{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:I3UFHJTDJRZERWMSPKY6TIFPXW","short_pith_number":"pith:I3UFHJTD","canonical_record":{"source":{"id":"2501.06612","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-11T18:22:35Z","cross_cats_sorted":[],"title_canon_sha256":"a11163a6338ac2fe5be4890e2f03dad53c651e3c2cae7226afdec144ec45ed72","abstract_canon_sha256":"2755e7dffb847e9f01fad16ee341151ea21c94be3c7d338613c95ae386f69742"},"schema_version":"1.0"},"canonical_sha256":"46e853a6634c7248d9927ab1e9a0afbd82b19bb020b5703919370065c0aabb54","source":{"kind":"arxiv","id":"2501.06612","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.06612","created_at":"2026-07-05T11:54:43Z"},{"alias_kind":"arxiv_version","alias_value":"2501.06612v2","created_at":"2026-07-05T11:54:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.06612","created_at":"2026-07-05T11:54:43Z"},{"alias_kind":"pith_short_12","alias_value":"I3UFHJTDJRZE","created_at":"2026-07-05T11:54:43Z"},{"alias_kind":"pith_short_16","alias_value":"I3UFHJTDJRZERWMS","created_at":"2026-07-05T11:54:43Z"},{"alias_kind":"pith_short_8","alias_value":"I3UFHJTD","created_at":"2026-07-05T11:54:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:I3UFHJTDJRZERWMSPKY6TIFPXW","target":"record","payload":{"canonical_record":{"source":{"id":"2501.06612","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-11T18:22:35Z","cross_cats_sorted":[],"title_canon_sha256":"a11163a6338ac2fe5be4890e2f03dad53c651e3c2cae7226afdec144ec45ed72","abstract_canon_sha256":"2755e7dffb847e9f01fad16ee341151ea21c94be3c7d338613c95ae386f69742"},"schema_version":"1.0"},"canonical_sha256":"46e853a6634c7248d9927ab1e9a0afbd82b19bb020b5703919370065c0aabb54","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:54:43.526033Z","signature_b64":"RaebYPKC1shCzAXtI0HZLy7Ud8B1iOm8YH0bYwDFGvVcofw/E8GHKzpfSopalq2FqumK+ii/E74ytjjFAOCqDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46e853a6634c7248d9927ab1e9a0afbd82b19bb020b5703919370065c0aabb54","last_reissued_at":"2026-07-05T11:54:43.525630Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:54:43.525630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.06612","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":"2026-07-05T11:54:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gNZ1/ZJD/hhQL2miAUtOjfRFJBcXVHA+jcMXKzwSUe/kJ/g1IeA+bxtBV1ZEKH00NBt5djoafI6bx1yKSzfWAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T07:38:36.203267Z"},"content_sha256":"eee25e00e03c2c8f442d1d3c482cbbcd54b2827ae46101af74a0c41829d12680","schema_version":"1.0","event_id":"sha256:eee25e00e03c2c8f442d1d3c482cbbcd54b2827ae46101af74a0c41829d12680"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:I3UFHJTDJRZERWMSPKY6TIFPXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ajay Chandra, Ilya Chevyrev","submitted_at":"2025-01-11T18:22:35Z","abstract_excerpt":"We propose an elementary method to show non-Gaussianity of invariant measures of parabolic stochastic partial differential equations with polynomial non-linearities in the Da Prato--Debussche regime. The approach is essentially algebraic and involves using the generator equation of the SPDE at stationarity. Our results in particular cover the $\\Phi^4_\\delta$ measures in dimensions $\\delta<\\frac{14}{5}$, which includes cases where the invariant measure is singular with respect to the invariant measure of the linear solution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.06612","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.06612/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":"2026-07-05T11:54:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2mwfoLPiCG6M+aHKM4a21jYTtXj56njczMvGrVY7XVctUNveqxei5AAYKPujjla/q6eM8pb8DQaot0TSzbPaCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T07:38:36.203764Z"},"content_sha256":"fabcb1a40fd94beda5b116fbde26e918fd4f626291f8ace417ce1a344df85076","schema_version":"1.0","event_id":"sha256:fabcb1a40fd94beda5b116fbde26e918fd4f626291f8ace417ce1a344df85076"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I3UFHJTDJRZERWMSPKY6TIFPXW/bundle.json","state_url":"https://pith.science/pith/I3UFHJTDJRZERWMSPKY6TIFPXