13:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aDkhKFzpLetnTmZ3Jhs/J1TQr191Md4ZDgAunIXxfQBFdHOFUtttpoH4lljTSp0dM1AnHfNzO9psBIa5XMkMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T19:15:18.119856Z"},"content_sha256":"a761b4aa1f4c154f1b22e3f6bb2ad1c0718efbd0aa26fff7a0899007393dcaf8","schema_version":"1.0","event_id":"sha256:a761b4aa1f4c154f1b22e3f6bb2ad1c0718efbd0aa26fff7a0899007393dcaf8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RGINHPT45WCCHJAOD62OKLFKRR/bundle.json","state_url":"https://pith.science/pith/RGINHPT45WCCHJAOD62OKLFKRR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RGINHPT45WCCHJAOD62OKLFKRR/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":"2026-08-13T19:15:18Z","links":{"resolver":"https://pith.science/pith/RGINHPT45WCCHJAOD62OKLFKRR","bundle":"https://pith.science/pith/RGINHPT45WCCHJAOD62OKLFKRR/bundle.json","state":"https://pith.science/pith/RGINHPT45WCCHJAOD62OKLFKRR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RGINHPT45WCCHJAOD62OKLFKRR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:RGINHPT45WCCHJAOD62OKLFKRR","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":"0d487d92e15facbe69eb888959a6ef247f5ec0b02b154623648941a101e56dc1","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-30T16:10:06Z","title_canon_sha256":"cf072bb4b32af213da0d169ab3a8d16308219e03191a41b7aabcbc447ffd9b25"},"schema_version":"1.0","source":{"id":"2409.20451","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.20451","created_at":"2026-07-05T09:13:43Z"},{"alias_kind":"arxiv_version","alias_value":"2409.20451v1","created_at":"2026-07-05T09:13:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.20451","created_at":"2026-07-05T09:13:43Z"},{"alias_kind":"pith_short_12","alias_value":"RGINHPT45WCC","created_at":"2026-07-05T09:13:43Z"},{"alias_kind":"pith_short_16","alias_value":"RGINHPT45WCCHJAO","created_at":"2026-07-05T09:13:43Z"},{"alias_kind":"pith_short_8","alias_value":"RGINHPT4","created_at":"2026-07-05T09:13:43Z"}],"graph_snapshots":[{"event_id":"sha256:a761b4aa1f4c154f1b22e3f6bb2ad1c0718efbd0aa26fff7a0899007393dcaf8","target":"graph","created_at":"2026-07-05T09:13:43Z","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/2409.20451/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider the stochastic damped nonlinear wave equation $\\partial_t^{2}u+\\partial_t u+u-\\Delta u +u^{3} = \\sqrt{2} {\\langle{\\nabla}\\rangle^{-s}} \\xi$ on the two-dimensional torus $\\mathbb T^2$, where $\\xi$ denotes a space-time white noise and $s>0$. We show that the measure $\\vec{\\mu}_s$ corresponding to the unique invariant measure for the flow of the associated linear equation is quasi-invariant under the nonlinear stochastic flow.","authors_text":"Justin Forlano, Leonardo Tolomeo","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-30T16:10:06Z","title":"Quasi-invariance of the Gaussian measure for the two-dimensional stochastic cubic nonlinear wave equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.20451","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:d0b1a0ee967dc2e0c895e7ed394ac3dbf5aac0755f014e91b1501820262075f9","target":"record","created_at":"2026-07-05T09:13:43Z","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":"0d487d92e15facbe69eb888959a6ef247f5ec0b02b154623648941a101e56dc1","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2024-09-30T16:10:06Z","title_canon_sha256":"cf072bb4b32af213da0d169ab3a8d16308219e03191a41b7aabcbc447ffd9b25"},"schema_version":"1.0","source":{"id":"2409.20451","kind":"arxiv","version":1}},"canonical_sha256":"8990d3be7ced8423a40e1fb4e52caa8c77efa9357f6a08cccde2c47512e6ad38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8990d3be7ced8423a40e1fb4e52caa8c77efa9357f6a08cccde2c47512e6ad38","first_computed_at":"2026-07-05T09:13:43.717963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:13:43.717963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SH4w0b13XSj1o3U5J9Gd4tYEwTaMIyVwAqKcBFfT7eBCIJPYqZyE+T3NUFT2baOY5utuZrPDpxeGE+ZKvpKfAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:13:43.718645Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.20451","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d0b1a0ee967dc2e0c895e7ed394ac3dbf5aac0755f014e91b1501820262075f9","sha256:a761b4aa1f4c154f1b22e3f6bb2ad1c0718efbd0aa26fff7a0899007393dcaf8"],"state_sha256":"68e4a8de66b710ae7267d33b90d0f7037e3014edd5c4bc1f62c0e950e13128cb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tthWxBbIqXZDADHjFjW9F+F0WFZLE7h8OLZfoxOCsUU5S2o72aG5MCaKedY4dpWEHUOg74NbI1PJTUhY9FUuBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T19:15:18.122700Z","bundle_sha256":"58ae235d551c1091d00abe6e26acbdbf81c54880d9c8fcdbc245ea3820a559df"}}