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I3UFHJTDJRZERWMSPKY6TIFPXW/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":"2026-08-11T07:38:36Z","links":{"resolver":"https://pith.science/pith/I3UFHJTDJRZERWMSPKY6TIFPXW","bundle":"https://pith.science/pith/I3UFHJTDJRZERWMSPKY6TIFPXW/bundle.json","state":"https://pith.science/pith/I3UFHJTDJRZERWMSPKY6TIFPXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I3UFHJTDJRZERWMSPKY6TIFPXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:I3UFHJTDJRZERWMSPKY6TIFPXW","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":"2755e7dffb847e9f01fad16ee341151ea21c94be3c7d338613c95ae386f69742","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-11T18:22:35Z","title_canon_sha256":"a11163a6338ac2fe5be4890e2f03dad53c651e3c2cae7226afdec144ec45ed72"},"schema_version":"1.0","source":{"id":"2501.06612","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.06612","created_at":"2026-07-05T11:54:43Z"},{"alias_kind":"arxiv_version","alias_value":"2501.06612v2","created_at":"2026-07-05T11:54:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.06612","created_at":"2026-07-05T11:54:43Z"},{"alias_kind":"pith_short_12","alias_value":"I3UFHJTDJRZE","created_at":"2026-07-05T11:54:43Z"},{"alias_kind":"pith_short_16","alias_value":"I3UFHJTDJRZERWMS","created_at":"2026-07-05T11:54:43Z"},{"alias_kind":"pith_short_8","alias_value":"I3UFHJTD","created_at":"2026-07-05T11:54:43Z"}],"graph_snapshots":[{"event_id":"sha256:fabcb1a40fd94beda5b116fbde26e918fd4f626291f8ace417ce1a344df85076","target":"graph","created_at":"2026-07-05T11:54:43Z","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/2501.06612/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose an elementary method to show non-Gaussianity of invariant measures of parabolic stochastic partial differential equations with polynomial non-linearities in the Da Prato--Debussche regime. The approach is essentially algebraic and involves using the generator equation of the SPDE at stationarity. Our results in particular cover the $\\Phi^4_\\delta$ measures in dimensions $\\delta<\\frac{14}{5}$, which includes cases where the invariant measure is singular with respect to the invariant measure of the linear solution.","authors_text":"Ajay Chandra, Ilya Chevyrev","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-11T18:22:35Z","title":"Non-Gaussianity of invariant measures to SPDEs in Da Prato-Debussche regime"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.06612","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:eee25e00e03c2c8f442d1d3c482cbbcd54b2827ae46101af74a0c41829d12680","target":"record","created_at":"2026-07-05T11:54:43Z","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":"2755e7dffb847e9f01fad16ee341151ea21c94be3c7d338613c95ae386f69742","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-01-11T18:22:35Z","title_canon_sha256":"a11163a6338ac2fe5be4890e2f03dad53c651e3c2cae7226afdec144ec45ed72"},"schema_version":"1.0","source":{"id":"2501.06612","kind":"arxiv","version":2}},"canonical_sha256":"46e853a6634c7248d9927ab1e9a0afbd82b19bb020b5703919370065c0aabb54","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46e853a6634c7248d9927ab1e9a0afbd82b19bb020b5703919370065c0aabb54","first_computed_at":"2026-07-05T11:54:43.525630Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:54:43.525630Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RaebYPKC1shCzAXtI0HZLy7Ud8B1iOm8YH0bYwDFGvVcofw/E8GHKzpfSopalq2FqumK+ii/E74ytjjFAOCqDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:54:43.526033Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.06612","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eee25e00e03c2c8f442d1d3c482cbbcd54b2827ae46101af74a0c41829d12680","sha256:fabcb1a40fd94beda5b116fbde26e918fd4f626291f8ace417ce1a344df85076"],"state_sha256":"bdf2782f0034d289548cece6370462e97ae5dc741b0dbb869321b3a4cfd61326"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BIBRCpMDXRhypRIeFAh3W6RNK3LZhZU2H4go4x/tVhe6Q+1FtT0PFxoiaDZdm/msYJRW3w4fDaDH9ZTonExACg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T07:38:36.209089Z","bundle_sha256":"26cbb8987fb0a94ea975e2af64f6bf2f449e6e3e7b08e0a1acd844f3cefb63ab"}}